line_citations.cpp

Go to the documentation of this file.

// Copyright (c) 2012-2026, QORE Lab, Imperial College London
// All rights reserved.
 
/**
 * @file
 * The citation registry table and its lookup. See line/io/line_citations.h.
 *
 * The table is GENERATED FROM `matlab/src/io/line_citations.m`, which is the
 * reference implementation, so the four registries carry the same 505 entries
 * and the same wording. When a method is added or renamed, add it there and to
 * the JAR and python twins in the same change, and regenerate this file rather
 * than editing it by hand in isolation.
 *
 * It lives in a .cpp rather than the header because a 505-entry initializer
 * compiled into every translation unit that wants a reference would be a real
 * cost for a table that is consulted once, at write-up time.
 */
 
#include "line/io/line_citations.h"
 
#include <algorithm>
#include <cctype>
#include <set>
 
namespace line {
namespace io {
 
namespace {
 
/** Lowercase and trim, the normalisation every codebase applies to a token. */
std::string normalise(const std::string& raw) {
    std::size_t b = 0, e = raw.size();
    while (b < e && std::isspace(static_cast<unsigned char>(raw[b]))) ++b;
    while (e > b && std::isspace(static_cast<unsigned char>(raw[e - 1]))) --e;
    std::string t = raw.substr(b, e - b);
    std::transform(t.begin(), t.end(), t.begin(),
                   [](unsigned char c) { return static_cast<char>(std::tolower(c)); });
    return t;
}
 
}  // namespace
 
const std::map<std::string, Citation>& citation_registry() {
    static const std::map<std::string, Citation> reg = {
        {"mva.exact", {"ReiL80",
         "M. Reiser, S. Lavenberg, \"Mean-Value Analysis of Closed Multichain Queuing Networks\", J. ACM 27(2), 1980",
         "exact mean queue lengths of the product-form network"}},
        {"exact", {"ReiL80",
         "M. Reiser, S. Lavenberg, \"Mean-Value Analysis of Closed Multichain Queuing Networks\", J. ACM 27(2), 1980",
         "exact mean queue lengths of the product-form network"}},
        {"mva.mva", {"ReiL80",
         "M. Reiser, S. Lavenberg, \"Mean-Value Analysis of Closed Multichain Queuing Networks\", J. ACM 27(2), 1980",
         "exact mean queue lengths of the product-form network"}},
        {"reiser", {"ReiL80",
         "M. Reiser, S. Lavenberg, \"Mean-Value Analysis of Closed Multichain Queuing Networks\", J. ACM 27(2), 1980",
         "exact mean queue lengths of the product-form network"}},
        {"bs", {"Sch79",
         "P. J. Schweitzer, \"Approximate Analysis of Multiclass Closed Networks of Queues\", Int. Conf. Stoch. Control Optim., 1979",
         "Bard-Schweitzer fixed point for the mean queue lengths"}},
        {"amva.bs", {"Sch79",
         "P. J. Schweitzer, \"Approximate Analysis of Multiclass Closed Networks of Queues\", Int. Conf. Stoch. Control Optim., 1979",
         "Bard-Schweitzer fixed point for the mean queue lengths"}},
        {"aql", {"ZahES88",
         "J. Zahorjan, D. L. Eager, H. M. Sweillam, \"Accuracy, Speed, and Convergence of Approximate Mean Value Analysis\", Perform. Eval. 8, 1988",
         "aggregate queue-length AMVA iteration"}},
        {"amva.aql", {"ZahES88",
         "J. Zahorjan, D. L. Eager, H. M. Sweillam, \"Accuracy, Speed, and Convergence of Approximate Mean Value Analysis\", Perform. Eval. 8, 1988",
         "aggregate queue-length AMVA iteration"}},
        {"scat", {"NeuC81",
         "D. Neuse, K. M. Chandy, \"SCAT: A Heuristic Algorithm for Queueing Network Models of Computing Systems\", ACM SIGMETRICS Perform. Eval. Rev. 10(3), 1981",
         "Linearizer correction of the arrival-instant queue lengths refreshed once instead of three times"}},
        {"amva.scat", {"NeuC81",
         "D. Neuse, K. M. Chandy, \"SCAT: A Heuristic Algorithm for Queueing Network Models of Computing Systems\", ACM SIGMETRICS Perform. Eval. Rev. 10(3), 1981",
         "Linearizer correction of the arrival-instant queue lengths refreshed once instead of three times"}},
        {"cntol", {"ChaN82",
         "K. M. Chandy, D. Neuse, \"Linearizer: A Heuristic Algorithm for Queuing Network Models of Computing Systems\", Commun. ACM 25(2), 1982",
         "population-scaled termination test 1/(4000+16*sum(N)) of the approximate-MVA fixed point"}},
        {"lin", {"ChaN82",
         "K. M. Chandy, D. Neuse, \"Linearizer: A Heuristic Algorithm for Queuing Network Models of Computing Systems\", Commun. ACM 25(2), 1982",
         "Linearizer correction of the arrival-instant queue lengths"}},
        {"amva.lin", {"ChaN82",
         "K. M. Chandy, D. Neuse, \"Linearizer: A Heuristic Algorithm for Queuing Network Models of Computing Systems\", Commun. ACM 25(2), 1982",
         "Linearizer correction of the arrival-instant queue lengths"}},
        {"gflin", {"ChaN82",
         "K. M. Chandy, D. Neuse, \"Linearizer: A Heuristic Algorithm for Queuing Network Models of Computing Systems\", Commun. ACM 25(2), 1982",
         "Linearizer correction of the arrival-instant queue lengths"}},
        {"egflin", {"ChaN82",
         "K. M. Chandy, D. Neuse, \"Linearizer: A Heuristic Algorithm for Queuing Network Models of Computing Systems\", Commun. ACM 25(2), 1982",
         "Linearizer correction of the arrival-instant queue lengths"}},
        {"qsa", {"SchSB98",
         "P. J. Schweitzer, G. Serazzi, M. Broglia, \"A Queue-Shift Approximation Technique for Product-Form Queueing Networks\", Tools'98, LNCS 1469, 1998",
         "queue-shift correction of the arrival-instant queue lengths"}},
        {"amva.qsa", {"SchSB98",
         "P. J. Schweitzer, G. Serazzi, M. Broglia, \"A Queue-Shift Approximation Technique for Product-Form Queueing Networks\", Tools'98, LNCS 1469, 1998",
         "queue-shift correction of the arrival-instant queue lengths"}},
        {"dmlin", {"SilvaM90",
         "E. de Souza e Silva, R. R. Muntz, \"A Note on the Computational Cost of the Linearizer Algorithm for Queueing Networks\", IEEE TC 39(6), 1990",
         "de Souza e Silva-Muntz cost reduction of Linearizer"}},
        {"amva.dmlin", {"SilvaM90",
         "E. de Souza e Silva, R. R. Muntz, \"A Note on the Computational Cost of the Linearizer Algorithm for Queueing Networks\", IEEE TC 39(6), 1990",
         "de Souza e Silva-Muntz cost reduction of Linearizer"}},
        {"lcp", {"Bar79",
         "Y. Bard, \"Some Extensions to Multiclass Queueing Network Analysis\", Performance of Computer Systems, North-Holland, 1979",
         "large-customer-population estimate of the arrival-instant queue lengths"}},
        {"amva.lcp", {"Bar79",
         "Y. Bard, \"Some Extensions to Multiclass Queueing Network Analysis\", Performance of Computer Systems, North-Holland, 1979",
         "large-customer-population estimate of the arrival-instant queue lengths"}},
        {"chow", {"Cho83",
         "W.-M. Chow, \"Approximations for Large Scale Closed Queueing Networks\", Perform. Eval. 3(1), 1983",
         "second-approximation theta-correction of the arrival-instant queue lengths, taken off the Bard LCP solution"}},
        {"amva.chow", {"Cho83",
         "W.-M. Chow, \"Approximations for Large Scale Closed Queueing Networks\", Perform. Eval. 3(1), 1983",
         "second-approximation theta-correction of the arrival-instant queue lengths, taken off the Bard LCP solution"}},
        {"pamb", {"HsiL88",
         "C. T. Hsieh, S. S. Lam, \"PAM - A Noniterative Approximate Solution Method for Closed Multichain Queueing Networks\", ACM SIGMETRICS Perform. Eval. Rev. 16(1), 1988",
         "noniterative proportional seed of the queue lengths plus the last MVA step"}},
        {"amva.pamb", {"HsiL88",
         "C. T. Hsieh, S. S. Lam, \"PAM - A Noniterative Approximate Solution Method for Closed Multichain Queueing Networks\", ACM SIGMETRICS Perform. Eval. Rev. 16(1), 1988",
         "noniterative proportional seed of the queue lengths plus the last MVA step"}},
        {"pami", {"HsiL88",
         "C. T. Hsieh, S. S. Lam, \"PAM - A Noniterative Approximate Solution Method for Closed Multichain Queueing Networks\", ACM SIGMETRICS Perform. Eval. Rev. 16(1), 1988",
         "noniterative proportional seed with the throughputs capped at full centre utilization"}},
        {"amva.pami", {"HsiL88",
         "C. T. Hsieh, S. S. Lam, \"PAM - A Noniterative Approximate Solution Method for Closed Multichain Queueing Networks\", ACM SIGMETRICS Perform. Eval. Rev. 16(1), 1988",
         "noniterative proportional seed with the throughputs capped at full centre utilization"}},
        {"pamt", {"HsiL88",
         "C. T. Hsieh, S. S. Lam, \"PAM - A Noniterative Approximate Solution Method for Closed Multichain Queueing Networks\", ACM SIGMETRICS Perform. Eval. Rev. 16(1), 1988",
         "noniterative proportional seed plus the last two MVA steps"}},
        {"amva.pamt", {"HsiL88",
         "C. T. Hsieh, S. S. Lam, \"PAM - A Noniterative Approximate Solution Method for Closed Multichain Queueing Networks\", ACM SIGMETRICS Perform. Eval. Rev. 16(1), 1988",
         "noniterative proportional seed plus the last two MVA steps"}},
        {"clust", {"SilLM86",
         "E. de Souza e Silva, S. S. Lavenberg, R. R. Muntz, \"A Clustering Approximation Technique for Queueing Network Models with a Large Number of Chains\", IEEE TC C-35(5), 1986",
         "decomposition into subnetworks with local classes solved exactly and foreign classes carried as a per-centre utilization"}},
        {"amva.clust", {"SilLM86",
         "E. de Souza e Silva, S. S. Lavenberg, R. R. Muntz, \"A Clustering Approximation Technique for Queueing Network Models with a Large Number of Chains\", IEEE TC C-35(5), 1986",
         "decomposition into subnetworks with local classes solved exactly and foreign classes carried as a per-centre utilization"}},
        {"looping", {"Eag84",
         "D. L. Eager, \"Bounding Algorithms for Queueing Network Models of Computer Systems\", Ph.D. thesis, Tech. Rept. CSRG-156, University of Toronto, 1984",
         "multiclass queue-length bracket built from the unaccounted-congestion heaps, the initial estimate of the multiple-class performance bound hierarchy"}},
        {"looping.upper", {"Eag84",
         "D. L. Eager, \"Bounding Algorithms for Queueing Network Models of Computer Systems\", Ph.D. thesis, Tech. Rept. CSRG-156, University of Toronto, 1984",
         "multiclass queue-length bracket built from the unaccounted-congestion heaps, the initial estimate of the multiple-class performance bound hierarchy"}},
        {"looping.lower", {"Eag84",
         "D. L. Eager, \"Bounding Algorithms for Queueing Network Models of Computer Systems\", Ph.D. thesis, Tech. Rept. CSRG-156, University of Toronto, 1984",
         "multiclass queue-length bracket built from the unaccounted-congestion heaps, the initial estimate of the multiple-class performance bound hierarchy"}},
        {"qd", {"CasPW15",
         "G. Casale, J. F. Perez, W. Wang, \"QD-AMVA: Evaluating Systems with Queue-Dependent Service Requirements\", IFIP PERFORMANCE, 2015",
         "queue-dependent AMVA for load-dependent stations"}},
        {"amva.qd", {"CasPW15",
         "G. Casale, J. F. Perez, W. Wang, \"QD-AMVA: Evaluating Systems with Queue-Dependent Service Requirements\", IFIP PERFORMANCE, 2015",
         "queue-dependent AMVA for load-dependent stations"}},
        {"qdlin", {"CasPW15",
         "G. Casale, J. F. Perez, W. Wang, \"QD-AMVA: Evaluating Systems with Queue-Dependent Service Requirements\", IFIP PERFORMANCE, 2015",
         "queue-dependent AMVA for load-dependent stations"}},
        {"softmin", {"CasPW15",
         "G. Casale, J. F. Perez, W. Wang, \"QD-AMVA: Evaluating Systems with Queue-Dependent Service Requirements\", IFIP PERFORMANCE, 2015",
         "queue-dependent AMVA for load-dependent stations"}},
        {"pfqn_qdamva", {"CasPW15",
         "G. Casale, J. F. Perez, W. Wang, \"QD-AMVA: Evaluating Systems with Queue-Dependent Service Requirements\", IFIP PERFORMANCE, 2015",
         "queue-dependent AMVA on plain demand matrices, the layer solver of lqn_mol"}},
        {"pfqn_qdlin", {"CasPW15",
         "G. Casale, J. F. Perez, W. Wang, \"QD-AMVA: Evaluating Systems with Queue-Dependent Service Requirements\", IFIP PERFORMANCE, 2015",
         "the queue-dependent AMVA framework the Linearizer arm runs inside, on plain demand matrices; the Linearizer correction itself is ChaN82"}},
        {"cftp", {"KijM05",
         "S. Kijima, T. Matsui, \"Approximate/Perfect Samplers for Closed Jackson Networks\", Proc. Winter Simulation Conference, 2005",
         "monotone coupling-from-the-past perfect sampler of the closed product-form stationary distribution"}},
        {"ctmc.cftp", {"KijM05",
         "S. Kijima, T. Matsui, \"Approximate/Perfect Samplers for Closed Jackson Networks\", Proc. Winter Simulation Conference, 2005",
         "monotone coupling-from-the-past perfect sampler of the closed product-form stationary distribution"}},
        {"oi", {"BonP03",
         "T. Bonald, A. Proutiere, \"Insensitive bandwidth sharing in data networks\", Queueing Systems 44(1), 2003",
         "balanced-fairness balance function of the order-independent station"}},
        {"compat", {"DorG24",
         "J.-P. Dorsman, K. Gardner, \"New directions in pass-and-swap queues\", Queueing Systems 107(3), 2024",
         "activated-server rate of a compatibility structure, the order-independent reading used by sn_compat_rate"}},
        {"balancedfairness", {"BonP03",
         "T. Bonald, A. Proutiere, \"Insensitive bandwidth sharing in data networks\", Queueing Systems 44(1), 2003",
         "balanced-fairness balance function of the order-independent station"}},
        {"globaldependence", {"Whi85",
         "P. Whittle, \"Partial balance and insensitivity\", J. Appl. Prob. 22(1), 1985",
         "balance property of a globally state-dependent rate phi(n) (setGlobalDependence), which yields the reversible product form and insensitivity"}},
        {"gd", {"Whi85",
         "P. Whittle, \"Partial balance and insensitivity\", J. Appl. Prob. 22(1), 1985",
         "balance property of a globally state-dependent rate phi(n) (setGlobalDependence), which yields the reversible product form and insensitivity"}},
        {"fli", {"WangS00",
         "H. Wang, K. C. Sevcik, \"Experiments with improved approximate mean value analysis algorithms\", Perform. Eval. 39, 2000",
         "improved AMVA arrival-instant estimators"}},
        {"amva.fli", {"WangS00",
         "H. Wang, K. C. Sevcik, \"Experiments with improved approximate mean value analysis algorithms\", Perform. Eval. 39, 2000",
         "improved AMVA arrival-instant estimators"}},
        {"qli", {"WangS00",
         "H. Wang, K. C. Sevcik, \"Experiments with improved approximate mean value analysis algorithms\", Perform. Eval. 39, 2000",
         "improved AMVA arrival-instant estimators"}},
        {"amva.qli", {"WangS00",
         "H. Wang, K. C. Sevcik, \"Experiments with improved approximate mean value analysis algorithms\", Perform. Eval. 39, 2000",
         "improved AMVA arrival-instant estimators"}},
        {"conway", {"Con89",
         "A. E. Conway, \"Fast Approximate Solution of Queueing Networks with Multi-Server Chain-Dependent FCFS Queues\", 1989",
         "multi-server chain-dependent AMVA"}},
        {"linearizerms", {"Con89",
         "A. E. Conway, \"Fast Approximate Solution of Queueing Networks with Multi-Server Chain-Dependent FCFS Queues\", 1989",
         "multi-server chain-dependent AMVA"}},
        {"suri", {"SurSV07",
         "R. Suri, S. K. Sahu, M. Vernon, \"Approximate Mean Value Analysis for Closed Queuing Networks with Multiple-Server Stations\", IERC, 2007",
         "multi-server station correction in AMVA"}},
        {"schmidt", {"SurSV07",
         "R. Suri, S. K. Sahu, M. Vernon, \"Approximate Mean Value Analysis for Closed Queuing Networks with Multiple-Server Stations\", IERC, 2007",
         "multi-server station correction in AMVA"}},
        {"schmidt-ext", {"SurSV07",
         "R. Suri, S. K. Sahu, M. Vernon, \"Approximate Mean Value Analysis for Closed Queuing Networks with Multiple-Server Stations\", IERC, 2007",
         "multi-server station correction in AMVA"}},
        {"schmidtext", {"SurSV07",
         "R. Suri, S. K. Sahu, M. Vernon, \"Approximate Mean Value Analysis for Closed Queuing Networks with Multiple-Server Stations\", IERC, 2007",
         "multi-server station correction in AMVA"}},
        {"seidmann", {"SeiSS87",
         "A. Seidmann, P. J. Schweitzer, S. Shalev-Oren, \"Computerized closed queueing network models of flexible manufacturing systems\", Large Scale Systems 12, 1987",
         "multi-server to single-server flow-equivalent reduction"}},
        {"priomva", {"ChaL83",
         "K. M. Chandy, M. S. Lakshmi, \"An Approximation Technique for Queueing Networks with Preemptive Priority Queues\", Tech. Rep., Univ. of Texas at Austin, 1983",
         "preemptive-resume priority arm of AMVA; PRIOMVA is Bolch's PEPSY-QNS name for it"}},
        {"amva.priomva", {"ChaL83",
         "K. M. Chandy, M. S. Lakshmi, \"An Approximation Technique for Queueing Networks with Preemptive Priority Queues\", Tech. Rep., Univ. of Texas at Austin, 1983",
         "preemptive-resume priority arm of AMVA; PRIOMVA is Bolch's PEPSY-QNS name for it"}},
        {"cl", {"ChaL83",
         "K. M. Chandy, M. S. Lakshmi, \"An Approximation Technique for Queueing Networks with Preemptive Priority Queues\", Tech. Rep., Univ. of Texas at Austin, 1983",
         "priority approximation inside AMVA; the AMVA formulation follows Eager & Lipscomb [EagL88]"}},
        {"chandy-lakshmi", {"ChaL83",
         "K. M. Chandy, M. S. Lakshmi, \"An Approximation Technique for Queueing Networks with Preemptive Priority Queues\", Tech. Rep., Univ. of Texas at Austin, 1983",
         "priority approximation inside AMVA; the AMVA formulation follows Eager & Lipscomb [EagL88]"}},
        {"amva.cl", {"ChaL83",
         "K. M. Chandy, M. S. Lakshmi, \"An Approximation Technique for Queueing Networks with Preemptive Priority Queues\", Tech. Rep., Univ. of Texas at Austin, 1983",
         "priority approximation inside AMVA; the AMVA formulation follows Eager & Lipscomb [EagL88]"}},
        {"shadow", {"Sev77",
         "K. Sevcik, \"Priority Scheduling Disciplines in Queuing Network Models of Computer Systems\", IFIP Congress, 1977",
         "shadow-server treatment of priority scheduling"}},
        {"zhou", {"Woo22",
