pfqn Directory Reference

Directory dependency graph for pfqn:

Files
	cd_peak_scaling.h
	Peak of a class-dependence handle over the reachable population lattice.
	infradius_h.h
	Integrands of the Norlund-Rice inversion of the normalizing constant, in their two changes of variable.
	laplaceapprox.h
	Laplace approximation of a multidimensional integral around a given point.
	pas_placement.h
	Placement order of a pass-and-swap (P&S) order-independent network.
	pas_swap2order.h
	Global placement-order DAG of a closed two-station pass-and-swap tandem.
	pfqn_ab_amva.h
	Akyildiz-Bolch approximate MVA for multi-server BCMP networks.
	pfqn_aghq.h
	Adaptive Gauss-Hermite quadrature of the simplex factor of the McKenna-Mitra integral.
	pfqn_amva_common.h
	Scaffolding shared by the approximate-MVA family.
	pfqn_aql.h
	Aggregate Queue Length (AQL) approximate MVA.
	pfqn_asympt_common.h
	Shared scalar machinery for the integration / asymptotic members of the pfqn family (pfqn_le, pfqn_lap, pfqn_ls, pfqn_cub, pfqn_kt, pfqn_panacea, the McKenna-Mitra quadratures, pfqn_nrl / pfqn_nrp).
	pfqn_bk.h
	Birman-Kogan asymptotic evaluation of closed networks with many stations.
	pfqn_bkt.h
	Knessl-Tier expansion with the Stirling-remainder correction (BKT).
	pfqn_ble.h
	Logistic expansion with the eps->0 bias correction (BLE).
	pfqn_bs.h
	Bard-Schweitzer approximate MVA.
	pfqn_busyp.h
	Mean busy period of order n for a subnetwork of a product-form network.
	pfqn_busyp_clw.h
	Busy period of a subnetwork from point evaluations of the normalizing constant.
	pfqn_busyp_multiclass.h
	Multichain generalization of pfqn_busyp.
	pfqn_ca.h
	Convolution algorithm for the exact normalizing constant of a closed product-form network (Buzen 1973, Reiser-Kobayashi 1975).
	pfqn_cbh.h
	Convolutional Bound Hierarchy (Dowdy, Eager, Gordon and Saxton 1984) on the throughput of a single-class closed product-form network.
	pfqn_cdfun.h
	AMVA-QD class-dependence function.
	pfqn_cftp.h
	Perfect stationary state sampling for closed single-class multiserver product-form networks, by monotone Coupling From The Past.
	pfqn_chow.h
	Chow Second Approximation (SA) approximate MVA.
	pfqn_clust.h
	de Souza e Silva-Lavenberg-Muntz Clustering Approximation (CA).
	pfqn_clw.h
	Choudhury-Leung-Whitt normalization constant by numerical inversion of the generating function (JACM 42(5):935-970, 1995), and its limited load-dependent extension through the per-center transforms of Bertozzi and McKenna (SIAM Review 35(2):239-268, 1993).
	pfqn_clwjd.h
	Normalizing constant of a closed network of LIMITED JOINT-DEPENDENT (LJD) stations plus one aggregated delay, by numerical inversion of the multichain generating function (Choudhury-Leung-Whitt, J.
	pfqn_clwoi.h
	Normalizing constant of a closed network of ORDER-INDEPENDENT (OI) stations plus one aggregated delay, by numerical inversion of the multichain generating function (Choudhury-Leung-Whitt, J.
	pfqn_cntol.h
	Chandy-Neuse population-scaled termination cutoff for approximate MVA.
	pfqn_comb_common.h
	Integer-composition enumeration shared by the CoMoM and MVAC ports.
	pfqn_comom.h
	CoMoM (class-oriented method of moments), the general basis formulation, and the original repairman-model implementation that preceded pfqn_comomrm.
	pfqn_comomrm.h
	CoMoM (class-oriented method of moments) for the finite repairman model: one queueing station of multiplicity m plus a delay.
	pfqn_comomrm_ld.h
	CoMoM for the repairman model with an arbitrary LOAD-DEPENDENT rate lattice at the single queueing station.
	pfqn_comomrm_ms.h
	CoMoM for the MULTISERVER repairman model: one queueing station with S servers (optionally replicated m times), plus a delay.
	pfqn_conv.h
	Multichain convolution algorithm with class-dependent service rates (Sauer 1983, "Computational Algorithms for State-Dependent Queueing Networks", ACM TOCS 1(1):67-92, Section 5.2).