         "S. Zhou, M. Woodside, \"A Multiserver Approximation for Cloud Scaling Analysis\", ICPE Companion, 2022",
         "multiserver scaling approximation"}},
        {"rolia", {"RolS95",
         "J. A. Rolia, K. C. Sevcik, \"The Method of Layers\", IEEE Trans. Software Engineering 21(8), 1995",
         "multi-server station approximation of the method of layers"}},
        {"interpos", {"casale2016m3a",
         "G. Casale, A. Sansottera, P. Cremonesi, \"Compact Markov-Modulated Models for Multiclass Trace Fitting\", Eur. J. Oper. Res. 255(3), 2016",
         "lumped interleaving of the per-flow M3PP(2,m) counting-process fits"}},
        {"m3pp", {"casale2016m3a",
         "G. Casale, A. Sansottera, P. Cremonesi, \"Compact Markov-Modulated Models for Multiclass Trace Fitting\", Eur. J. Oper. Res. 255(3), 2016",
         "M3PP(2,m) fitted to the counting process, per-class rates exact"}},
        {"m3pp2m_fitc", {"casale2016m3a",
         "G. Casale, A. Sansottera, P. Cremonesi, \"Compact Markov-Modulated Models for Multiclass Trace Fitting\", Eur. J. Oper. Res. 255(3), 2016",
         "M3PP(2,m) fitted to the counting process, per-class rates exact"}},
        {"m3pp_superpos", {"casale2016m3a",
         "G. Casale, A. Sansottera, P. Cremonesi, \"Compact Markov-Modulated Models for Multiclass Trace Fitting\", Eur. J. Oper. Res. 255(3), 2016",
         "superposition of one second-order M3PP per class"}},
        {"qna", {"Whi83a",
         "W. Whitt, \"The Queueing Network Analyzer\", Bell Syst. Tech. J. 62, 1983",
         "two-moment decomposition of the open network, including the deterministic (round-robin) traffic split"}},
        {"tvfluid", {"LiuW12",
         "Y. Liu, W. Whitt, \"The Gt/GI/st+GI Many-Server Fluid Queue\", Queueing Systems 71, 2012",
         "the two-regime fluid limit, the boundary waiting time ODE and the age-based queue content"}},
        {"gtmtst", {"LiuW12",
         "Y. Liu, W. Whitt, \"The Gt/GI/st+GI Many-Server Fluid Queue\", Queueing Systems 71, 2012",
         "the two-regime fluid limit, the boundary waiting time ODE and the age-based queue content"}},
        {"tvfluidnet", {"LiuW14",
         "Y. Liu, W. Whitt, \"Algorithms for Time-Varying Networks of Many-Server Fluid Queues\", INFORMS J. on Computing 26(1), 2014",
         "the regime-switching algorithm and the traffic-rate fixed point that couples the queues"}},
        {"ggnmdiffusion", {"Whi04",
         "W. Whitt, \"A Diffusion Approximation for the GI/GI/n/m Queue\", Operations Research 52(6), 2004",
         "the two-region diffusion, the asymptotic peakedness z and the blocking approximation at the upper boundary"}},
        {"peakedness", {"Whi04",
         "W. Whitt, \"A Diffusion Approximation for the GI/GI/n/m Queue\", Operations Research 52(6), 2004",
         "the two-region diffusion, the asymptotic peakedness z and the blocking approximation at the upper boundary"}},
        {"tga", {"LiuWY16",
         "Y. Liu, W. Whitt, Y. Yu, \"Approximations for Heavily-Loaded G/GI/n+GI Queues\", Naval Research Logistics 63(3), 2016",
         "the truncated Gaussian refinement of the fluid limit, and the (cs+1)rho term that carries a general service law"}},
        {"ggingi", {"LiuWY16",
         "Y. Liu, W. Whitt, Y. Yu, \"Approximations for Heavily-Loaded G/GI/n+GI Queues\", Naval Research Logistics 63(3), 2016",
         "the truncated Gaussian refinement of the fluid limit, and the (cs+1)rho term that carries a general service law"}},
        {"feedbackelim", {"WhiY22",
         "W. Whitt, W. You, \"A Robust Queueing Network Analyzer Based on Indices of Dispersion\", Naval Research Logistics 69, 2022",
         "near-immediate feedback elimination and the geometric-sum service law it leaves behind"}},
        {"longtailfit", {"FelW98",
         "A. Feldmann, W. Whitt, \"Fitting Mixtures of Exponentials to Long-Tail Distributions to Analyze Network Performance Models\", Perform. Eval. 31, 1998",
         "the recursive fit of a hyperexponential to a ccdf over successive time scales"}},
        {"hyperexpfit", {"FelW98",
         "A. Feldmann, W. Whitt, \"Fitting Mixtures of Exponentials to Long-Tail Distributions to Analyze Network Performance Models\", Perform. Eval. 31, 1998",
         "the recursive fit of a hyperexponential to a ccdf over successive time scales"}},
        {"mol", {"MasW94",
         "W. A. Massey, W. Whitt, \"An Analysis of the Modified Offered Load Approximation for the Nonstationary Erlang Loss Model\", Ann. Appl. Prob. 4(4), 1994",
         "the infinite-server offered load fed into the stationary Erlang formula, which carries the time lag"}},
        {"psa", {"Whi91",
         "W. Whitt, \"The Pointwise Stationary Approximation for Mt/Mt/s Queues is Asymptotically Correct as the Rates Increase\", Management Science 37(3), 1991",
         "the instantaneous-load approximation and the regime where it is asymptotically correct"}},
        {"runlength", {"Whi89",
         "W. Whitt, \"Planning Queueing Simulations\", Management Science 35(11), 1989",
         "the asymptotic variance as the cost of a steady-state estimate, and the run length it implies"}},
        {"nhppks", {"KimW14",
         "S.-H. Kim, W. Whitt, \"Are Call Center and Hospital Arrivals Well Modeled by Nonhomogeneous Poisson Processes?\", M&SOM 16(3), 2014",
         "the conditional-uniform KS test and the Durbin-transformed Lewis variant that gives it power"}},
        {"maxima", {"CroGW07",
         "C. Crow, D. Goldberg, W. Whitt, \"Two-Moment Approximations for Maxima\", Operations Research 55(3), 2007",
         "the extreme-value form of the maximum from two moments, its n* validity threshold and the fitted-distribution route"}},
        {"extremal", {"CheW20",
         "Y. Chen, W. Whitt, \"Algorithms for the Upper Bound Mean Waiting Time in the GI/GI/1 Queue\", Queueing Systems 94, 2020",
         "the conjectured tight two-moment upper bound and the D/RS/1 reduction that computes it"}},
        {"gig1bnds", {"CheW20",
         "Y. Chen, W. Whitt, \"Algorithms for the Upper Bound Mean Waiting Time in the GI/GI/1 Queue\", Queueing Systems 94, 2020",
         "the conjectured tight two-moment upper bound and the D/RS/1 reduction that computes it"}},
        {"erlanga", {"Whi05",
         "W. Whitt, \"Engineering Solution of a Basic Call-Center Model\", Management Science 51(2), 2005",
         "birth-and-death solution of M/M/s/r+M and the customer-experience recursions it shares with the general model"}},
        {"mgisrgi", {"Whi05",
         "W. Whitt, \"Engineering Solution of a Basic Call-Center Model\", Management Science 51(2), 2005",
         "state-dependent Markovian approximation of general patience and the exponential replacement of general service"}},
        {"ggisgi.fluid", {"Whi06",
         "W. Whitt, \"Fluid Models for Multiserver Queues with Abandonments\", Operations Research 54(1), 2006",
         "deterministic fluid limit of the overloaded multiserver queue, including the queue boundary F^c(w)=1/rho"}},
        {"qed", {"HalW81",
         "S. Halfin, W. Whitt, \"Heavy-Traffic Limits for Queues with Many Exponential Servers\", Operations Research 29(3), 1981",
         "the many-server heavy-traffic delay probability alpha(beta) and the square-root staffing rule that inverts it"}},
        {"sqrtstaffing", {"HalW81",
         "S. Halfin, W. Whitt, \"Heavy-Traffic Limits for Queues with Many Exponential Servers\", Operations Research 29(3), 1981",
         "the many-server heavy-traffic delay probability alpha(beta) and the square-root staffing rule that inverts it"}},
        {"mtginf", {"EicMW93",
         "S. G. Eick, W. A. Massey, W. Whitt, \"The Physics of the Mt/G/infinity Queue\", Operations Research 41(4), 1993",
         "exact Poisson law of the time-varying infinite-server queue, its mean ES E[lambda(t-Se)] and the time lag"}},
        {"gigk.diffusion", {"Whi04",
         "W. Whitt, \"A Diffusion Approximation for the GI/GI/n/m Queue\", Operations Research 52(6), 2004",
         "the two-region diffusion, the asymptotic peakedness z and the blocking approximation at the upper boundary"}},
        {"gigk.whitt", {"Whi93",
         "W. Whitt, \"Approximations for the GI/G/m Queue\", Production and Operations Management 2(2), 1993",
         "the phi interpolation between the M/D/k and D/M/k correction factors of the M/M/k waiting time"}},
        {"gig1.extremal", {"CheW20",
         "Y. Chen, W. Whitt, \"Algorithms for the Upper Bound Mean Waiting Time in the GI/GI/1 Queue\", Queueing Systems 94, 2020",
         "the conjectured tight two-moment upper bound and the D/RS/1 reduction that computes it"}},
        {"ggingi.tga", {"LiuWY16",
         "Y. Liu, W. Whitt, Y. Yu, \"Approximations for Heavily-Loaded G/GI/n+GI Queues\", Naval Research Logistics 63(3), 2016",
         "the truncated Gaussian refinement of the fluid limit, and the (cs+1)rho term that carries a general service law"}},
        {"tvms", {"LiuW14",
         "Y. Liu, W. Whitt, \"Algorithms for Time-Varying Networks of Many-Server Fluid Queues\", INFORMS J. on Computing 26(1), 2014",
         "the time-varying many-server fluid queue solved forward on a grid, at the staffing the model declares"}},
        {"runlengthplan", {"Whi89",
         "W. Whitt, \"Planning Queueing Simulations\", Management Science 35(11), 1989",
         "the asymptotic variance as the cost of a steady-state estimate, and the run length it implies"}},
        {"asymvar", {"Whi89",
         "W. Whitt, \"Planning Queueing Simulations\", Management Science 35(11), 1989",
         "the asymptotic variance as the cost of a steady-state estimate, and the run length it implies"}},
        {"rqna", {"WhiY22",
         "W. Whitt, W. You, \"A Robust Queueing Network Analyzer Based on Indices of Dispersion\", Naval Research Logistics 69, 2022",
         "index-of-dispersion decomposition and robust queueing bounds"}},
        {"rqt", {"bandi2015rqt",
         "C. Bandi, D. Bertsimas, N. Youssef, \"Robust Queueing Theory\", Operations Research 63(3), 2015",
         "polyhedral uncertainty sets and the worst-case system time of each node, with the robust Burke calculus for the network"}},
        {"highvar", {"BonW86",
         "A. B. Bondi, W. Whitt, \"The influence of service-time variability in a closed network of queues\", Perform. Eval. 6, 1986",
         "high-variability service correction of the demands"}},
        {"interp", {"BonW86",
         "A. B. Bondi, W. Whitt, \"The influence of service-time variability in a closed network of queues\", Perform. Eval. 6, 1986",
         "high-variability service correction of the demands"}},
        {"kraemer", {"KraLB78",
         "W. Kraemer, M. Langenbach-Belz, \"Approximate Formulae for General Single Server Systems with Single and Batch Arrivals\", Angewandte Informatik 9, 1978",
         "G/G/1 waiting time approximation"}},
        {"gig1.gelenbe", {"Gel75",
         "E. Gelenbe, \"On Approximate Computer System Models\", Journal of the ACM 22(2), 1975",
         "the diffusion approximation with instantaneous-return boundary, whose geometric fit rhat=exp(-2(1-rho)/(rho ca^2+cs^2)) gives the mean queue length"}},
        {"gelenbe", {"Gel75",
         "E. Gelenbe, \"On Approximate Computer System Models\", Journal of the ACM 22(2), 1975",
         "the diffusion approximation with instantaneous-return boundary, whose geometric fit rhat=exp(-2(1-rho)/(rho ca^2+cs^2)) gives the mean queue length"}},
        {"gig1.kimura", {"Kim86",
         "T. Kimura, \"A Two-Moment Approximation for the Mean Waiting Time in the GI/G/s Queue\", Management Science 32(6), 1986",
         "the diffusion-interpolation waiting time rho(ca^2+cs^2)/(mu(1-rho)(1+ca^2)), exact for M/M/1 and M/G/1"}},
        {"kimura", {"Kim86",
         "T. Kimura, \"A Two-Moment Approximation for the Mean Waiting Time in the GI/G/s Queue\", Management Science 32(6), 1986",
         "the diffusion-interpolation waiting time rho(ca^2+cs^2)/(mu(1-rho)(1+ca^2)), exact for M/M/1 and M/G/1"}},
        {"klb", {"KraLB78",
         "W. Kraemer, M. Langenbach-Belz, \"Approximate Formulae for General Single Server Systems with Single and Batch Arrivals\", Angewandte Informatik 9, 1978",
         "G/G/1 waiting time approximation"}},
        {"nc.ca", {"ReiK75",
         "M. Reiser, H. Kobayashi, \"Queueing Networks with Multiple Closed Chains: Theory and Computational Algorithms\", IBM J. Res. Dev. 19(3), 1975",
         "exact normalizing constant by the multiclass convolution algorithm, Buzen's single-chain recursion (CACM 16(9), 1973) generalized to multiple closed chains"}},
        {"ca", {"ReiK75",
         "M. Reiser, H. Kobayashi, \"Queueing Networks with Multiple Closed Chains: Theory and Computational Algorithms\", IBM J. Res. Dev. 19(3), 1975",
         "exact normalizing constant by the multiclass convolution algorithm, Buzen's single-chain recursion (CACM 16(9), 1973) generalized to multiple closed chains"}},
        {"pfqn.manjunath", {"ManSik07",
         "D. Manjunath, B. Sikdar, \"Integral Expressions for the Numerical Evaluation of Product Form Expressions Over Irregular Multidimensional Integer Spaces\"",
         "exact normalizing constant of a closed product-form network over a state space cut by linear integer constraints, by residue extraction from the multivariate generating function"}},
        {"manjunath", {"ManSik07",
         "D. Manjunath, B. Sikdar, \"Integral Expressions for the Numerical Evaluation of Product Form Expressions Over Irregular Multidimensional Integer Spaces\"",
         "exact normalizing constant of a closed product-form network over a state space cut by linear integer constraints, by residue extraction from the multivariate generating function"}},
        {"passage", {"harr.knot02",
         "P. G. Harrison and W. J. Knottenbelt, \"Passage Time Distributions in Large Markov Chains\", ACM SIGMETRICS Perf. Eval. Review 30(1), 2002",
         "first passage time into a target state set: the transform of Eqs. 1-2 and the moment recursion of Eq. 3"}},
        {"ctmc.passage", {"harr.knot02",
         "P. G. Harrison and W. J. Knottenbelt, \"Passage Time Distributions in Large Markov Chains\", ACM SIGMETRICS Perf. Eval. Review 30(1), 2002",
         "first passage time into a target state set: the transform of Eqs. 1-2 and the moment recursion of Eq. 3"}},
        {"smp.passage", {"harr.knot02",
         "P. G. Harrison and W. J. Knottenbelt, \"Passage Time Distributions in Large Markov Chains\", ACM SIGMETRICS Perf. Eval. Review 30(1), 2002",
         "semi-Markov first passage time: the kernel transform of Eqs. 4-5 and the u_i(r) moment recurrence of Eqs. 7-8"}},
        {"cyclet", {"harr90",
         "P. G. Harrison, \"Laplace transform inversion and passage-time distributions in Markov processes\", J. Appl. Prob. 27(1), 1990",
         "Laplace transform of the cycle time along an overtake-free path of a closed tree-like network, and its inversion"}},
        {"cyclet.ofree", {"dadu82",
         "H. Daduna, \"Passage times for overtake-free paths in Gordon-Newell networks\", Adv. Appl. Prob. 14(3), 1982",
         "the overtake-free path passage time in a Gordon-Newell network, which the closed-form density of Theorem 2 evaluates"}},
        {"lti.weeks", {"week66",
         "W. T. Weeks, \"Numerical inversion of Laplace transforms using Laguerre functions\", J. ACM 13(3), 1966",
         "inversion of a Laplace transform by a Laguerre function series"}},
        {"lti.laguerre", {"abat.chou.whit96",
         "J. Abate, G. L. Choudhury and W. Whitt, \"On the Laguerre method for numerically inverting Laplace transforms\", INFORMS J. Computing 8(4), 1996",
         "the Laguerre inversion made practical: coefficient quadrature, scaling and truncation"}},
        {"lti.talbot", {"Talb79",
         "A. Talbot, \"The accurate numerical inversion of Laplace transforms\", IMA J. Appl. Math. 23(1), 1979",
         "inversion on a deformed contour around the negative real axis, whose nodes and weights this method uses"}},
        {"ctmc.transient.sens", {"TriBob17",
         "K. S. Trivedi, A. Bobbio, \"Reliability and Availability Engineering\", Cambridge Univ. Press, 2017, Eq. (9.82)",
         "sensitivity of the transient distribution to a scalar parameter, integrated with the state as one augmented system"}},
        {"busyp", {"Dad88",
         "H. Daduna, \"Busy Periods for Subnetworks in Stochastic Networks: Mean Value Analysis\", J. ACM 35(3), 1988",
         "mean duration of the busy period of order n for a subnetwork, from the subnetwork and complement normalizing constants"}},
        {"nc.busyp", {"Dad88",
         "H. Daduna, \"Busy Periods for Subnetworks in Stochastic Networks: Mean Value Analysis\", J. ACM 35(3), 1988",
         "mean duration of the busy period of order n for a subnetwork, from the subnetwork and complement normalizing constants"}},
        {"fes", {"ChaHW75",
         "K. M. Chandy, U. Herzog, L. Woo, \"Parametric Analysis of Queuing Networks\", IBM J. Res. Dev. 19(1), 1975",
         "replacement of a subnetwork by a load-dependent station carrying its isolated throughputs"}},
        {"ctmc.fes", {"ChaHW75",
         "K. M. Chandy, U. Herzog, L. Woo, \"Parametric Analysis of Queuing Networks\", IBM J. Res. Dev. 19(1), 1975",
         "hierarchical decomposition: the reduced chain is enumerated with the subnetwork replaced by its flow-equivalent server, and the collapsed stations are recovered by conditioning on its population"}},
        {"ctmc.chainaggr", {"ReiL80",
         "M. Reiser, S. S. Lavenberg, \"Mean-Value Analysis of Closed Multichain Queuing Networks\", J. ACM 27(2), 1980",
         "the chain, not the class, as the unit a product-form network is solved in, which is what makes chain aggregation exact and the alpha-weighted deaggregation its inverse"}},
        {"chains", {"ReiL80",
         "M. Reiser, S. S. Lavenberg, \"Mean-Value Analysis of Closed Multichain Queuing Networks\", J. ACM 27(2), 1980",
         "the chain, not the class, as the unit a product-form network is solved in, which is what makes the chains transformation exact and the alpha-weighted deaggregation its inverse"}},
        {"fes.map", {"CasMCS11",
         "G. Casale, N. Mi, L. Cherkasova, E. Smirni, \"Dealing with Burstiness in Multi-Tier Applications: Models and Their Parameterization\", IEEE TSE 37(5), 2011",
         "load-dependent MAP flow-equivalent server, whose inter-departure moments and index of dispersion carry the burstiness of the aggregated subnetwork"}},
        {"map2.idc", {"CasMCS11",
         "G. Casale, N. Mi, L. Cherkasova, E. Smirni, \"Dealing with Burstiness in Multi-Tier Applications: Models and Their Parameterization\", IEEE TSE 37(5), 2011",
         "inversion of the index of dispersion into the autocorrelation decay rate of a MAP(2), and the fallbacks when it is not representable"}},
        {"map2.fit", {"HeiHG06",
         "A. Heindl, G. Horvath, K. Gross, \"Explicit Inverse Characterizations of Acyclic MAPs of Second Order\", EPEW, 2006",
         "explicit MAP(2) from three moments and the autocorrelation decay rate"}},
        {"lossn.exact", {"ManSik07",
         "D. Manjunath, B. Sikdar, \"Integral Expressions for the Numerical Evaluation of Product Form Expressions Over Irregular Multidimensional Integer Spaces\"",
         "exact normalizing constant over a state space cut by linear integer constraints"}},
        {"lossn.ms", {"ManSik07",
         "D. Manjunath, B. Sikdar, \"Integral Expressions for the Numerical Evaluation of Product Form Expressions Over Irregular Multidimensional Integer Spaces\"",
         "exact normalizing constant over a state space cut by linear integer constraints"}},
        {"lossn.manjunath", {"ManSik07",
         "D. Manjunath, B. Sikdar, \"Integral Expressions for the Numerical Evaluation of Product Form Expressions Over Irregular Multidimensional Integer Spaces\"",
         "exact normalizing constant over a state space cut by linear integer constraints"}},
        {"lossn.erlangfp", {"Kelly91",
         "F. P. Kelly, \"Loss Networks\", Ann. Appl. Probab. 1(3), 1991",
         "reduced-load (Erlang fixed point) approximation of link blocking"}},
        {"erlangfp", {"Kelly91",
         "F. P. Kelly, \"Loss Networks\", Ann. Appl. Probab. 1(3), 1991",
         "reduced-load (Erlang fixed point) approximation of link blocking"}},
        {"lossn.mci", {"RosWan92",
         "K. W. Ross, J. Wang, \"Monte Carlo Summation Applied to Product-Form Loss Networks\", Prob. Eng. Inf. Sci. 6, 1992",
         "Monte Carlo summation of the loss-network normalizing constant"}},
        {"mci", {"RosWan92",
         "K. W. Ross, J. Wang, \"Monte Carlo Summation Applied to Product-Form Loss Networks\", Prob. Eng. Inf. Sci. 6, 1992",
         "Monte Carlo summation of the loss-network normalizing constant"}},
        {"imci", {"WangCS16",
         "W. Wang, G. Casale, C. A. Sutton, \"A Bayesian Approach to Parameter Inference in Queueing Networks\", ACM TOMACS 27(1), 2016",
         "improved (tilted) Monte Carlo integration sampler for the normalizing constant"}},
        {"comom", {"Cas09",
         "G. Casale, \"CoMoM: Efficient Class-Oriented Evaluation of Multiclass Performance Models\", IEEE TSE 35(2), 2009",
         "class-oriented recursion for the normalizing constant"}},
        {"nc.comom", {"Cas09",
         "G. Casale, \"CoMoM: Efficient Class-Oriented Evaluation of Multiclass Performance Models\", IEEE TSE 35(2), 2009",
         "class-oriented recursion for the normalizing constant"}},
        {"clw", {"ChoLW95",
         "G. L. Choudhury, K. K. Leung, W. Whitt, \"Calculating Normalization Constants of Closed Queuing Networks by Numerically Inverting Their Generating Functions\", J. ACM 42, 1995",
         "numerical inversion of the generating function"}},
        {"nc.clw", {"ChoLW95",
         "G. L. Choudhury, K. K. Leung, W. Whitt, \"Calculating Normalization Constants of Closed Queuing Networks by Numerically Inverting Their Generating Functions\", J. ACM 42, 1995",
         "numerical inversion of the generating function"}},
        {"clw.lld", {"BerM93",
         "A. L. Bertozzi, J. McKenna, \"Multidimensional Residues, Generating Functions, and Their Application to Queueing Networks\", SIAM Review 35(2), 1993",
         "per-center transform of the load-dependent station"}},
        {"nc.clw.lld", {"BerM93",
         "A. L. Bertozzi, J. McKenna, \"Multidimensional Residues, Generating Functions, and Their Application to Queueing Networks\", SIAM Review 35(2), 1993",
         "per-center transform of the load-dependent station"}},
        {"clw.oi", {"ChoLW95",
         "G. L. Choudhury, K. K. Leung, W. Whitt, \"Calculating Normalization Constants of Closed Queuing Networks by Numerically Inverting Their Generating Functions\", J. ACM 42, 1995",
         "numerical inversion of the generating function of the order-independent network"}},
        {"nc.clw.oi", {"ChoLW95",
         "G. L. Choudhury, K. K. Leung, W. Whitt, \"Calculating Normalization Constants of Closed Queuing Networks by Numerically Inverting Their Generating Functions\", J. ACM 42, 1995",
         "numerical inversion of the generating function of the order-independent network"}},
        {"clw.jd", {"ChoLW95",
         "G. L. Choudhury, K. K. Leung, W. Whitt, \"Calculating Normalization Constants of Closed Queuing Networks by Numerically Inverting Their Generating Functions\", J. ACM 42, 1995",
         "numerical inversion of the generating function of the joint-dependent network"}},
        {"nc.clw.jd", {"ChoLW95",
         "G. L. Choudhury, K. K. Leung, W. Whitt, \"Calculating Normalization Constants of Closed Queuing Networks by Numerically Inverting Their Generating Functions\", J. ACM 42, 1995",
         "numerical inversion of the generating function of the joint-dependent network"}},
        {"jd", {"BonP03",
         "T. Bonald, A. Proutiere, \"Insensitive bandwidth sharing in data networks\", Queueing Systems 44(1), 2003",
         "balance function of the joint-dependent (balanced-fair) station"}},
        {"jointdependence", {"BonP03",
         "T. Bonald, A. Proutiere, \"Insensitive bandwidth sharing in data networks\", Queueing Systems 44(1), 2003",
         "balance function of the joint-dependent (balanced-fair) station"}},
        {"nc.jd", {"BonP03",
         "T. Bonald, A. Proutiere, \"Insensitive bandwidth sharing in data networks\", Queueing Systems 44(1), 2003",
         "balance function of the joint-dependent (balanced-fair) station"}},
        {"mva.jd", {"BonP03",
         "T. Bonald, A. Proutiere, \"Insensitive bandwidth sharing in data networks\", Queueing Systems 44(1), 2003",
         "balance function of the joint-dependent (balanced-fair) station"}},
        {"nc.mva", {"Rei81",
         "M. Reiser, \"Mean-Value Analysis and Convolution Method for Queue-Dependent Servers in Closed Queueing Networks\", Perform. Eval. 1, 1981",
         "convolution and MVA with queue-dependent servers"}},
        {"le", {"Cas17",
         "G. Casale, \"Accelerating Performance Inference over Closed Systems by Asymptotic Methods\", ACM SIGMETRICS, 2017",
         "asymptotic expansion of the normalizing constant integral"}},
        {"ble", {"Cas17",
         "G. Casale, \"Accelerating Performance Inference over Closed Systems by Asymptotic Methods\", ACM SIGMETRICS, 2017",
         "asymptotic expansion of the normalizing constant integral, plus an empirical (1-log(2*pi)/2) correction per Laplaced direction for the eps->0 evaluation, M-1 with Z=0 and M with Z>0 (not from the paper)"}},
        {"aghq", {"LiuP94",
         "Q. Liu, D. A. Pierce, \"A Note on Gauss-Hermite Quadrature\", Biometrika 81(3), 1994",
         "adaptive Gauss-Hermite rule over the simplex factor of the normalizing-constant integral, rescaled by the logistic-expansion mode and curvature; q=1 reproduces pfqn_le"}},
        {"ls", {"Cas17",
         "G. Casale, \"Accelerating Performance Inference over Closed Systems by Asymptotic Methods\", ACM SIGMETRICS, 2017",
         "asymptotic expansion of the normalizing constant integral"}},
        {"sdr", {"Krz87",
         "A. E. Krzesinski, \"Multiclass Queueing Networks with State-Dependent Routing\", Perform. Eval. 7(2):125-143, 1987",
         "product-form joint distribution (eq. 16) and routing probabilities (eq. 10) of a closed multiclass network whose entry center routes on branch and subnetwork populations"}},
        {"sdr.mva", {"Krz87",
         "A. E. Krzesinski, \"Multiclass Queueing Networks with State-Dependent Routing\", Perform. Eval. 7(2):125-143, 1987",
         "Section 4 mean value analysis and convolution of the state-dependent routing product form, single-center branches"}},
        {"sdr.towsley", {"Tow80",
         "D. Towsley, \"Queuing Network Models with State-Dependent Routing\", J. ACM 27(2):323-337, 1980",
         "single-class antecedent: p-subnetworks, the affine routing functions and the Norton-type composite queue"}},
        {"cub", {"Cas17",
         "G. Casale, \"Accelerating Performance Inference over Closed Systems by Asymptotic Methods\", ACM SIGMETRICS, 2017",
         "asymptotic expansion of the normalizing constant integral"}},
        {"nc.le", {"Cas17",
         "G. Casale, \"Accelerating Performance Inference over Closed Systems by Asymptotic Methods\", ACM SIGMETRICS, 2017",
         "asymptotic expansion of the normalizing constant integral"}},
        {"nc.ble", {"Cas17",
         "G. Casale, \"Accelerating Performance Inference over Closed Systems by Asymptotic Methods\", ACM SIGMETRICS, 2017",
         "asymptotic expansion of the normalizing constant integral, plus an empirical (1-log(2*pi)/2) correction per Laplaced direction for the eps->0 evaluation, M-1 with Z=0 and M with Z>0 (not from the paper)"}},
        {"nc.aghq", {"LiuP94",
         "Q. Liu, D. A. Pierce, \"A Note on Gauss-Hermite Quadrature\", Biometrika 81(3), 1994",
         "adaptive Gauss-Hermite rule over the simplex factor of the normalizing-constant integral, rescaled by the logistic-expansion mode and curvature; q=1 reproduces pfqn_le"}},
        {"nc.ls", {"Cas17",
         "G. Casale, \"Accelerating Performance Inference over Closed Systems by Asymptotic Methods\", ACM SIGMETRICS, 2017",
         "asymptotic expansion of the normalizing constant integral"}},
        {"nc.cub", {"Cas17",
         "G. Casale, \"Accelerating Performance Inference over Closed Systems by Asymptotic Methods\", ACM SIGMETRICS, 2017",
         "asymptotic expansion of the normalizing constant integral"}},
        {"divdiff", {"Cas17",
         "G. Casale, \"Accelerating Performance Inference over Closed Systems by Asymptotic Methods\", ACM SIGMETRICS, 2017",
         "explicit O(1)-space closed forms of the multiclass normalizing constant: Eq. (15) at pairwise distinct induced demands, Eq. (16) at repeated ones"}},
        {"nc.divdiff", {"Cas17",
         "G. Casale, \"Accelerating Performance Inference over Closed Systems by Asymptotic Methods\", ACM SIGMETRICS, 2017",
         "explicit O(1)-space closed forms of the multiclass normalizing constant: Eq. (15) at pairwise distinct induced demands, Eq. (16) at repeated ones"}},
        {"pfqn_divdiff_ld", {"Cas17",
         "G. Casale, \"Accelerating Performance Inference over Closed Systems by Asymptotic Methods\", ACM SIGMETRICS, 2017",
         "divided-difference form of the multiclass normalizing constant (Cor. 3.2), generalized here to load-dependent rates alpha_i(.), which the paper left as future work"}},
        {"divdiff.ld", {"CasHH21",
         "G. Casale, P. G. Harrison, O. W. Hong, \"Facilitating Load-Dependent Queueing Analysis Through Factorization\", Perform. Eval., 2021",
         "limited load-dependent closed form of the single-class normalizing constant (Thm. 1), used as the inner kernel of the divided-difference expansion"}},
        {"nc.divdiff.ld", {"CasHH21",
         "G. Casale, P. G. Harrison, O. W. Hong, \"Facilitating Load-Dependent Queueing Analysis Through Factorization\", Perform. Eval., 2021",
         "limited load-dependent closed form of the single-class normalizing constant (Thm. 1), used as the inner kernel of the divided-difference expansion"}},
        {"rd", {"CasHH21",
         "G. Casale, P. G. Harrison, O. W. Hong, \"Facilitating Load-Dependent Queueing Analysis Through Factorization\", Perform. Eval., 2021",
         "factorization of the load-dependent normalizing constant"}},
        {"nrp", {"CasHH21",
         "G. Casale, P. G. Harrison, O. W. Hong, \"Facilitating Load-Dependent Queueing Analysis Through Factorization\", Perform. Eval., 2021",
         "Norlund-Rice integral form of the load-dependent normalizing constant, evaluated by Laplace approximation of the contour under a probit substitution"}},
        {"nrl", {"CasHH21",
         "G. Casale, P. G. Harrison, O. W. Hong, \"Facilitating Load-Dependent Queueing Analysis Through Factorization\", Perform. Eval., 2021",
         "Norlund-Rice integral form of the load-dependent normalizing constant, evaluated by Laplace approximation of the contour under a logit substitution"}},
        {"nre", {"CasHH21",
         "G. Casale, P. G. Harrison, O. W. Hong, \"Facilitating Load-Dependent Queueing Analysis Through Factorization\", Perform. Eval., 2021",
         "Norlund-Rice integral form of the load-dependent normalizing constant, evaluated by Daniels steepest descent (Ann. Math. Statist. 25(4), 1954) with the Barndorff-Nielsen-Cox second-order Edgeworth correction (J. R. Stat. Soc. B 41(3), 1979)"}},
        {"comomld", {"CasHH21",
         "G. Casale, P. G. Harrison, O. W. Hong, \"Facilitating Load-Dependent Queueing Analysis Through Factorization\", Perform. Eval., 2021",
         "factorization of the load-dependent normalizing constant"}},
        {"ncldmx", {"AfBaBr84",
         "S. C. Bruell, G. Balbo, P. V. Afshari, \"Mean value analysis of mixed, multiple class BCMP networks with load dependent service stations\", Perform. Eval. 4, 1984",
         "exact mean value analysis of a mixed network whose queues carry limited load-dependent rates, through the effective capacity of the open classes"}},
        {"kt", {"KneT92",
         "C. Knessl, C. Tier, \"Asymptotic Expansions for Large Closed Queueing Networks with Multiple Job Classes\", IEEE TC 41(4), 1992",
         "asymptotic expansion for large populations"}},
        {"bkt", {"KneT92",
         "C. Knessl, C. Tier, \"Asymptotic Expansions for Large Closed Queueing Networks with Multiple Job Classes\", IEEE TC 41(4), 1992",
         "asymptotic expansion for large populations, minus the exact Stirling remainder log(N_r!)-(N_r log N_r - N_r + log(2 pi N_r)/2) that steepest descent drops in each Laplaced class direction (BKT, not from the paper)"}},
        {"lekt", {"Cas17",
         "G. Casale, \"Accelerating Performance Inference over Closed Systems by Asymptotic Methods\", ACM SIGMETRICS, 2017",
         "the corrected logistic expansion (ble) and the corrected Knessl-Tier expansion (bkt, Knessl and Tier, IEEE TC 41(4), 1992) are one estimator, evaluated in M-1 and in R dimensions; computed on the cheaper side, with the Z=0 constant M(1-log(2*pi)/2)-r(N+M) so that the two sides agree there too (not from the papers)"}},
        {"nc.lekt", {"Cas17",
         "G. Casale, \"Accelerating Performance Inference over Closed Systems by Asymptotic Methods\", ACM SIGMETRICS, 2017",
         "the corrected logistic expansion (ble) and the corrected Knessl-Tier expansion (bkt, Knessl and Tier, IEEE TC 41(4), 1992) are one estimator, evaluated in M-1 and in R dimensions; computed on the cheaper side, with the Z=0 constant M(1-log(2*pi)/2)-r(N+M) so that the two sides agree there too (not from the papers)"}},
        {"nc.bkt", {"KneT92",
         "C. Knessl, C. Tier, \"Asymptotic Expansions for Large Closed Queueing Networks with Multiple Job Classes\", IEEE TC 41(4), 1992",
         "asymptotic expansion for large populations, minus the exact Stirling remainder log(N_r!)-(N_r log N_r - N_r + log(2 pi N_r)/2) that steepest descent drops in each Laplaced class direction (BKT, not from the paper)"}},
        {"bk", {"BirK92",
         "A. Birman, Y. Kogan, \"Asymptotic Evaluation of Closed Queueing Networks with Many Stations\", Commun. Statist. Stochastic Models 8(3), 1992",
         "saddle point expansion of the multichain partition function, with Algorithm 1 detecting the chains whose dedicated station is a bottleneck"}},
        {"bkue", {"BirK92",
         "A. Birman, Y. Kogan, \"Asymptotic Evaluation of Closed Queueing Networks with Many Stations\", Commun. Statist. Stochastic Models 8(3), 1992",
         "van der Waerden uniform expansion, which keeps the dominant pole and the saddle point in one erfc formula"}},
        {"mcmc", {"CheO98",
         "W. Chen, C. A. O'Cinneide, \"Towards a Polynomial-Time Randomized Algorithm for Closed Product-Form Networks\", ACM TOMACS 8(3), 1998",
         "regularization of a closed multiclass network into a reversible unit-rate processor-sharing network with the same steady state, simulated at service-completion epochs for the class throughput ratios G(N-e_r)/G(N) and the queue lengths"}},
        {"nc.mcmc", {"CheO98",
         "W. Chen, C. A. O'Cinneide, \"Towards a Polynomial-Time Randomized Algorithm for Closed Product-Form Networks\", ACM TOMACS 8(3), 1998",
         "regularization of a closed multiclass network into a reversible unit-rate processor-sharing network with the same steady state, simulated at service-completion epochs for the class throughput ratios G(N-e_r)/G(N) and the queue lengths"}},
        {"lc", {"BirK92",
         "A. Birman, Y. Kogan, \"Asymptotic Evaluation of Closed Queueing Networks with Many Stations\", Commun. Statist. Stochastic Models 8(3), 1992",
         "Algorithm 2, the load concealment reduction of a multichain network to single chain problems"}},
        {"lc.ue", {"BirK92",
         "A. Birman, Y. Kogan, \"Asymptotic Evaluation of Closed Queueing Networks with Many Stations\", Commun. Statist. Stochastic Models 8(3), 1992",
         "Algorithm 2 with the uniform expansion as the single chain solver"}},
        {"pana", {"McKM82",
         "J. McKenna, D. Mitra, \"Integral Representations and Asymptotic Expansions for Closed Markovian Queueing Networks: Normal Usage\", Bell Syst. Tech. J. 61(5), 1982",
         "normal-usage asymptotic expansion of the normalizing constant, the series the original PANACEA package (Ramakrishnan-Mitra, BSTJ 61(10), 1982) truncates at 1 to 3 terms"}},
        {"panald", {"MitM86",
         "D. Mitra, J. McKenna, \"Asymptotic Expansions for Closed Markovian Networks with State-Dependent Service Rates\", J. ACM 33(3), 1986",
         "load-dependent PANACEA expansion and its pseudonetwork coefficients"}},
        {"psrespt", {"MitMo83",
         "D. Mitra, J. A. Morrison, \"Asymptotic Expansions of Moments of the Waiting Time in Closed and Open Processor-Sharing Systems with Multiple Job Classes\", Adv. Appl. Prob. 15(4), 1983",
         "sojourn-time moments at a multiclass processor-sharing station"}},
        {"mm1ps", {"MitMo83",
         "D. Mitra, J. A. Morrison, \"Asymptotic Expansions of Moments of the Waiting Time in Closed and Open Processor-Sharing Systems with Multiple Job Classes\", Adv. Appl. Prob. 15(4), 1983",
         "sojourn-time moments at a multiclass processor-sharing station"}},
        {"mem", {"Kou94",
         "D. D. Kouvatsos, \"Entropy Maximisation and Queueing Network Models\", Annals of Operations Research 48, 1994",
         "maximum-entropy approximation of the network"}},
        {"mem.blocking", {"TahMB99",
         "H. Tahilramani, D. Manjunath, S. K. Bose, \"Approximate Analysis of Open Network of GE/GE/m/N Queues with Transfer Blocking\", MASCOTS, 1999",
         "holding-node expansion that makes transfer blocking work conserving"}},
        {"recal", {"ConG86",
         "A. E. Conway, N. D. Georganas, \"RECAL: A New Efficient Algorithm for the Exact Analysis of Multiple-Chain Closed Queueing Networks\", J. ACM 33, 1986",
         "recursive exact evaluation by chain"}},
        {"mvac", {"CSL89",
         "A. E. Conway, E. de Souza e Silva, S. S. Lavenberg, \"Mean Value Analysis by Chain of Product Form Queueing Networks\", IEEE Trans. Computers 38(3), 1989",
         "exact mean value analysis by chain (SolverMVA method mvac)"}},
        {"conv", {"Sau83",
         "C. H. Sauer, \"Computational Algorithms for State-Dependent Queueing Networks\", ACM TOCS 1(1), 1983",
         "convolution with chain-dependent service rates"}},
        {"nc.conv", {"Sau83",
         "C. H. Sauer, \"Computational Algorithms for State-Dependent Queueing Networks\", ACM TOCS 1(1), 1983",
         "convolution with chain-dependent service rates"}},
        {"aba", {"BolGMT06",
         "G. Bolch, S. Greiner, H. de Meer, K. S. Trivedi, \"Queueing Networks and Markov Chains\", Wiley, 2006",
         "asymptotic bounds on throughput and response time"}},
        {"aba.upper", {"BolGMT06",
         "G. Bolch, S. Greiner, H. de Meer, K. S. Trivedi, \"Queueing Networks and Markov Chains\", Wiley, 2006",
         "asymptotic bounds on throughput and response time"}},
        {"aba.lower", {"BolGMT06",
         "G. Bolch, S. Greiner, H. de Meer, K. S. Trivedi, \"Queueing Networks and Markov Chains\", Wiley, 2006",
         "asymptotic bounds on throughput and response time"}},
        {"bjb", {"CasMS08",
         "G. Casale, R. R. Muntz, G. Serazzi, \"Geometric Bounds: A Noniterative Analysis Technique for Closed Queueing Networks\", IEEE TC 57(6), 2008",
         "geometric and balanced-job bounds"}},
        {"gb", {"CasMS08",
         "G. Casale, R. R. Muntz, G. Serazzi, \"Geometric Bounds: A Noniterative Analysis Technique for Closed Queueing Networks\", IEEE TC 57(6), 2008",
         "geometric and balanced-job bounds"}},
        {"pb", {"CasMS08",
         "G. Casale, R. R. Muntz, G. Serazzi, \"Geometric Bounds: A Noniterative Analysis Technique for Closed Queueing Networks\", IEEE TC 57(6), 2008",
         "geometric and balanced-job bounds"}},
        {"bjb.upper", {"CasMS08",
         "G. Casale, R. R. Muntz, G. Serazzi, \"Geometric Bounds: A Noniterative Analysis Technique for Closed Queueing Networks\", IEEE TC 57(6), 2008",
         "geometric and balanced-job bounds"}},
        {"bjb.lower", {"CasMS08",
         "G. Casale, R. R. Muntz, G. Serazzi, \"Geometric Bounds: A Noniterative Analysis Technique for Closed Queueing Networks\", IEEE TC 57(6), 2008",
         "geometric and balanced-job bounds"}},
        {"gb.upper", {"CasMS08",
         "G. Casale, R. R. Muntz, G. Serazzi, \"Geometric Bounds: A Noniterative Analysis Technique for Closed Queueing Networks\", IEEE TC 57(6), 2008",
         "geometric and balanced-job bounds"}},
        {"gb.lower", {"CasMS08",
         "G. Casale, R. R. Muntz, G. Serazzi, \"Geometric Bounds: A Noniterative Analysis Technique for Closed Queueing Networks\", IEEE TC 57(6), 2008",
         "geometric and balanced-job bounds"}},
        {"pb.upper", {"CasMS08",
         "G. Casale, R. R. Muntz, G. Serazzi, \"Geometric Bounds: A Noniterative Analysis Technique for Closed Queueing Networks\", IEEE TC 57(6), 2008",
         "geometric and balanced-job bounds"}},
        {"pb.lower", {"CasMS08",
         "G. Casale, R. R. Muntz, G. Serazzi, \"Geometric Bounds: A Noniterative Analysis Technique for Closed Queueing Networks\", IEEE TC 57(6), 2008",
         "geometric and balanced-job bounds"}},
        {"auto", {"CasMS08",
         "Composite over the noniterative bound families; the applicable reference is that of the family selected at run time, most often G. Casale, R. R. Muntz, G. Serazzi, \"Geometric Bounds\", IEEE TC 57(6), 2008",
         "automatic selection of the tightest feasible noniterative upper and lower throughput bound"}},
        {"auto.upper", {"CasMS08",
         "Composite over the noniterative bound families; the applicable reference is that of the family selected at run time, most often G. Casale, R. R. Muntz, G. Serazzi, \"Geometric Bounds\", IEEE TC 57(6), 2008",
         "automatic selection of the tightest feasible noniterative upper and lower throughput bound"}},
        {"auto.lower", {"CasMS08",
         "Composite over the noniterative bound families; the applicable reference is that of the family selected at run time, most often G. Casale, R. R. Muntz, G. Serazzi, \"Geometric Bounds\", IEEE TC 57(6), 2008",
         "automatic selection of the tightest feasible noniterative upper and lower throughput bound"}},
        {"pbh", {"EagS83",
         "D. L. Eager, K. C. Sevcik, \"Performance Bound Hierarchies for Queueing Networks\", ACM TOCS 1(2), 1983",
         "level-parameterized bracket: the MVA recursion is unrolled for LEVEL steps from the population of interest and the truncated queue lengths are replaced by their extreme admissible values (eqs. 5-13), exact once LEVEL reaches N"}},
        {"pbh.upper", {"EagS83",
         "D. L. Eager, K. C. Sevcik, \"Performance Bound Hierarchies for Queueing Networks\", ACM TOCS 1(2), 1983",
         "level-parameterized bracket: the MVA recursion is unrolled for LEVEL steps from the population of interest and the truncated queue lengths are replaced by their extreme admissible values (eqs. 5-13), exact once LEVEL reaches N"}},
        {"pbh.lower", {"EagS83",
         "D. L. Eager, K. C. Sevcik, \"Performance Bound Hierarchies for Queueing Networks\", ACM TOCS 1(2), 1983",
         "level-parameterized bracket: the MVA recursion is unrolled for LEVEL steps from the population of interest and the truncated queue lengths are replaced by their extreme admissible values (eqs. 5-13), exact once LEVEL reaches N"}},
        {"pbk", {"CasMS08",
         "G. Casale, R. R. Muntz, G. Serazzi, \"Geometric Bounds: A Noniterative Analysis Technique for Closed Queueing Networks\", IEEE TC 57(6), 2008",
         "PB(k), the Eager-Sevcik performance bound hierarchy evaluated at iteration count k over the populations N, N-1, ..., N-k, the iterative form tabulated in Tables 5 and 7"}},
        {"pbk.upper", {"CasMS08",
         "G. Casale, R. R. Muntz, G. Serazzi, \"Geometric Bounds: A Noniterative Analysis Technique for Closed Queueing Networks\", IEEE TC 57(6), 2008",
         "PB(k), the Eager-Sevcik performance bound hierarchy evaluated at iteration count k over the populations N, N-1, ..., N-k, the iterative form tabulated in Tables 5 and 7"}},
        {"pbk.lower", {"CasMS08",
         "G. Casale, R. R. Muntz, G. Serazzi, \"Geometric Bounds: A Noniterative Analysis Technique for Closed Queueing Networks\", IEEE TC 57(6), 2008",
         "PB(k), the Eager-Sevcik performance bound hierarchy evaluated at iteration count k over the populations N, N-1, ..., N-k, the iterative form tabulated in Tables 5 and 7"}},
        {"bjbk", {"CasMS08",
         "G. Casale, R. R. Muntz, G. Serazzi, \"Geometric Bounds: A Noniterative Analysis Technique for Closed Queueing Networks\", IEEE TC 57(6), 2008",
         "BJB(k), the iterative balanced job bound of Tables 5 and 7: BJB(1) is the noniterative bound and each further iteration is one exact MVA step from the balanced seed"}},
        {"bjbk.upper", {"CasMS08",
         "G. Casale, R. R. Muntz, G. Serazzi, \"Geometric Bounds: A Noniterative Analysis Technique for Closed Queueing Networks\", IEEE TC 57(6), 2008",
         "BJB(k), the iterative balanced job bound of Tables 5 and 7: BJB(1) is the noniterative bound and each further iteration is one exact MVA step from the balanced seed"}},
        {"bjbk.lower", {"CasMS08",
         "G. Casale, R. R. Muntz, G. Serazzi, \"Geometric Bounds: A Noniterative Analysis Technique for Closed Queueing Networks\", IEEE TC 57(6), 2008",
         "BJB(k), the iterative balanced job bound of Tables 5 and 7: BJB(1) is the noniterative bound and each further iteration is one exact MVA step from the balanced seed"}},
        {"cbh", {"DowEGS84",
         "L. W. Dowdy, D. L. Eager, K. D. Gordon, L. V. Saxton, \"Throughput Concavity and Response Time Convexity\", Information Processing Letters 19(4), 1984",
         "convolutional bound hierarchy: column M-LEVEL of Buzen's g-array is filled with balanced-job-bound estimates and the remaining stations are convolved exactly, exact once LEVEL reaches M"}},
        {"cbh.upper", {"DowEGS84",
         "L. W. Dowdy, D. L. Eager, K. D. Gordon, L. V. Saxton, \"Throughput Concavity and Response Time Convexity\", Information Processing Letters 19(4), 1984",
         "convolutional bound hierarchy: column M-LEVEL of Buzen's g-array is filled with balanced-job-bound estimates and the remaining stations are convolved exactly, exact once LEVEL reaches M"}},
        {"cbh.lower", {"DowEGS84",
         "L. W. Dowdy, D. L. Eager, K. D. Gordon, L. V. Saxton, \"Throughput Concavity and Response Time Convexity\", Information Processing Letters 19(4), 1984",
         "convolutional bound hierarchy: column M-LEVEL of Buzen's g-array is filled with balanced-job-bound estimates and the remaining stations are convolved exactly, exact once LEVEL reaches M"}},
        {"sib", {"Sri85",
         "V. Srinivasan, \"Successively Improving Bounds on Performance Measures for Single Class Product Form Queueing Networks\", IEEE Trans. Computers C-34(11), 1985",
         "successively improving closed-form hierarchy on the cycle time W(N) and the throughput X(N), built from the power sums S_i of the relative utilizations (Thm 2.1 at level 1, Thms 3.5 and 3.6 above it); never looser than the balanced job bounds"}},
        {"sib.upper", {"Sri85",
         "V. Srinivasan, \"Successively Improving Bounds on Performance Measures for Single Class Product Form Queueing Networks\", IEEE Trans. Computers C-34(11), 1985",
         "successively improving closed-form hierarchy on the cycle time W(N) and the throughput X(N), built from the power sums S_i of the relative utilizations (Thm 2.1 at level 1, Thms 3.5 and 3.6 above it); never looser than the balanced job bounds"}},
        {"sib.lower", {"Sri85",
         "V. Srinivasan, \"Successively Improving Bounds on Performance Measures for Single Class Product Form Queueing Networks\", IEEE Trans. Computers C-34(11), 1985",
         "successively improving closed-form hierarchy on the cycle time W(N) and the throughput X(N), built from the power sums S_i of the relative utilizations (Thm 2.1 at level 1, Thms 3.5 and 3.6 above it); never looser than the balanced job bounds"}},
        {"rgf", {"HarL04",
         "P. G. Harrison, T. T. Lee, \"A New Recursive Algorithm for Computing Generating Functions in Closed Multi-Class Queueing Networks\", IEEE MASCOTS, 2004",
         "residue elimination of one class at a time (Harrison-Coury 2002, Thm 1) down to the grouped single-class convolution of Coury-Harrison 1997 Property 1, with think times carried by the Bertozzi-McKenna 1993 truncation that neither RGF paper has"}},
        {"ger", {"Ger95",
         "A. I. Gerasimov, \"On Normalizing Constants in Multiclass Queueing Networks\", Oper. Res. 43(4), 1995",
         "exact normalizing constant of a closed multiclass product-form network in closed form, by iterated residues of its rational generating function, one class per elimination"}},
        {"dnc", {"DowGor84",
         "L. W. Dowdy, K. D. Gordon, \"Algorithms for Nonintegral Degrees of Multiprogramming in Closed Queuing Networks\", Perform. Eval. 4(1), 1984",
         "normalizing constant and throughput at a real-valued population, by partial-fraction inversion of the network generating function"}},
        {"mvainterval", {"LutHar98",
         "J. Luthi, G. Haring, \"Mean value analysis for queueing network models with intervals as input parameters\", Perform. Eval. 32(3), 1998",
         "exact hull of single-class MVA over interval-valued demands, think time and population, by endpoint evaluation at the corners the monotonicity theorems select"}},
        {"nintmva", {"DowGor84",
         "L. W. Dowdy, K. D. Gordon, \"Algorithms for Nonintegral Degrees of Multiprogramming in Closed Queuing Networks\", Perform. Eval. 4(1), 1984",
         "exact MVA recursion started from the fractional base N - floor(N), giving mean measures at a nonintegral degree of multiprogramming"}},
        {"momlin", {"AkyS91",
         "I. F. Akyildiz, J. C. Strelen, \"Moment Analysis for Load-Dependent Mixed Product Form Queueing Networks\", IEEE Trans. Commun. 39(6), 1991",
         "covariance identity Cov[n(i,r),n(j,s)] = D(j,s) dQ(i,r)/dD(j,s), evaluated with the demand derivatives of the linearized Schweitzer-Bard fixed point instead of the exact recursion"}},
        {"sens", {"SouM88",
         "E. de Souza e Silva, R. R. Muntz, \"Simple Relationships Among Moments of Queue Lengths in Product Form Queueing Networks\", IEEE Trans. Comput. 37(9), 1988",
         "exact queue-length moments obtained by differentiating the MVA recursion"}},
        {"tay", {"TaySur85",
         "Y. C. Tay, R. Suri, \"Error bounds for performance prediction in queuing networks\", ACM TOCS 3(4), 1985; P. J. Schweitzer, G. Serazzi, M. Broglia, \"A survey of bottleneck analysis in closed queueing networks\", Sec. 4.8.2",
         "arrival-instant approximate MVA whose auxiliary queue lengths come from the throughput elasticities, solved as R linear equations per station-class pair"}},
        {"amva.tay", {"TaySur85",
         "Y. C. Tay, R. Suri, \"Error bounds for performance prediction in queuing networks\", ACM TOCS 3(4), 1985; P. J. Schweitzer, G. Serazzi, M. Broglia, \"A survey of bottleneck analysis in closed queueing networks\", Sec. 4.8.2",
         "arrival-instant approximate MVA whose auxiliary queue lengths come from the throughput elasticities, solved as R linear equations per station-class pair"}},
        {"hst", {"Suri83",
         "R. Suri, \"Robustness of Queuing Network Formulas\", JACM 30(3), 1983",
         "first-order sensitivity of throughput to homogeneous-service-time violations (eq. 3.11) and the operationally constrained worst case (P1)"}},
        {"amci", {"RosWan92",
         "K. W. Ross, J. Wang, \"Monte Carlo Summation Applied to Product-Form Loss Networks\", Prob. Eng. Inf. Sci. 6(3), 1992",
         "antithetic-variate sampling of the importance-sampled Monte Carlo normalizing-constant estimator"}},
        {"lhsmci", {"RosWan92",
         "K. W. Ross, J. Wang, \"Monte Carlo Summation Applied to Product-Form Loss Networks\", Prob. Eng. Inf. Sci. 6(3), 1992",
         "Latin-hypercube stratified sampling of the importance-sampled Monte Carlo normalizing-constant estimator"}},
        {"ssd", {"DalS86",
         "Y. Dallery, R. Suri, \"Approximate Disaggregation and Performance Bounds for Queueing Networks with Multiple-Server Stations\", ACM SIGMETRICS, 1986",
         "multiserver server-station disaggregation throughput bounds, with the Lazowska et al. 1984 Table 5.2 think-time correction"}},
        {"ssd.upper", {"DalS86",
         "Y. Dallery, R. Suri, \"Approximate Disaggregation and Performance Bounds for Queueing Networks with Multiple-Server Stations\", ACM SIGMETRICS, 1986",
         "multiserver server-station disaggregation throughput bounds, with the Lazowska et al. 1984 Table 5.2 think-time correction"}},
        {"ssd.lower", {"DalS86",
         "Y. Dallery, R. Suri, \"Approximate Disaggregation and Performance Bounds for Queueing Networks with Multiple-Server Stations\", ACM SIGMETRICS, 1986",
         "multiserver server-station disaggregation throughput bounds, with the Lazowska et al. 1984 Table 5.2 think-time correction"}},
        {"ldbcmp", {"AnsC08",
         "J. Anselmi, P. Cremonesi, \"On the Property of Product-Form Queueing Networks with Load-Dependent Stations\", Perform. Eval. 65(11-12), 2008",
         "lower throughput bound (upper response time) of a closed single-class BCMP network from the asymptotic closed-open equivalence (eq. 15), refined to a monotone fixed point by Algorithm 1; applicable at N >= Qhat"}},
        {"ldbcmp.lower", {"AnsC08",
         "J. Anselmi, P. Cremonesi, \"On the Property of Product-Form Queueing Networks with Load-Dependent Stations\", Perform. Eval. 65(11-12), 2008",
         "lower throughput bound (upper response time) of a closed single-class BCMP network from the asymptotic closed-open equivalence (eq. 15), refined to a monotone fixed point by Algorithm 1; applicable at N >= Qhat"}},
        {"sb", {"Harel1999",
         "A. Harel, S. Namn, J. Sturm, \"Simple bounds for closed queueing networks\", Queueing Systems 31, 1999",
         "simple closed-network bounds"}},
        {"sb.upper", {"Harel1999",
         "A. Harel, S. Namn, J. Sturm, \"Simple bounds for closed queueing networks\", Queueing Systems 31, 1999",
         "simple closed-network bounds"}},
        {"sb.lower", {"Harel1999",
         "A. Harel, S. Namn, J. Sturm, \"Simple bounds for closed queueing networks\", Queueing Systems 31, 1999",
         "simple closed-network bounds"}},
        {"harel", {"Harel1999",
         "A. Harel, S. Namn, J. Sturm, \"Simple bounds for closed queueing networks\", Queueing Systems 31, 1999",
         "sharp throughput bounds extrapolated from the exact normalizing constant at small populations (distinct from the power-sum 'sb' family of the same paper)"}},
        {"harel.upper", {"Harel1999",
         "A. Harel, S. Namn, J. Sturm, \"Simple bounds for closed queueing networks\", Queueing Systems 31, 1999",
         "upper throughput bound UB(n) extrapolated from the exact throughput at population n <= 7"}},
        {"harel.lower", {"Harel1999",
         "A. Harel, S. Namn, J. Sturm, \"Simple bounds for closed queueing networks\", Queueing Systems 31, 1999",
         "lower throughput bound from the first and N-th power sums of the relative utilizations"}},
        {"bgt", {"BerGT01",
         "D. Bertsimas, D. Gamarnik, J. N. Tsitsiklis, \"Performance of Multiclass Markovian Queueing Networks Via Piecewise Linear Lyapunov Functions\", Ann. Appl. Prob. 11(4), 2001",
         "piecewise-linear Lyapunov function whose Down-Meyn linear program certifies global stability and bounds the mean queue lengths under any work-conserving policy"}},
        {"bgt.upper", {"BerGT01",
         "D. Bertsimas, D. Gamarnik, J. N. Tsitsiklis, \"Performance of Multiclass Markovian Queueing Networks Via Piecewise Linear Lyapunov Functions\", Ann. Appl. Prob. 11(4), 2001",
         "piecewise-linear Lyapunov function whose Down-Meyn linear program certifies global stability and bounds the mean queue lengths under any work-conserving policy"}},
        {"bpt", {"BerPT94",
         "D. Bertsimas, I. Paschalidis, J. Tsitsiklis, \"Optimization of Multiclass Queueing Networks: Polyhedral and Nonlinear Characterizations of Achievable Performance\", Ann. Appl. Prob. 4(1), 1994",
         "first-order linear-programming relaxation of the achievable region: quadratic test functions bound the mean sojourn times attainable by any non-idling policy"}},
        {"bpt.lower", {"BerPT94",
         "D. Bertsimas, I. Paschalidis, J. Tsitsiklis, \"Optimization of Multiclass Queueing Networks: Polyhedral and Nonlinear Characterizations of Achievable Performance\", Ann. Appl. Prob. 4(1), 1994",
         "first-order linear-programming relaxation of the achievable region: quadratic test functions bound the mean sojourn times attainable by any non-idling policy"}},
        {"snc", {"FidR15",
         "M. Fidler, A. Rizk, \"A Guide to the Stochastic Network Calculus\", IEEE Commun. Surveys and Tutorials 17(1), 2015",
         "MGF (sigma,rho) arrival and service envelopes, blind-multiplexing leftover and min-plus concatenation, giving delay and backlog tail bounds valid under any work-conserving policy"}},
        {"snc.upper", {"FidR15",
         "M. Fidler, A. Rizk, \"A Guide to the Stochastic Network Calculus\", IEEE Commun. Surveys and Tutorials 17(1), 2015",
         "MGF (sigma,rho) arrival and service envelopes propagated hop by hop over a feed-forward open network; the mean columns integrate the delay tail bound, the quantiles read it directly"}},
        {"scb", {"DowCKT92",
         "L. W. Dowdy, B. M. Carlson, A. T. Krantz, S. K. Tripathi, \"Single-Class Bounds of Multi-Class Queuing Networks\", J. ACM 39(1), 1992",
         "bracket on the multiclass system a single-class model aggregates: the exact single-class solution as a lower bound (Thm 2, Cor 2) and the demand-free (min(N,K)-1)/(N+min(N,K)-1) aggregation gap as an upper bound (Thm 3)"}},
        {"scb.upper", {"DowCKT92",
         "L. W. Dowdy, B. M. Carlson, A. T. Krantz, S. K. Tripathi, \"Single-Class Bounds of Multi-Class Queuing Networks\", J. ACM 39(1), 1992",
         "demand-free upper bound on multiclass throughput, X_1*(N+m-1)/N with m=min(N,K) (Thm 3, Expression 3), capped by the single-server limit U_k <= 1"}},
        {"scb.lower", {"DowCKT92",
         "L. W. Dowdy, B. M. Carlson, A. T. Krantz, S. K. Tripathi, \"Single-Class Bounds of Multi-Class Queuing Networks\", J. ACM 39(1), 1992",
         "exact single-class throughput as a lower bound on the multiclass throughput, and exact single-class utilizations as lower bounds on the multiclass ones (Thm 2, Cor 2)"}},
        {"mwba", {"MajW98",
         "S. Majumdar, C. M. Woodside, \"Robust bounds and throughput guarantees for closed multiclass queueing networks\", Perform. Eval. 32, 1998",
         "robust throughput bounds"}},
        {"mwba.upper", {"MajW98",
         "S. Majumdar, C. M. Woodside, \"Robust bounds and throughput guarantees for closed multiclass queueing networks\", Perform. Eval. 32, 1998",
         "robust throughput bounds"}},
        {"mwba.lower", {"MajW98",
         "S. Majumdar, C. M. Woodside, \"Robust bounds and throughput guarantees for closed multiclass queueing networks\", Perform. Eval. 32, 1998",
         "robust throughput bounds"}},
        {"cub.upper", {"Kerola86",
         "T. Kerola, \"The Composite Bound Method for Computing Throughput Bounds in Multiple Class Environments\", Perform. Eval. 6(1), 1986",
         "composite upper bound on per-class throughput, X_r <= min_k [1 - sum_{s~=r} X_s^- L_ks] / L_kr, from the residual utilization the other classes leave at each device (eqs. 13-16)"}},
        {"mbjb", {"Kerola86",
         "T. Kerola, \"The Composite Bound Method for Computing Throughput Bounds in Multiple Class Environments\", Perform. Eval. 6(1), 1986",
         "multiclass balanced job bounds lower throughput bound (eq. 10), the per-class seed X_s^- the composite upper bound is built on"}},
        {"mbjb.lower", {"Kerola86",
         "T. Kerola, \"The Composite Bound Method for Computing Throughput Bounds in Multiple Class Environments\", Perform. Eval. 6(1), 1986",
         "multiclass balanced job bounds lower throughput bound (eq. 10), the per-class seed X_s^- the composite upper bound is built on"}},
        {"balanced", {"LazZGS84",
         "E. D. Lazowska, J. Zahorjan, G. S. Graham, K. C. Sevcik, \"Quantitative System Performance\", Prentice-Hall, 1984",
         "operational analysis and balanced-system bounds"}},
        {"mna", {"ZhuC24",
         "Z. Li, G. Casale, \"Matrix Network Analyzer: A New Decomposition Algorithm for Phase-type Queueing Networks\", ICPE Companion, 2024",
         "phase-type network decomposition, including the deterministic (round-robin) traffic split"}},
        {"inap", {"CasH13",
         "G. Casale, P. G. Harrison, \"AutoCAT: Automated Product-Form Solution of Stochastic Models\", MAM in Stochastic Models 27, 2013",
         "RCAT product-form solution of the cooperating processes, with the reversed rate of each action estimated by the mean of its state-wise ratios"}},
        {"inapplus", {"CasH13",
         "G. Casale, P. G. Harrison, \"AutoCAT: Automated Product-Form Solution of Stochastic Models\", MAM in Stochastic Models 27, 2013",
         "RCAT product-form solution of the cooperating processes, with the reversed rate of each action estimated by rate conservation"}},
        {"inapinf", {"MarinRB12",
         "A. Marin, S. Rota Bulo, S. Balsamo, \"A numerical algorithm for the decomposition of cooperating structured Markov processes\", IEEE MASCOTS, 2012",
         "matrix-geometric decomposition on the infinite state space"}},
        {"rcat.qbd", {"Neu81",
         "M. F. Neuts, \"Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach\", Johns Hopkins University Press, 1981",
         "quasi-birth-death form of each isolated RCAT component -- level = queue length, phase = (arrival phase, service phase) -- and the rate matrix R of its geometric tail"}},
        {"ldqbd", {"PhungDuc10",
         "T. Phung-Duc, H. Masuyama, S. Kasahara, Y. Takahashi, \"A Simple Algorithm for the Rate Matrices of Level-Dependent QBD Processes\", QTNA, 2010",
         "rate matrices and stationary vector of the level-dependent quasi-birth-death process"}},
        {"ldqbd_mphc", {"AsmM01",
         "S. Asmussen, J. R. Moller, \"Calculation of the steady state waiting time distribution in GI/PH/c and MAP/PH/c queues\", Queueing Systems 37(1), 2001",
         "exact multiserver phase-type chain inside the level-dependent QBD: the level carries the MULTISET of the phases the min(n,c) busy servers sit in, of order nchoosek(min(n,c)+p-1,p-1) rather than p^min(n,c)"}},
        {"bgchain", {"ChaHW75",
         "K. M. Chandy, U. Herzog, L. Woo, \"Parametric Analysis of Queuing Networks\", IBM J. Res. Dev. 19(1), 1975",
         "flow-equivalent aggregation of the untagged closed classes into the second class of the background modulating chain"}},
        {"qbd", {"Hor17",
         "G. Horvath, M. Telek, \"BuTools 2: A Rich Toolbox for Markovian Performance Evaluation\", VALUETOOLS, 2017",
         "quasi-birth-death and matrix-analytic routines"}},
        {"mam.qbd", {"Hor17",
         "G. Horvath, M. Telek, \"BuTools 2: A Rich Toolbox for Markovian Performance Evaluation\", VALUETOOLS, 2017",
         "quasi-birth-death and matrix-analytic routines"}},
        {"mam.setupdelayoff", {"gand.harc.adan10",
         "A. Gandhi, M. Harchol-Balter, I. Adan, \"Server farms with setup costs\", Performance Evaluation 67(11), 2010",
         "open setup/delay-off server as a QBD: the server runs a delay-off timer when it empties and pays a setup only if an arrival finds it already shut down"}},
        {"mam.setupdelayoff.closed", {"Bis01",
         "W. Bischof, \"Analysis of M/G/1-queues with setup times and vacations under six different service disciplines\", Queueing Systems 39(4), 2001",
         "closed setup/delay-off server: the setup-with-close-down discipline in which an arrival during the close-down resumes the server without setup, solved on the FINITE level-dependent chain lambda(n) = (N-n)/Z rather than by a per-instance cold-start race"}},
        {"dt.qmam", {"PerVV08",
         "J. F. Perez, J. Van Velthoven, B. Van Houdt, \"Q-MAM: A Tool for Solving Infinite Queues using Matrix-Analytic Methods\", VALUETOOLS, 2008",
         "exact discrete-time single-station queue length under the late arrival system with delayed access (Q_DT_MAP_MAP_1, Q_DT_PH_PH_1)"}},
        {"mapmc", {"PerVV08",
         "J. F. Perez, J. Van Velthoven, B. Van Houdt, \"Q-MAM: A Tool for Solving Infinite Queues using Matrix-Analytic Methods\", VALUETOOLS, 2008",
         "exact MAP/M/c queue length and phase-type waiting time, level dependent below level c and matrix geometric above it (Q_CT_MAP_M_C)"}},
        {"mapmc.boundary", {"GavJL84",
         "D. P. Gaver, P. A. Jacobs, G. Latouche, \"Finite birth-and-death models in randomly changing environments\", Adv. Appl. Probab. 16, 1984",
         "backward recursion for the boundary levels 0..c-1 of the level-dependent multiserver QBD"}},
        {"mapphc", {"AsmM01",
         "S. Asmussen, J. R. Moller, \"Calculation of the steady state waiting time distribution in GI/PH/c and MAP/PH/c queues\", Queueing Systems 37(1), 2001",
         "exact MAP/PH/c FCFS queue on the MULTISET configuration space of the busy servers, whose order is nchoosek(ms+c-1,c) rather than ms^c, and the phase-type waiting time it carries"}},
        {"mmapgk1", {"He01",
         "Q.-M. He, \"The versatility of MMAP[K] and the MMAP[K]/G[K]/1 queue\", Queueing Systems 38(4), 2001",
         "per-type actual waiting times of the marked queue with class-dependent GENERAL service: Thm 4.1 workload transform, eq (4.4)-(4.5) and Thm 4.2 for the idle vector, Thm 5.1 for the per-type bias; single customer per arrival, his Special case 3.3"}},
        {"dt.dec", {"Dad01",
         "H. Daduna, \"Queueing Networks with Discrete Time Scale\", LNCS 2046, Springer, 2001",
         "slotted time scale, the LA/DA event ordering within a slot and the geometric-server product form the decomposition reproduces on tandem networks"}},
        {"dt.dec.mg1", {"BinMS06",
         "D. A. Bini, B. Meini, S. Steffe, B. Van Houdt, \"Structured Markov chains solver: software tools\", SMCtools, 2006",
         "M/G/1-type solution of each slotted station under batch arrivals, via cyclic reduction"}},
        {"dt.bernoulli1", {"Dad01",
         "H. Daduna, \"Queueing Networks with Discrete Time Scale\", LNCS 2046, Springer, 2001",
         "exact queue length and arrival-instant law of a state dependent Bernoulli server (Thm 2.3, Cor 2.7-2.8, Thm 2.11), including the finite-buffer loss system"}},
        {"dt.cycle", {"Dad01",
         "H. Daduna, \"Queueing Networks with Discrete Time Scale\", LNCS 2046, Springer, 2001",
         "discrete-time product form of the closed cycle of Bernoulli servers and its Buzen-style normalizing constants (Cor 3.4, Prop 3.17-3.19, Cor 3.20)"}},
        {"dt.cycleld", {"Dad01",
         "H. Daduna, \"Queueing Networks with Discrete Time Scale\", LNCS 2046, Springer, 2001",
         "discrete-time product form of the closed cycle with state dependent service probabilities (Thm 3.2) and the arrival theorem behind it (Prop 3.5)"}},
        {"mg1.fb", {"WieH03",
         "A. Wierman, M. Harchol-Balter, \"Classifying scheduling policies with respect to unfairness in an M/GI/1\", ACM SIGMETRICS, 2003",
         "size-based M/G/1 scheduling response times"}},
        {"mg1.lrpt", {"WieH03",
         "A. Wierman, M. Harchol-Balter, \"Classifying scheduling policies with respect to unfairness in an M/GI/1\", ACM SIGMETRICS, 2003",
         "size-based M/G/1 scheduling response times"}},
        {"mg1.psjf", {"WieH03",
         "A. Wierman, M. Harchol-Balter, \"Classifying scheduling policies with respect to unfairness in an M/GI/1\", ACM SIGMETRICS, 2003",
         "size-based M/G/1 scheduling response times"}},
        {"mg1.srpt", {"WieH03",
         "A. Wierman, M. Harchol-Balter, \"Classifying scheduling policies with respect to unfairness in an M/GI/1\", ACM SIGMETRICS, 2003",
         "size-based M/G/1 scheduling response times"}},
        {"fb", {"WieH03",
         "A. Wierman, M. Harchol-Balter, \"Classifying scheduling policies with respect to unfairness in an M/GI/1\", ACM SIGMETRICS, 2003",
         "size-based M/G/1 scheduling response times"}},
        {"lrpt", {"WieH03",
         "A. Wierman, M. Harchol-Balter, \"Classifying scheduling policies with respect to unfairness in an M/GI/1\", ACM SIGMETRICS, 2003",
         "size-based M/G/1 scheduling response times"}},
        {"psjf", {"WieH03",
         "A. Wierman, M. Harchol-Balter, \"Classifying scheduling policies with respect to unfairness in an M/GI/1\", ACM SIGMETRICS, 2003",
         "size-based M/G/1 scheduling response times"}},
        {"srpt", {"WieH03",
         "A. Wierman, M. Harchol-Balter, \"Classifying scheduling policies with respect to unfairness in an M/GI/1\", ACM SIGMETRICS, 2003",
         "size-based M/G/1 scheduling response times"}},
        {"sjn.mva", {"Kant92",
         "K. Kant, \"MVA approximations for SJN scheduling\", Perform. Eval. 15(1), 1992",
         "conditional waiting time equation of the shortest-job-next station, stepped over the population lattice"}},
        {"sjn.amva", {"Kant92",
         "K. Kant, \"MVA approximations for SJN scheduling\", Perform. Eval. 15(1), 1992; P. J. Schweitzer, \"Approximate Analysis of Multiclass Closed Networks of Queues\", Int. Conf. Stoch. Control Optim., 1979",
         "shortest-job-next conditional waiting time closed by a Schweitzer fixed point on the size-resolved queue length"}},
        {"sjf", {"Kant92",
         "K. Kant, \"MVA approximations for SJN scheduling\", Perform. Eval. 15(1), 1992",
         "conditional waiting time equation of the shortest-job-next station"}},
        {"mg1.setf", {"NuyW08",
         "M. Nuyens, A. Wierman, \"The Foreground-Background queue: A survey\", Perform. Eval. 65, 2008",
         "foreground-background M/G/1 response times"}},
        {"setf", {"NuyW08",
         "M. Nuyens, A. Wierman, \"The Foreground-Background queue: A survey\", Perform. Eval. 65, 2008",
         "foreground-background M/G/1 response times"}},
        {"mapm1ps", {"MasuyamaTakine2003",
         "H. Masuyama, T. Takine, \"Sojourn time distribution in a MAP/M/1 processor-sharing queue\", Oper. Res. Lett. 31, 2003",
         "MAP/M/1-PS sojourn time distribution"}},
        {"mapg1k", {"NiuC93",
         "Z. Niu, R. B. Cooper, \"Transform-Free Analysis of M/G/1/K and Related Queues\", Math. Oper. Res. 18(3), 1993",
         "the departure-epoch embedded chain and its Markov renewal reward, which give the MAP/G/1/K loss and level law without a transform"}},
        {"mmapg1k", {"Chy26",
         "A. Chydzinski, \"Per-Flow Throughput of a FIFO Buffer\", Applied System Innovation 9(5), 2026",
         "per-class throughput and loss ratio of a finite FIFO buffer, told apart by the arrival process rather than by rate alone"}},
        {"mapg1k.perflow", {"Chy26",
         "A. Chydzinski, \"Per-Flow Throughput of a FIFO Buffer\", Applied System Innovation 9(5), 2026, Theorem 1",
         "per-flow analysis by keeping one flow exact and replacing the rest by a Poisson stream of the same rate"}},
        {"mmt", {"DobNC24",
         "R.-A. Dobre, Z. Niu, G. Casale, \"Approximating Fork-Join Systems via Mixed Model Transformations\", ICPE Companion, 2024",
         "mixed model transformation of the fork-join network"}},
        {"fjt", {"DobNC24",
         "R.-A. Dobre, Z. Niu, G. Casale, \"Approximating Fork-Join Systems via Mixed Model Transformations\", ICPE Companion, 2024",
         "mixed model transformation of the fork-join network"}},
        {"ht", {"HeiT82",
         "P. Heidelberger, K. Trivedi, \"Queueing network models for parallel processing with asynchronous tasks\", IEEE TC C-31(11), 1982",
         "fork-join transformation with auxiliary asynchronous tasks"}},
        {"heidelberger-trivedi", {"HeiT82",
         "P. Heidelberger, K. Trivedi, \"Queueing network models for parallel processing with asynchronous tasks\", IEEE TC C-31(11), 1982",
         "fork-join transformation with auxiliary asynchronous tasks"}},
        {"quorum", {"Thomasian14",
         "A. Thomasian, \"Analysis of Fork/Join and Related Queueing Systems\", ACM Comput. Surv. 47(2), 2014",
         "k-of-n join fired by the k-th order statistic of the branch completion times"}},
        {"forktail", {"NguALCJ18",
         "M. Nguyen, S. Alesawi, N. Li, H. Che, H. Jiang, \"ForkTail: A Black-Box Fork-Join Tail Latency Prediction Model\", ACM HPDC, 2018",
         "response time tail of the fork-join request from the branch moments"}},
        {"fjgb", {"CasMS08",
         "G. Casale, R. R. Muntz, G. Serazzi, \"Geometric Bounds: A Noniterative Analysis Technique for Closed Queueing Networks\", IEEE Trans. Computers 57(6), 2008",
         "geometric bound on the queue length of a fork-join subnetwork"}},
        {"fjamva", {"Varki01",
         "E. Varki, \"Response Time Analysis of Parallel Computer and Storage Systems\", IEEE Trans. Parallel Distrib. Syst. 12(11), 2001",
         "harmonic-inflated mean value analysis of a closed fork-join network"}},
        {"varki", {"Varki01",
         "E. Varki, \"Response Time Analysis of Parallel Computer and Storage Systems\", IEEE Trans. Parallel Distrib. Syst. 12(11), 2001",
         "bound on the residence time of a closed parallel subsystem"}},
        {"harrison-zertal", {"HarZ07",
         "P. G. Harrison, S. Zertal, \"Queueing Models of RAID Systems with Maxima of Waiting Times\", Perform. Eval. 64(7-8), 2007",
         "transform and moment recurrences for the maximum of heterogeneous branch times"}},
        {"gravey", {"Gravey85",
         "A. Gravey, \"A Simple Construction of an Upper Bound for the Mean of the Maximum of N Identically Distributed Random Variables\", J. Applied Probability 22(4), 1985",
         "characteristic maximum as an upper bound on the expected maximum"}},
        {"blom", {"Blom58",
         "G. Blom, \"Statistical Estimates and Transformed Beta Variables\", Wiley, 1958",
         "bias-corrected plotting position of the characteristic maximum"}},
        {"marie-cox", {"Marie78",
         "R. Marie, \"Methodes iteratives de resolution de modeles mathematiques de systemes informatiques\", RAIRO Informatique 12(2), 1978",
         "balanced-stage two-phase Coxian fit of a mean and a squared coefficient of variation"}},
        {"dispersion", {"TsimK13",
         "I. Tsimashenka, W. J. Knottenbelt, \"Reduction of Subtask Dispersion in Fork-Join Systems\", EPEW, 2013",
         "mean subtask dispersion and the deterministic delays that minimise it"}},
        {"nosplit", {"NelsonTT88",
         "R. Nelson, D. Towsley, A. N. Tantawi, \"Performance Analysis of Parallel Processing Systems\", IEEE Trans. Software Eng. 14(4), 1988",
         "splitting and no-splitting policies for parallel task assignment"}},
        {"green-ism", {"Green80",
         "L. Green, \"A Queueing System in Which Customers Require a Random Number of Servers\", Operations Research 28(6), 1980",
         "cycle decomposition of the independent server model"}},
        {"tsm", {"OmahenS72",
         "A. Thomasian, \"A Performance Study of Dynamic Load Balancing in Distributed Systems\", 1978; K. Omahen, L. Schrage, \"A Queueing Analysis of a Multiprocessor System with Shared Memory\", 1972",
         "attainable capacity of the team service model"}},
        {"serialization", {"Thomasian83",
         "A. Thomasian, \"Queueing Network Models to Estimate Serialization Delays in Computer Systems\", Performance, 1983",
         "blocking probability and pseudoserver delay of a serialization phase"}},
        {"dag-makespan", {"ThomasianB86",
         "A. Thomasian, P. F. Bay, \"Analytic Queueing Network Models for Parallel Processing of Task Systems\", IEEE Trans. Computers C-35(12), 1986",
         "makespan of a task system whose completion rates depend on the concurrency"}},
        {"thomasian-fj", {"Thomasian14",
         "A. Thomasian, \"Analysis of Fork/Join and Related Queueing Systems\", ACM Comput. Surv. 47(2), Article 17, 2014",
         "survey collecting the fork-join response time, order statistic and parallel processing formulas"}},
        {"qiu", {"QiuPH15",
         "Z. Qiu, J. F. Perez, P. G. Harrison, \"Beyond the Mean in Fork-Join Queues: Efficient Approximation for Response-Time Tails\", IFIP PERFORMANCE, 2015",
         "response time tail of a homogeneous fork-join network"}},
        {"mdd", {"MinC99",
         "A. S. Miner, G. Ciardo, \"Efficient Reachability Set Generation and Storage Using Decision Diagrams\", ICATPN, LNCS 1639, 1999",
         "multi-valued decision diagram storage of the reachable state space and its O(K) indexing"}},
        {"mdd.reachset", {"MinC99",
         "A. S. Miner, G. Ciardo, \"Efficient Reachability Set Generation and Storage Using Decision Diagrams\", ICATPN, LNCS 1639, 1999",
         "multi-valued decision diagram storage of the reachable state space and its O(K) indexing"}},
        {"mcd", {"MinCD00",
         "A. S. Miner, G. Ciardo, S. Donatelli, \"Using the exact state space of a Markov model to compute approximate stationary measures\", ACM SIGMETRICS, 2000",
         "decision-diagram-guided aggregation into K coupled level-CTMCs, exact on product-form models"}},
        {"mdd.mcd", {"MinCD00",
         "A. S. Miner, G. Ciardo, S. Donatelli, \"Using the exact state space of a Markov model to compute approximate stationary measures\", ACM SIGMETRICS, 2000",
         "decision-diagram-guided aggregation into K coupled level-CTMCs, exact on product-form models"}},
        {"ctmc.mdd", {"MinCD00",
         "A. S. Miner, G. Ciardo, S. Donatelli, \"Using the exact state space of a Markov model to compute approximate stationary measures\", ACM SIGMETRICS, 2000",
         "decision-diagram-guided aggregation into K coupled level-CTMCs, exact on product-form models"}},
        {"rec", {"BalMS20",
         "S. Balsamo, A. Marin, I. Stojic, \"Computation of the normalising constant for product-form models of distributed systems with synchronisation\", Future Generation Computer Systems 111, 2020",
         "normalising constant of a product form by one memoised walk of the decision diagram holding the reachable set"}},
        {"mdd.rec", {"BalMS20",
         "S. Balsamo, A. Marin, I. Stojic, \"Computation of the normalising constant for product-form models of distributed systems with synchronisation\", Future Generation Computer Systems 111, 2020",
         "normalising constant of a product form by one memoised walk of the decision diagram holding the reachable set"}},
        {"spn.rec_enabled", {"BalMS20",
         "S. Balsamo, A. Marin, I. Stojic, \"Computation of the normalising constant for product-form models of distributed systems with synchronisation\", Future Generation Computer Systems 111, 2020",
         "enabling-degree distribution of a transition mode from the masked MDD-rec recursion"}},
        {"spn.metrics", {"BalMS20",
         "S. Balsamo, A. Marin, I. Stojic, \"Computation of the normalising constant for product-form models of distributed systems with synchronisation\", Future Generation Computer Systems 111, 2020",
         "stationary token, utilization and throughput measures of a product-form Petri net from the MDD-rec masses"}},
        {"spn.pf", {"ColHT96",
         "J. L. Coleman, W. Henderson, P. G. Taylor, \"Product form equilibrium distributions and a convolution algorithm for stochastic Petri nets\", Performance Evaluation 26(3), 1996",
         "the condition under which a stochastic Petri net has a product form, and the complex-balance equations its per-place factors solve"}},
        {"pf", {"ColHT96",
         "J. L. Coleman, W. Henderson, P. G. Taylor, \"Product form equilibrium distributions and a convolution algorithm for stochastic Petri nets\", Performance Evaluation 26(3), 1996",
         "the condition under which a stochastic Petri net has a product form, and the complex-balance equations its per-place factors solve"}},
        {"spn.pf.deficiency", {"Fei72",
         "M. Feinberg, \"Complex balancing in general kinetic systems\", Archive for Rational Mechanics and Analysis 49(3), 1972",
         "existence of a positive complex-balanced point at deficiency zero with weak reversibility, which is what makes the log-linear solve for y consistent"}},
        {"spn.pf.massaction", {"AndCK10",
         "D. F. Anderson, G. Craciun, T. G. Kurtz, \"Product-form stationary distributions for deficiency zero chemical reaction networks\", Bulletin of Mathematical Biology 72(8), 2010",
         "the Poisson product form g_l(k) = y_l^k/k! of a net whose modes fire at mass-action rates"}},
        {"lossn.rec", {"Kelly91",
         "F. P. Kelly, \"Loss networks\", Annals of Applied Probability 1(3), 1991",
         "the truncated-Poisson product form of a loss network and the G(C - A e_r)/G(C) acceptance ratio MDD-rec evaluates"}},
        {"spn.conv", {"ColHT96",
         "J. L. Coleman, W. Henderson, P. G. Taylor, \"Product form equilibrium distributions and a convolution algorithm for stochastic Petri nets\", Performance Evaluation 26(3), 1996",
         "normalising constant by convolution over the S-invariant load vector of an S-invariant reachable net"}},
        {"spn.sinvariants", {"MarS82",
         "J. Martinez, M. Silva, \"A simple and fast algorithm to obtain all invariants of a generalised Petri net\", Application and Theory of Petri Nets, 1982",
         "the Farkas algorithm on the incidence matrix for the minimal-support S-invariants"}},
        {"ctmc", {"BolGMT06",
         "G. Bolch, S. Greiner, H. de Meer, K. S. Trivedi, \"Queueing Networks and Markov Chains\", Wiley, 2006",
         "CTMC formulation, uniformization and its stationary solution"}},
        {"uniformization", {"BolGMT06",
         "G. Bolch, S. Greiner, H. de Meer, K. S. Trivedi, \"Queueing Networks and Markov Chains\", Wiley, 2006",
         "CTMC formulation, uniformization and its stationary solution"}},
        {"foxglynn", {"FoxG88",
         "B. L. Fox, P. W. Glynn, \"Computing Poisson Probabilities\", Communications of the ACM 31(4), 1988",
         "the truncation window and the Poisson weights of the uniformized mixture"}},
        {"foxglynn.jansen", {"Jan11",
         "D. N. Jansen, \"Understanding Fox and Glynn's Computing Poisson probabilities\", CTIT Technical Report 11-16, University of Twente, 2011",
         "the correction factor that repairs the Fox-Glynn right tail estimate at moderate lambda"}},
        {"daniels2", {"Jen91",
         "J. L. Jensen, \"Saddlepoint Expansions for Sums of Markov Dependent Variables on a Continuous State Space\", Probab. Th. Rel. Fields 89, 1991",
         "the Perron-projection amplitude gamma_0 and the second-order bracket of Eq. (4.4), i.e. the daniels2 correction: the eigenvector projection the large-deviation limit discards"}},
        {"jensen", {"Jen91",
         "J. L. Jensen, \"Saddlepoint Expansions for Sums of Markov Dependent Variables on a Continuous State Space\", Probab. Th. Rel. Fields 89, 1991",
         "the Perron-projection amplitude gamma_0 and the second-order bracket of Eq. (4.4), i.e. the daniels2 correction: the eigenvector projection the large-deviation limit discards"}},
        {"saddlepoint", {"Dan54",
         "H. E. Daniels, \"Saddlepoint Approximations in Statistics\", Ann. Math. Statist. 25(4), 1954",
         "steepest-descent inversion of the counting generating function exp(t*(D0+z*D1)) at the saddle of its cumulant generating function, with the O(1/t) correction term"}},
        {"ctmc.saddlepoint", {"Dan54",
         "H. E. Daniels, \"Saddlepoint Approximations in Statistics\", Ann. Math. Statist. 25(4), 1954",
         "steepest-descent inversion of the counting generating function exp(t*(D0+z*D1)) at the saddle of its cumulant generating function, with the O(1/t) correction term"}},
        {"daniels", {"Dan54",
         "H. E. Daniels, \"Saddlepoint Approximations in Statistics\", Ann. Math. Statist. 25(4), 1954",
         "steepest-descent inversion of the counting generating function exp(t*(D0+z*D1)) at the saddle of its cumulant generating function, with the O(1/t) correction term"}},
        {"au", {"MooS94",
         "A. P. A. van Moorsel, W. H. Sanders, \"Adaptive uniformization\", Communications in Statistics - Stochastic Models 10(3), 1994",
         "the per-step uniformization rate taken from the occupied support, and the birth process that subordinates it"}},
        {"fau", {"MatWDH10",
         "A. Mateescu, V. Wolf, F. Didier, T. A. Henzinger, \"Fast adaptive uniformisation of the chemical master equation\", IET Systems Biology 4(6), 2010",
         "the dropping of states below an occupancy threshold, so the support tracks the probability mass rather than the reachable set"}},
        {"gmres", {"SaaS86",
         "Y. Saad, M. H. Schultz, \"GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems\", SIAM J. Sci. Stat. Comput. 7(3), 1986",
         "restarted Krylov solution of the stationary balance equations, ILUT-preconditioned"}},
        {"ilut", {"Saa94",
         "Y. Saad, \"ILUT: A dual threshold incomplete LU factorization\", Numerical Linear Algebra with Applications 1(4), 1994",
         "the threshold incomplete LU preconditioner of the Krylov path"}},
        {"bicgstab", {"Vor92",
         "H. A. van der Vorst, \"Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems\", SIAM J. Sci. Stat. Comput. 13(2), 1992",
         "short-recurrence Krylov solution of the stationary balance equations, tried when restarted GMRES stagnates"}},
        {"courtois", {"Cou77",
         "P. J. Courtois, \"Decomposability: Queueing and Computer System Applications\", Academic Press, 1977",
         "nearly-completely-decomposable aggregation of the chain"}},
        {"kms", {"KouMS84",
         "J. R. Koury, D. F. McAllister, W. J. Stewart, \"Iterative methods for computing stationary distributions of nearly completely decomposable Markov chains\", SIAM J. Alg. Disc. Meth. 5, 1984",
         "iterative aggregation-disaggregation of the chain"}},
        {"takahashi", {"Tak75",
         "Y. Takahashi, \"A lumping method for numerical calculations of stationary distributions of Markov chains\", 1975",
         "lumping-based iterative solution of the chain"}},
        {"qrf", {"CasNPS16",
         "G. Casale, V. De Nitto Persone, E. Smirni, \"QRF: An Optimization-Based Framework for Evaluating Complex Stochastic Networks\", ACM TOMACS 26, 2016",
         "quadratic reduction bounds on the chain"}},
        {"qrf.mmi", {"CasNPS16",
         "G. Casale, V. De Nitto Persone, E. Smirni, \"QRF: An Optimization-Based Framework for Evaluating Complex Stochastic Networks\", ACM TOMACS 26, 2016",
         "quadratic reduction bounds on the chain"}},
        {"qrf.mem", {"CasNPS16",
         "G. Casale, V. De Nitto Persone, E. Smirni, \"QRF: An Optimization-Based Framework for Evaluating Complex Stochastic Networks\", ACM TOMACS 26, 2016",
         "quadratic reduction bounds on the chain"}},
        {"qrf.bethe", {"CasNPS16",
         "G. Casale, V. De Nitto Persone, E. Smirni, \"QRF: An Optimization-Based Framework for Evaluating Complex Stochastic Networks\", ACM TOMACS 26, 2016",
         "quadratic reduction of the chain and the no-blocking polytope minimised over"}},
        {"qrf.trw", {"WaiJW05",
         "M. J. Wainwright, T. S. Jaakkola, A. S. Willsky, \"A New Class of Upper Bounds on the Log Partition Function\", IEEE Trans. Inform. Theory 51(7), 2005",
         "tree-reweighted free entropy of the qrf.bethe objective, and the spanning-tree polytope condition rho_ij <= 2/M that makes it convex"}},
        {"qrf.bas.bethe", {"CasNPS16",
         "G. Casale, V. De Nitto Persone, E. Smirni, \"QRF: An Optimization-Based Framework for Evaluating Complex Stochastic Networks\", ACM TOMACS 26, 2016",
         "quadratic reduction of the chain and the BAS blocking polytope minimised over"}},
        {"qrf.bas", {"CasNPS16",
         "G. Casale, V. De Nitto Persone, E. Smirni, \"QRF: An Optimization-Based Framework for Evaluating Complex Stochastic Networks\", ACM TOMACS 26, 2016",
         "quadratic reduction bounds on the chain"}},
        {"qrf.rsrd", {"CasNPS16",
         "G. Casale, V. De Nitto Persone, E. Smirni, \"QRF: An Optimization-Based Framework for Evaluating Complex Stochastic Networks\", ACM TOMACS 26, 2016",
         "quadratic reduction bounds on the chain"}},
        {"qr", {"CasNPS16",
         "G. Casale, V. De Nitto Persone, E. Smirni, \"QRF: An Optimization-Based Framework for Evaluating Complex Stochastic Networks\", ACM TOMACS 26, 2016",
         "quadratic reduction bounds on the chain; qr is the friendly alias that resolves to qrf.mmi"}},
        {"qrf.bas.mmi", {"CasNPS16",
         "G. Casale, V. De Nitto Persone, E. Smirni, \"QRF: An Optimization-Based Framework for Evaluating Complex Stochastic Networks\", ACM TOMACS 26, 2016",
         "quadratic reduction of the chain with the mutual-information objective over the BAS blocking polytope"}},
        {"qrf.bas.mem", {"CasNPS16",
         "G. Casale, V. De Nitto Persone, E. Smirni, \"QRF: An Optimization-Based Framework for Evaluating Complex Stochastic Networks\", ACM TOMACS 26, 2016",
         "quadratic reduction of the chain with the maximum-entropy objective over the BAS blocking polytope"}},
        {"mapamva", {"CasSmi09",
         "G. Casale, E. Smirni, \"MAP-AMVA: Approximate Mean Value Analysis of Bursty Systems\", IEEE/IFIP DSN 2009",
         "linear program over the exact mean-value balances of a closed MAP queueing network, in the per-phase queue-length and utilization variables"}},
        {"mapqn", {"CasSmi09",
         "G. Casale, E. Smirni, \"MAP-AMVA: Approximate Mean Value Analysis of Bursty Systems\", IEEE/IFIP DSN 2009",
         "horizontal-cut mean value recursion: the exact per-phase balances of the MAP queue closed by the arrival theorem (SolverMVA amva.mapqn)"}},
        {"amva.mapqn", {"CasSmi09",
         "G. Casale, E. Smirni, \"MAP-AMVA: Approximate Mean Value Analysis of Bursty Systems\", IEEE/IFIP DSN 2009",
         "horizontal-cut mean value recursion: the exact per-phase balances of the MAP queue closed by the arrival theorem (SolverMVA amva.mapqn)"}},
        {"mapamva.upper", {"CasSmi09",
         "G. Casale, E. Smirni, \"MAP-AMVA: Approximate Mean Value Analysis of Bursty Systems\", IEEE/IFIP DSN 2009",
         "linear program over the exact mean-value balances of a closed MAP queueing network, in the per-phase queue-length and utilization variables"}},
        {"mapamva.lower", {"CasSmi09",
         "G. Casale, E. Smirni, \"MAP-AMVA: Approximate Mean Value Analysis of Bursty Systems\", IEEE/IFIP DSN 2009",
         "linear program over the exact mean-value balances of a closed MAP queueing network, in the per-phase queue-length and utilization variables"}},
        {"lr", {"CasNPS16",
         "G. Casale, V. De Nitto Persone, E. Smirni, \"QRF: An Optimization-Based Framework for Evaluating Complex Stochastic Networks\", ACM TOMACS 26, 2016",
         "linear reduction bounds on the chain"}},
        {"lr.upper", {"CasNPS16",
         "G. Casale, V. De Nitto Persone, E. Smirni, \"QRF: An Optimization-Based Framework for Evaluating Complex Stochastic Networks\", ACM TOMACS 26, 2016",
         "linear reduction bounds on the chain"}},
        {"lr.lower", {"CasNPS16",
         "G. Casale, V. De Nitto Persone, E. Smirni, \"QRF: An Optimization-Based Framework for Evaluating Complex Stochastic Networks\", ACM TOMACS 26, 2016",
         "linear reduction bounds on the chain"}},
        {"qrf.mmi.ld", {"CasNPS16",
         "G. Casale, V. De Nitto Persone, E. Smirni, \"QRF: An Optimization-Based Framework for Evaluating Complex Stochastic Networks\", ACM TOMACS 26, 2016",
         "quadratic reduction bounds on the load-dependent chain"}},
        {"qrf.mmi.linear", {"CasNPS16",
         "G. Casale, V. De Nitto Persone, E. Smirni, \"QRF: An Optimization-Based Framework for Evaluating Complex Stochastic Networks\", ACM TOMACS 26, 2016",
         "quadratic reduction bounds on the chain"}},
        {"spnlp", {"Liu98",
         "Z. Liu, \"Performance Analysis of Stochastic Timed Petri Nets Using Linear Programming Approach\", IEEE Trans. Software Engineering 24(11), 1998",
         "uniformized moment relaxation of the marking process, and the linear program bounding the mean tokens and the throughputs over it"}},
        {"spnlp.upper", {"Liu98",
         "Z. Liu, \"Performance Analysis of Stochastic Timed Petri Nets Using Linear Programming Approach\", IEEE Trans. Software Engineering 24(11), 1998",
         "uniformized moment relaxation of the marking process, and the linear program bounding the mean tokens and the throughputs over it"}},
        {"spnlp.lower", {"Liu98",
         "Z. Liu, \"Performance Analysis of Stochastic Timed Petri Nets Using Linear Programming Approach\", IEEE Trans. Software Engineering 24(11), 1998",
         "uniformized moment relaxation of the marking process, and the linear program bounding the mean tokens and the throughputs over it"}},
        {"spnlp.op.upper", {"Liu98",
         "Z. Liu, \"Performance Analysis of Stochastic Timed Petri Nets Using Linear Programming Approach\", IEEE Trans. Software Engineering 24(11), 1998",
         "the same relaxation without its Markovian families, so the bound rests on flow balance, the place invariants and the state equation alone"}},
        {"spnlp.op.lower", {"Liu98",
         "Z. Liu, \"Performance Analysis of Stochastic Timed Petri Nets Using Linear Programming Approach\", IEEE Trans. Software Engineering 24(11), 1998",
         "the same relaxation without its Markovian families, so the bound rests on flow balance, the place invariants and the state equation alone"}},
        {"ssa", {"Gill77",
         "D. T. Gillespie, \"Exact stochastic simulation of coupled chemical reactions\", J. Phys. Chem. 81(25), 1977",
         "stochastic simulation of the Markov process sample path"}},
        {"firingdep", {"AjmCB84",
         "M. Ajmone Marsan, G. Conte, G. Balbo, \"A class of generalized stochastic Petri nets for the performance evaluation of multiprocessor systems\", ACM TOCS 2(2), 1984",
         "marking-dependent transition firing rates (setFiringRateDependence)"}},
        {"nc.oi", {"BonP03",
         "T. Bonald, A. Proutiere, \"Insensitive bandwidth sharing in data networks\", Queueing Systems 44(1), 2003",
         "balanced-fairness balance function of the order-independent station"}},
        {"mva.oi", {"BonP03",
         "T. Bonald, A. Proutiere, \"Insensitive bandwidth sharing in data networks\", Queueing Systems 44(1), 2003",
         "balanced-fairness balance function of the order-independent station"}},
        {"pas", {"ComD21",
         "C. Comte, J.-P. Dorsman, \"Pass-and-swap queues\", Queueing Systems, 2021 (arXiv:2009.12299)",
         "per-communicating-class product form of the pass-and-swap network"}},
        {"nrm", {"And07",
         "D. F. Anderson, \"A modified next reaction method for simulating chemical systems with time dependent propensities and delays\", J. Chem. Phys. 127, 2007",
         "next-reaction method for the simulation"}},
        {"fld", {"PerC17",
         "J. F. Perez, G. Casale, \"LINE: Evaluating Software Applications in Unreliable Environments\", IEEE Trans. Reliability 66(3), 2017",
         "mean-field fluid ODEs for the queueing network"}},
        {"fluid", {"PerC17",
         "J. F. Perez, G. Casale, \"LINE: Evaluating Software Applications in Unreliable Environments\", IEEE Trans. Reliability 66(3), 2017",
         "mean-field fluid ODEs for the queueing network"}},
        {"statedep", {"PerC17",
         "J. F. Perez, G. Casale, \"LINE: Evaluating Software Applications in Unreliable Environments\", IEEE Trans. Reliability 66(3), 2017",
         "mean-field fluid ODEs for the queueing network"}},
        {"closing", {"PerC17",
         "J. F. Perez, G. Casale, \"LINE: Evaluating Software Applications in Unreliable Environments\", IEEE Trans. Reliability 66(3), 2017",
         "mean-field fluid ODEs for the queueing network"}},
        {"kp", {"ko.pend17",
         "Y. M. Ko, J. Pender, \"Diffusion limits for the (MAP_t/Ph_t/inf)^N queueing network\", Oper. Res. Lett. 45(3), 2017",
         "fluid and diffusion limits of the time-varying infinite-server network, i.e. the mean and covariance ODEs"}},
        {"matrix", {"RuuskanenBAC21",
         "J. Ruuskanen, T. Berner, K.-E. Arzen, A. Cervin, \"Improving the mean-field fluid model of processor sharing queueing networks\", Perform. Eval. 151, 2021",
         "matrix form of the processor-sharing fluid model"}},
        {"cache.exact", {"CasG21",
         "G. Casale, N. Gast, \"Performance Analysis Methods for List-Based Caches With Non-Uniform Access\", IEEE/ACM Trans. Networking 29(2), 2021",
         "product-form normalizing constant of the tree cache with non-uniform access, and its recursion under per-list storage cost caps"}},
        {"cache.sampling", {"CasG21",
         "G. Casale, N. Gast, \"Performance Analysis Methods for List-Based Caches With Non-Uniform Access\", IEEE/ACM Trans. Networking 29(2), 2021",
         "Monte Carlo summation of the (cost-capped) normalizing constant over sampled cache permutations"}},
        {"cache.itemsize", {"CasG21",
         "G. Casale, N. Gast, \"Performance Analysis Methods for List-Based Caches With Non-Uniform Access\", IEEE/ACM Trans. Networking 29(2), 2021",
         "per-item storage costs with per-list cost caps, and the mean per-list cost at steady state"}},
        {"rayint", {"CasG21",
         "G. Casale, N. Gast, \"Performance Analysis Methods for List-Based Caches With Non-Uniform Access\", IEEE/ACM Trans. Networking 29(2), 2021",
         "product-form normalizing constant of the list-based cache that the ray expansion approximates"}},
        {"spm", {"CasG21",
         "G. Casale, N. Gast, \"Performance Analysis Methods for List-Based Caches With Non-Uniform Access\", IEEE/ACM Trans. Networking 29(2), 2021",
         "product-form normalizing constant of the list-based cache by the saddle-point method (cache_spm); 'rayint' is an alias of the same route"}},
        {"cache.rayint", {"Cas17",
         "G. Casale, \"Accelerating Performance Inference over Closed Systems by Asymptotic Methods\", ACM SIGMETRICS, 2017",
         "asymptotic (saddle-point) expansion of the normalizing constant integral, here in eikonal/ray form with the geometrical-spreading amplitude 1/sqrt(det dx/dxi)"}},
        {"cache.spm", {"CasG21",
         "G. Casale, N. Gast, \"Performance Analysis Methods for List-Based Caches With Non-Uniform Access\", IEEE/ACM Trans. Networking 29(2), 2021",
         "saddle-point (SPM) expansion of the list-based cache normalizing constant over the exchangeable-family measure, served for any replacement policy"}},
        {"cache.spm.size", {"CasG21",
         "G. Casale, N. Gast, \"Performance Analysis Methods for List-Based Caches With Non-Uniform Access\", IEEE/ACM Trans. Networking 29(2), 2021",
         "cost-capped normalizing constant recursion whose size-tilted saddle point the ray expansion approximates, with the shadow price of each per-list cost cap"}},
        {"rmf", {"GastH16",
         "N. Gast, B. Van Houdt, \"Transient and steady-state regime of a family of list-based cache replacement algorithms\", Queueing Syst. 83, 2016",
         "refined mean-field approximation"}},
        {"fluid.rmf", {"GastH16",
         "N. Gast, B. Van Houdt, \"Transient and steady-state regime of a family of list-based cache replacement algorithms\", Queueing Syst. 83, 2016",
         "refined mean-field approximation"}},
        {"sfifo.rmf", {"GastH16",
         "N. Gast, B. Van Houdt, \"Transient and steady-state regime of a family of list-based cache replacement algorithms\", Queueing Syst. 83, 2016",
         "position-resolved mean field for the strict FIFO(m) replacement variant"}},
        {"fifo.rmf.tran", {"GastH16",
         "N. Gast, B. Van Houdt, \"Transient and steady-state regime of a family of list-based cache replacement algorithms\", Queueing Syst. 83, 2016",
         "position-resolved mean-field transient for FIFO(m) (steady state equals RANDOM(m))"}},
        {"asy", {"GastH16",
         "N. Gast, B. Van Houdt, \"Transient and steady-state regime of a family of list-based cache replacement algorithms\", Queueing Syst. 83, 2016",
         "leading-order (unrefined) mean-field limit in which each list deterministically holds its m most popular items, solved as a rank-threshold fixed point on the miss probabilities"}},
        {"diffusion", {"BolGMT06",
         "G. Bolch, S. Greiner, H. de Meer, K. S. Trivedi, \"Queueing Networks and Markov Chains\", Wiley, 2006",
         "diffusion approximation of the queue-length process"}},
        {"minnormal.covariance", {"StefanekHB10",
         "A. Stefanek, R. A. Hayden, J. T. Bradley, \"A new tool for the performance analysis of massively parallel computer systems\", QAPL, EPTCS 28, 2010",
         "covariance ODE d/dt Cov = Cov*Df' + Df*Cov + sum_k f^k l^k l^k' about the fluid trajectory, with non-smooth min() rates"}},
        {"minnormal.lyapunov", {"StefanekHB10",
         "A. Stefanek, R. A. Hayden, J. T. Bradley, \"A new tool for the performance analysis of massively parallel computer systems\", QAPL, EPTCS 28, 2010",
         "covariance ODE d/dt Cov = Cov*Df' + Df*Cov + sum_k f^k l^k l^k' about the fluid trajectory, with non-smooth min() rates"}},
        {"minnormal.origin", {"vanKampen07",
         "N. G. van Kampen, \"Stochastic Processes in Physics and Chemistry\", 3rd ed., North-Holland, 2007",
         "linear noise approximation: Lyapunov equation for the stationary covariance about the fluid fixed point"}},
        {"moments", {"Kur70",
         "T. G. Kurtz, \"Solutions of ordinary differential equations as limits of pure jump Markov processes\", J. Appl. Probab. 7(1), 1970",
         "density-dependent population limit justifying the fluid drift and its Gaussian fluctuation"}},
        {"minnormal", {"GuentherSB13",
         "M. C. Guenther, A. Stefanek, J. T. Bradley, \"Moment Closures for Performance Models with Highly Non-linear Rates\", EPEW/UKPEW 2012, LNCS 7587:32-47",
         "min-normal moment closure of E[min(X,Y)] for jointly normal populations, eq (4)"}},
        {"fluid.minnormal", {"GuentherSB13",
         "M. C. Guenther, A. Stefanek, J. T. Bradley, \"Moment Closures for Performance Models with Highly Non-linear Rates\", EPEW/UKPEW 2012, LNCS 7587:32-47",
         "min-normal moment closure of E[min(X,Y)] for jointly normal populations, eq (4)"}},
        {"dae", {"GuentherSB13",
         "M. C. Guenther, A. Stefanek, J. T. Bradley, \"Moment Closures for Performance Models with Highly Non-linear Rates\", EPEW/UKPEW 2012, LNCS 7587:32-47",
         "min-normal moment closure of E[min(X,Y)] for jointly normal populations, eq (4), here stated and solved as one differential-algebraic system"}},
        {"fluid.dae", {"GuentherSB13",
         "M. C. Guenther, A. Stefanek, J. T. Bradley, \"Moment Closures for Performance Models with Highly Non-linear Rates\", EPEW/UKPEW 2012, LNCS 7587:32-47",
         "min-normal moment closure of E[min(X,Y)] for jointly normal populations, eq (4), here stated and solved as one differential-algebraic system"}},
        {"dae.integrator", {"HairerW96",
         "E. Hairer, G. Wanner, \"Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems\", 2nd ed., Springer Series in Computational Mathematics 14, 1996",
         "RODAS, the Rosenbrock method of order (3)4 for M y' = f with a singular mass matrix, i.e. the index-1 DAE the transient is integrated as (ch. IV.7, VI.3)"}},
        {"dae.activeset", {"NocedalW06",
         "J. Nocedal, S. J. Wright, \"Numerical Optimization\", 2nd ed., Springer, 2006",
         "active-set treatment of every capacity limit -- a finite capacity region and a station buffer alike: an inequality has no residual for a Newton solver, so the loop iterates over WHICH caps bind and each pass is an equality-constrained solve (ch. 16)"}},
        {"dae.events", {"ShampineT00",
         "L. F. Shampine, S. Thompson, \"Event location for ordinary differential equations\", Computers & Mathematics with Applications 39(5-6):43-54, 2000",
         "the transient under a cap is a hybrid system: each crossing is located on the step's own interpolant, the segment stops there and the next one restarts with the binding set updated"}},
        {"dae.petri", {"SilvaR04",
         "M. Silva, L. Recalde, \"On fluidification of Petri nets: from discrete to hybrid and continuous models\", Annual Reviews in Control 28(2):253-266, 2004",
         "the continuous relaxation of a Petri net marking and its firing-speed law min over the input arcs of m_a/w_a, the drift SolverFLD closes"}},
        {"dae.petri.limit", {"Kurtz70",
         "T. G. Kurtz, \"Solutions of ordinary differential equations as limits of pure jump Markov processes\", J. Appl. Probab. 7(1):49-58, 1970",
         "the density-dependent population limit that makes a GSPN marking a fluid trajectory, and the linear noise approximation about it its covariance"}},
        {"dae.petri.minmulti", {"Clark61",
         "C. E. Clark, \"The greatest of a finite set of random variables\", Operations Research 9(2):145-162, 1961",
         "moment recursion closing E[min(X_1,...,X_A)] for a mode with several input arcs, each pairwise step being the two-population min-normal closure"}},
        {"dae.petri.vanishing", {"MarsanCB84",
         "M. Ajmone Marsan, G. Conte, G. Balbo, \"A class of generalized stochastic Petri nets for the performance evaluation of multiprocessor systems\", ACM Trans. Comput. Syst. 2(2):93-122, 1984",
         "the GSPN vanishing-marking semantics the algebraic firing flows reproduce: an immediate transition fires in zero time, and a conflict is resolved in proportion to the firing weights within the highest firing priority"}},
        {"dae.petri.invariants", {"BalsamoMS20",
         "S. Balsamo, A. Marin, I. Stojic, \"Computation of the normalising constant for product-form models of distributed systems with synchronisation\", Future Generation Computer Systems 111:475-490, 2020",
         "the P-invariants (S-invariants) of the incidence matrix, the conserved quantities the DAE states as constraints; SPN_SINVARIANTS computes the integral basis of the same space"}},
        {"minnormal.network", {"PendM17",
         "J. Pender, W. A. Massey, \"Approximating and stabilizing dynamic rate Jackson networks with abandonment\", Prob. Eng. Inf. Sci. 31(1), 2017",
         "the same closure in the queueing setting: coupled mean and covariance equations closing E[min(Q_i,c_i)] under a multivariate normal marginal"}},
        {"minnormal.station", {"MassP13",
         "W. A. Massey, J. Pender, \"Gaussian skewness approximation for dynamic rate multi-server queues with abandonment\", Queueing Syst. 75, 2013",
         "single-station Gaussian closure of the multiserver rate term E[min(Q,c)]; its own contribution is the third-cumulant (skewness) extension"}},
        {"minnormal.smoothing", {"KoG13",
         "Y. M. Ko, N. Gautam, \"Critically Loaded Time-Varying Multiserver Queues: Computational Challenges and Approximations\", INFORMS J. Comput. 25(2), 2013",
         "Gaussian smoothing of the non-smooth multiserver rate, the g-function form of the same closure"}},
        {"minnormal.share", {"Oehlert92",
         "G. W. Oehlert, \"A Note on the Delta Method\", The American Statistician 46(1), 1992",
         "second-order (delta method) closure of the capacity-share ratio E[w_k*X_k/sum_j w_j*X_j] at PS and DPS stations"}},
        {"minnormal.gps", {"ParekhG93",
         "A. K. Parekh, R. G. Gallager, \"A Generalized Processor Sharing Approach to Flow Control in Integrated Services Networks: The Single-Node Case\", IEEE/ACM Trans. Netw. 1(3), 1993",
         "generalized processor sharing: the server is divided by weight among the backlogged classes, the discipline whose capacity share the closure evaluates"}},
        {"minnormal.cache", {"GastH16",
         "N. Gast, B. Van Houdt, \"Transient and steady-state regime of a family of list-based cache replacement algorithms\", Queueing Syst. 83, 2016",
         "the RANDOM(m)/FIFO(m) occupancy process whose stationary covariance getMoments reports for a cache node"}},
        {"minnormal.jointprob", {"Genz92",
         "A. Genz, \"Numerical Computation of Multivariate Normal Probabilities\", J. Comput. Graph. Statist. 1(2):141-149, 1992",
         "separation-of-variables transformation evaluating the Gaussian rectangle probability P(n-1/2 <= Q <= n+1/2) returned by getProbAggr"}},
        {"minnormal.lattice", {"Niederreiter92",
         "H. Niederreiter, \"Random Number Generation and Quasi-Monte Carlo Methods\", SIAM, 1992",
         "deterministic Richtmyer lattice rule frac(k*sqrt(p_j)) integrating the transformed unit cube, so the three codebases return the same number"}},
        {"refined", {"Gast17",
         "N. Gast, \"Expected Values Estimated via Mean-Field Approximation are 1/N-Accurate\", Proc. ACM Meas. Anal. Comput. Syst. 1(1), 2017",
         "O(1/N) refinement term added to the mean-field fixed point"}},
        {"fluid.refined", {"Gast17",
         "N. Gast, \"Expected Values Estimated via Mean-Field Approximation are 1/N-Accurate\", Proc. ACM Meas. Anal. Comput. Syst. 1(1), 2017",
         "O(1/N) refinement term added to the mean-field fixed point"}},
        {"fluid.softmin", {"RuuskanenBAC21",
         "J. Ruuskanen, T. Berner, K.-E. Arzen, A. Cervin, \"Improving the mean-field fluid model of processor sharing queueing networks\", Perform. Eval. 151, 2021",
         "smoothing of the min() capacity term in the fluid drift"}},
        {"tbi", {"SheldonTC",
         "M. Sheldon, D. Tuncer, G. Casale, \"TBI: Transient Hierarchical Modeling of Large-Scale Vehicle Sharing Systems\", IEEE Trans. Intell. Transp. Syst., 2025",
         "cell-decomposed transient fluid solution: the station partition, the growing time segments, and the frozen cross-cell inflows the decomposed ODEs read"}},
        {"fluid.tbi", {"SheldonTC",
         "M. Sheldon, D. Tuncer, G. Casale, \"TBI: Transient Hierarchical Modeling of Large-Scale Vehicle Sharing Systems\", IEEE Trans. Intell. Transp. Syst., 2025",
         "cell-decomposed transient fluid solution: the station partition, the growing time segments, and the frozen cross-cell inflows the decomposed ODEs read"}},
        {"tbi.relaxation", {"Lelarasmee82",
         "E. Lelarasmee, A. E. Ruehli, A. L. Sangiovanni-Vincentelli, \"The Waveform Relaxation Method for Time-Domain Analysis of Large Scale Integrated Circuits\", IEEE Trans. CAD 1(3), 1982",
         "waveform relaxation: each cell's ODE is integrated over a time window against the other cells frozen at the previous sweep's trajectory, sweeping in Gauss-Seidel or Jacobi order until the sup-norm trajectory gap closes"}},
        {"jmt", {"BerCS07",
         "M. Bertoli, G. Casale, G. Serazzi, \"The JMT Simulator for Performance Evaluation of Non-Product-Form Queueing Networks\", ANSS, 2007",
         "discrete-event simulation and JMVA analysis"}},
        {"jsim", {"BerCS07",
         "M. Bertoli, G. Casale, G. Serazzi, \"The JMT Simulator for Performance Evaluation of Non-Product-Form Queueing Networks\", ANSS, 2007",
         "discrete-event simulation and JMVA analysis"}},
        {"jmva", {"BerCS07",
         "M. Bertoli, G. Casale, G. Serazzi, \"The JMT Simulator for Performance Evaluation of Non-Product-Form Queueing Networks\", ANSS, 2007",
         "discrete-event simulation and JMVA analysis"}},
        {"ln", {"RolS95",
         "J. A. Rolia, K. C. Sevcik, \"The Method of Layers\", IEEE TSE 21(8), 1995",
         "layer decomposition of the layered queueing network"}},
        {"layers", {"RolS95",
         "J. A. Rolia, K. C. Sevcik, \"The Method of Layers\", IEEE TSE 21(8), 1995",
         "layer decomposition of the layered queueing network"}},
        {"lqn_mol", {"RolS95",
         "J. A. Rolia, K. C. Sevcik, \"The Method of Layers\", IEEE TSE 21(8), 1995",
         "two-phase software-then-hardware sweep of the submodels, on the srvn decomposition of an entry-only layered model"}},
        {"lqns", {"FraMWPHM12",
         "G. Franks, P. Maly, M. Woodside, D. C. Petriu, A. Hubbard, M. Mroz, \"Layered Queueing Network Solver and Simulator User Manual\", Carleton University, 2012",
         "layered queueing solver and simulator"}},
        {"ln.flat", {"FraMWPHM12",
         "G. Franks, P. Maly, M. Woodside, D. C. Petriu, A. Hubbard, M. Mroz, \"Layered Queueing Network Solver and Simulator User Manual\", Carleton University, 2012",
         "squashed layering, a single submodel holding every processor and task"}},
        {"flat.cs", {"FraMWPHM12",
         "G. Franks, P. Maly, M. Woodside, D. C. Petriu, A. Hubbard, M. Mroz, \"Layered Queueing Network Solver and Simulator User Manual\", Carleton University, 2012",
         "squashed layering, a single submodel holding every processor and task, with the activity graph encoded as class routing"}},
        {"srvn.cs", {"FraAWDD09",
         "G. Franks, T. Al-Omari, M. Woodside, O. Das, S. Derisavi, \"Enhanced Modeling and Solution of Layered Queueing Networks\", IEEE TSE 35(2), 2009",
         "srvn layering: one submodel per served element, with the activity graph, its precedences and its calls encoded as the class routing of that submodel"}},
        {"ln.interlock", {"Franks1996",
         "R. G. Franks, \"Performance Analysis of Distributed Server Systems\", PhD thesis, Carleton University, 1999, Ch. 4",
         "interlocked flow: an arrival does not queue behind the work its own request caused, applied inside the layer MVA"}},
        {"ln.interlock.rate", {"Li2015",
         "L. Li, G. Franks, \"An Improved Interlocking Correction for Decomposition of Layered Queueing Networks\", IEEE CCECE, 2015",
         "the interlocked adjustment rate Pr(IL)*IR*IR of Eqs. (3)-(5), superseding the (n_s-1)/n_s discount of Franks (1999), Eq. (4.7)"}},
        {"interlock", {"Franks1996",
         "R. G. Franks, \"Performance Analysis of Distributed Server Systems\", PhD thesis, Carleton University, 1999, Ch. 4",
         "interlocked flow: an arrival does not queue behind the work its own request caused, applied inside the layer MVA"}},
        {"interlock.rate", {"Li2015",
         "L. Li, G. Franks, \"An Improved Interlocking Correction for Decomposition of Layered Queueing Networks\", IEEE CCECE, 2015",
         "the interlocked adjustment rate Pr(IL)*IR*IR of Eqs. (3)-(5), superseding the (n_s-1)/n_s discount of Franks (1999), Eq. (4.7)"}},
        {"srvn.ph", {"sahn.triv87",
         "R. A. Sahner, K. S. Trivedi, \"Performance and Reliability Analysis Using Directed Acyclic Graphs\", IEEE TSE 13(10), 1987",
         "exact series-parallel reduction of an activity graph into one phase-type entry service law"}},
        {"srvn.ph.setup", {"gand.harc.adan10",
         "A. Gandhi, M. Harchol-Balter, I. Adan, \"Server farms with setup costs\", Performance Evaluation 67(11), 2010",
         "a SetupTask under srvn.ph: the cold start a powered-down thread pays is prefixed to the composed entry law as the phase-type mixture p*(setup THEN entry) + (1-p)*entry, with p the probability the delay-off countdown expired first"}},
        {"flat.ph", {"sahn.triv87",
         "R. A. Sahner, K. S. Trivedi, \"Performance and Reliability Analysis Using Directed Acyclic Graphs\", IEEE TSE 13(10), 1987",
         "squashed layering with the composed encoding: the same single submodel as flat.cs, but each activity graph reduced by the exact series-parallel reduction into one phase-type entry service law, so a caller visits a server once per invocation"}},
        {"ln.dec", {"FraAWDD09",
         "G. Franks, T. Al-Omari, M. Woodside, O. Das, S. Derisavi, \"Enhanced Modeling and Solution of Layered Queueing Networks\", IEEE TSE 35(2), 2009",
         "enhanced decomposition of the layers"}},
        {"enhanced", {"FraAWDD09",
         "G. Franks, T. Al-Omari, M. Woodside, O. Das, S. Derisavi, \"Enhanced Modeling and Solution of Layered Queueing Networks\", IEEE TSE 35(2), 2009",
         "enhanced decomposition of the layers"}},
        {"ln.fluid", {"Tri13",
         "M. Tribastone, \"A Fluid Model for Layered Queueing Networks\", IEEE TSE 39(6), 2013",
         "fluid model of the layered network"}},
        {"ln.transient.coupled", {"Lelarasmee82",
         "E. Lelarasmee, A. E. Ruehli, A. L. Sangiovanni-Vincentelli, \"The Waveform Relaxation Method for Time-Domain Analysis of Large Scale Integrated Circuits\", IEEE Trans. CAD 1(3), 1982",
         "waveform relaxation over the LQN layers: each layer's transient is integrated against the other layers' latest demand trajectories, sweeping until the trajectories stop changing in the sup-norm"}},
        {"env", {"CasT11",
         "G. Casale, M. Tribastone, \"Fluid Analysis of Queueing in Two-Stage Random Environments\", QEST, 2011",
         "queueing in a random environment"}},
        {"env.blend", {"PerC13",
         "J. F. Perez, G. Casale, \"Assessing SLA Compliance from Palladio Component Models\", MICAS, 2013",
         "environment-stage blending of the metrics"}},
        {"map2renv", {"neut79",
         "M. F. Neuts, \"A Versatile Markovian Point Process\", Journal of Applied Probability 16(4), 1979",
         "the (D0,D1) modulating chain that the environment stages are frozen from"}},
        {"env.dec", {"Cou77",
         "P. J. Courtois, \"Decomposability: Queueing and Computer System Applications\", Academic Press, 1977",
         "quasi-stationary (slow-environment) limit in which each stage is solved in its own steady state"}},
        {"env.avg", {"yin.zhan98",
         "G. G. Yin, Q. Zhang, \"Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach\", Springer, 1998",
         "rate-averaged (fast-environment) limit in which the modulated rates are replaced by their stationary average"}},
        {"ubo", {"LiuHCA06",
         "Z. Liu, L. Wynter, C. H. Xia, L. Zhang, \"Parameter Inference of Queueing Models for IT Systems Using End-to-End Measurements\", Performance Evaluation 63(1), 2006",
         "utilization-based constrained optimization of service demands from end-to-end measurements"}},
        {"vi", {"PerC20",
         "I. Perez, G. Casale, \"Variational Inference for Markovian Queueing Networks\", Advances in Applied Probability 53(3), 2021",
         "the transition-count reparameterisation, the expanded state space that keeps the approximating measure absolutely continuous, and the mean-field rates and conjugate Gamma posteriors of the service rates"}},
        {"fquest", {"lolo.ea23",
         "A. Lolos, C. Alexopoulos, D. Goldsman, K. D. Dingec, A. C. Mokashi, J. R. Wilson, \"A Fixed-Sample-Size Method for Estimating Steady-State Quantiles\", Proc. Winter Simulation Conference, 2023",
         "automated fixed-sample-size confidence interval for a steady-state quantile from one sample path"}},
        {"firquest", {"lolo.ea25",
         "A. Lolos, C. Alexopoulos, D. Goldsman, K. D. Dingec, A. C. Mokashi, J. R. Wilson, \"A Fixed-Sample-Size Procedure for Estimating Steady-State Quantiles Based on Independent Replications\", Proc. Winter Simulation Conference, 2025",
         "the same interval pooled over independent replications"}},
        {"sts", {"alex.ea23",
         "C. Alexopoulos, D. Goldsman, A. Lolos, K. D. Dingec, J. R. Wilson, \"Steady-State Quantile Estimation Using Standardized Time Series\", 2023",
         "standardized time series variance-parameter estimators of the batched quantile process"}},
        {"nbq", {"alex.ea23",
         "C. Alexopoulos, D. Goldsman, A. Lolos, K. D. Dingec, J. R. Wilson, \"Steady-State Quantile Estimation Using Standardized Time Series\", 2023",
         "standardized time series variance-parameter estimators of the batched quantile process"}},
        {"bahadur", {"wu05",
         "W. B. Wu, \"On the Bahadur Representation of Sample Quantiles for Dependent Sequences\", Ann. Statist. 33(4), 2005",
         "Bahadur representation of the batched quantile under geometric moment contraction"}},
        {"vonneumann", {"vonn41",
         "J. von Neumann, \"Distribution of the Ratio of the Mean Square Successive Difference to the Variance\", Ann. Math. Statist. 12(4), 1941",
         "randomness test on the batch statistics"}},
        {"shapirowilk", {"royston95",
         "J. P. Royston, \"Remark AS R94: A Remark on Algorithm AS 181, The W Test for Normality\", Applied Statistics 44(4), 1995",
         "normality test on the batch statistics"}},
        {"willink", {"will05",
         "R. Willink, \"A Confidence Interval and Test for the Mean of an Asymmetric Distribution\", Commun. Statist. Theory Methods 34, 2005",
         "skewness adjustment of the fallback interval"}},
        {"perm", {"ryse63",
         "H. J. Ryser, \"Combinatorial Mathematics\", Carus Mathematical Monographs 14, MAA, 1963",
         "inclusion-exclusion formula for the exact permanent of the demand matrix"}},
        {"perm.ryser", {"ryse63",
         "H. J. Ryser, \"Combinatorial Mathematics\", Carus Mathematical Monographs 14, MAA, 1963",
         "inclusion-exclusion formula for the exact permanent of the demand matrix"}},
        {"ryser", {"ryse63",
         "H. J. Ryser, \"Combinatorial Mathematics\", Carus Mathematical Monographs 14, MAA, 1963",
         "inclusion-exclusion formula for the exact permanent of the demand matrix"}},
        {"perm.bethe", {"vont13",
         "P. O. Vontobel, \"The Bethe Permanent of a Nonnegative Matrix\", IEEE Trans. Inform. Theory 59(3), 2013",
         "sum-product approximation of the permanent and its Bethe free energy"}},
        {"bethe", {"vont13",
         "P. O. Vontobel, \"The Bethe Permanent of a Nonnegative Matrix\", IEEE Trans. Inform. Theory 59(3), 2013",
         "sum-product approximation of the permanent and its Bethe free energy"}},
        {"perm.heur", {"sink64",
         "R. Sinkhorn, \"A Relationship Between Arbitrary Positive Matrices and Doubly Stochastic Matrices\", Ann. Math. Statist. 35(2), 1964",
         "diagonal scaling of the matrix to doubly stochastic form"}},
        {"sinkhorn", {"sink64",
         "R. Sinkhorn, \"A Relationship Between Arbitrary Positive Matrices and Doubly Stochastic Matrices\", Ann. Math. Statist. 35(2), 1964",
         "diagonal scaling of the matrix to doubly stochastic form"}},
        {"perm.gurvits", {"gurv06",
         "L. Gurvits, \"Hyperbolic Polynomials Approach to Van der Waerden/Schrijver-Valiant Like Conjectures\", STOC, 2006",
         "van der Waerden capacity bound of the doubly stochastic permanent"}},
        {"gurvits", {"gurv06",
         "L. Gurvits, \"Hyperbolic Polynomials Approach to Van der Waerden/Schrijver-Valiant Like Conjectures\", STOC, 2006",
         "van der Waerden capacity bound of the doubly stochastic permanent"}},
        {"perm.spm", {"Cas17",
         "G. Casale, \"Accelerating Performance Inference over Closed Systems by Asymptotic Methods\", ACM SIGMETRICS, 2017",
         "saddle-point (Laplace) expansion of the coefficient integral, here of the homogeneous product of linear forms whose coefficient is the permanent"}},
        {"perm.spm.scaling", {"sink64",
         "R. Sinkhorn, \"A Relationship Between Arbitrary Positive Matrices and Doubly Stochastic Matrices\", Ann. Math. Statist. 35(2), 1964",
         "diagonal scaling to row sums 1 and column sums m, which is the saddle point equation"}},
        {"perm.spm.capacity", {"gurv06",
         "L. Gurvits, \"Hyperbolic Polynomials Approach to Van der Waerden/Schrijver-Valiant Like Conjectures\", STOC, 2006",
         "capacity at the saddle point, the upper bound on the permanent that the Gaussian factor corrects"}},
        {"perm.huberlaw", {"hube.law08",
         "M. Huber, J. Law, \"Fast Approximation of the Permanent for Very Dense Problems\", SODA, 2008",
         "acceptance-rejection sampling of permutations under the Huber-Law bound"}},
        {"huberlaw", {"hube.law08",
         "M. Huber, J. Law, \"Fast Approximation of the Permanent for Very Dense Problems\", SODA, 2008",
         "acceptance-rejection sampling of permutations under the Huber-Law bound"}},
        {"perm.adapart", {"kuck.ea19",
         "J. Kuck, T. Dao, H. Rezatofighi, A. Sabharwal, S. Ermon, \"Approximating the Permanent by Sampling from Adaptive Partitions\", NeurIPS, 2019",
         "adaptive partitioning of the permutation space and its rejection sampler"}},
        {"adapart", {"kuck.ea19",
         "J. Kuck, T. Dao, H. Rezatofighi, A. Sabharwal, S. Ermon, \"Approximating the Permanent by Sampling from Adaptive Partitions\", NeurIPS, 2019",
         "adaptive partitioning of the permutation space and its rejection sampler"}},
        {"soules", {"soul05",
         "G. W. Soules, \"Permanental Bounds for Nonnegative Matrices via Decomposition\", Linear Algebra Appl. 394, 2005",
         "column-decomposition upper bound of the permanent used by the partition sampler"}},
        {"mg1ps", {"ott84",
         "T. J. Ott, \"The Sojourn-Time Distribution in the M/G/1 Queue with Processor Sharing\", J. Appl. Prob. 21(2), 1984",
         "transform of the sojourn time conditioned on the service requirement"}},
        {"mg1ps.yashkov", {"yash83",
         "S. F. Yashkov, \"A Derivation of Response Time Distribution for an M/G/1 Processor-Sharing Queue\", Probl. Contr. Inform. Theory 12, 1983",
         "independent derivation of the same conditional sojourn-time transform"}},
        {"mg1ps.inversion", {"abat.whit95",
         "J. Abate, W. Whitt, \"Numerical Inversion of Laplace Transforms of Probability Distributions\", ORSA J. Computing 7(1), 1995",
         "Euler summation used to invert the sojourn-time transform"}},
        {"lindley", {"lind52",
         "D. V. Lindley, \"The Theory of Queues with a Single Server\", Proc. Camb. Phil. Soc. 48, 1952",
         "waiting-time recursion of the single-server queue"}},
        {"condlindley", {"palo.pend21",
         "S. Palomo, J. Pender, \"Learning the Tandem Network Lindley Recursion\", Proc. Winter Simulation Conference, 2021",
         "conditional waiting-time moments of one Lindley step and the tandem interdeparture coupling"}},
        {"tandemub", {"ciuc.mehr25",
         "F. Ciucu, S. Mehri, \"On the Distribution of Sojourn Times in Tandem Queues\", Proc. ACM Meas. Anal. Comput. Syst. 9(2), Article 27, 2025",
         "polynomial-exponential upper bounds on the end-to-end waiting and sojourn time tails of a two-station tandem"}},
        {"tandemlindley", {"palo.pend21",
         "S. Palomo, J. Pender, \"Learning the Tandem Network Lindley Recursion\", Proc. Winter Simulation Conference, 2021",
         "conditional waiting-time moments of one Lindley step and the tandem interdeparture coupling"}},
    };
    return reg;
}
 
std::vector<Citation> line_citations(const std::vector<std::string>& tokens) {
    const std::map<std::string, Citation>& reg = citation_registry();
    std::vector<Citation> out;
    std::set<std::string> seen;
    for (const std::string& raw : tokens) {
        const std::string t = normalise(raw);
        if (t.empty()) continue;
        auto it = reg.find(t);
        if (it == reg.end()) {
            // A family-qualified method name falls back to the bare method name, so
            // `nc.mva` finds `mva` when the qualified form is absent.
            const std::size_t dot = t.find('.');
            if (dot == std::string::npos) continue;
            it = reg.find(t.substr(dot + 1));
            if (it == reg.end()) continue;
        }
        // One paper is often reachable through several tokens; report it once.
        if (!seen.insert(it->second.key).second) continue;
        out.push_back(it->second);
    }
    return out;
}
 
std::vector<Citation> line_citations_for_method(const std::string& method) {
    std::vector<std::string> parts;
    std::size_t b = 0;
    while (b <= method.size()) {
        const std::size_t s = method.find('/', b);
        parts.push_back(method.substr(b, s == std::string::npos ? std::string::npos : s - b));
        if (s == std::string::npos) break;
        b = s + 1;
    }
    return line_citations(parts);
}
 
}  // namespace io
}  // namespace line