	pfqn_conwayms.h
	Conway's multiserver Linearizer for chain-dependent FCFS queues (Conway 1989, "Fast Approximate Solution of Queueing Networks with Multi-Server Chain-Dependent FCFS Queues").
	pfqn_cub.h
	Normalizing constant by Grundmann-Moeller cubature over the simplex.
	pfqn_cub_evals.h
	Integrand-evaluation count of pfqn_cub, and the budget pfqn_nc prices it against.
	pfqn_cyclet_ofree.h
	Exact passage-time law along an OVERTAKE-FREE PATH of a closed single-chain tree-like product-form network.
	pfqn_dac.h
	Distribution Analysis by Chain (de Souza e Silva, UCLA CSD-870023, 1987): the JOINT queue-length distribution of a closed product-form network with single-server, infinite-server and queue-dependent centers.
	pfqn_dmlin.h
	de Souza e Silva-Muntz Improved Linearizer (IL).
	pfqn_dnc.h
	Distinct-load Normalizing Constant (DNC) at a nonintegral population.
	pfqn_egflinearizer.h
	Extended generalized fixed-point Linearizer (De Souza e Silva and Muntz's generalization of Chandy and Neuse's Linearizer, with a per-class scaling exponent alpha_r).
	pfqn_expand.h
	Expand per-station metrics from a reduced model back to the original station set.
	pfqn_explicit.h
	Explicit closed-form normalizing constant of a multiclass closed network.
	pfqn_explicit_ld.h
	Explicit closed-form normalizing constant of a multiclass LIMITED LOAD-DEPENDENT network.
	pfqn_fnc.h
	Load-dependent rates of the functional server f(n) = n + c.
	pfqn_gerasimov.h
	Gerasimov's residue (closed-form) normalizing constant, generalized to R classes.
	pfqn_gflinearizer.h
	Generalized fixed-point Linearizer with a single scaling exponent shared by every class (De Souza e Silva and Muntz).
	pfqn_gld.h
	Exact normalizing constant of a closed product-form network whose stations may be load dependent (generalized Buzen, Reiser-Kobayashi 1975).
	pfqn_gldsingle.h
	Exact normalizing constant of a SINGLE-CLASS closed network whose stations are load dependent.
	pfqn_grnmol.h
	Normalizing constant by the closed-form Grundmann-Moeller rule.
	pfqn_harel_bounds.h
	Harel-Namn-Sturm throughput bounds for a single-class closed network.
	pfqn_hst.h
	Operational sensitivity of throughput to homogeneous-service-time (HST) violations, and the constrained worst case (Suri 1983).
	pfqn_is.h
	Importance-sampling estimate of the normalizing constant of a closed LOAD-INDEPENDENT product-form network.
	pfqn_jdfun.h
	AMVA joint-dependence function for non-product-form scaling.
	pfqn_joint.h
	Joint queue-length probability of a closed product-form network.
	pfqn_jointmarg.h
	Joint probability of the per-station TOTAL queue lengths.
	pfqn_kt.h
	Knessl-Tier asymptotic expansion of the normalizing constant.
	pfqn_lap.h
	Laplace approximation of the normalizing constant of a repairman (single-queue, multiclass) model.
	pfqn_lcfsqn_ca.h
	Convolution algorithm for the two-station multiclass LCFS queueing network of Casale, "A family of multiclass LCFS queueing networks with order-dependent product-form solutions", QUESTA 2026.
	pfqn_lcfsqn_mva.h
	Exact mean value analysis of the two-station multiclass LCFS network of Casale, QUESTA 2026 (station 1 LCFS, station 2 LCFS-PR).
	pfqn_lcfsqn_nc.h
	Normalizing constant of the two-station multiclass LCFS network as a sum of PERMANENTS, the closed form of Casale, QUESTA 2026.
	pfqn_lcp.h
	Bard Large Customer Population (LCP) approximate MVA.
	pfqn_ld_is.h
	Importance-sampling estimate of the normalizing constant of a closed LOAD-DEPENDENT product-form network.
	pfqn_ldbcmp.h
	Anselmi-Cremonesi (2008) lower throughput bound for a closed single-class BCMP network with load-dependent stations.
	pfqn_ldmx_ec.h
	Bruell-Balbo-Afshari effective-capacity terms for a MIXED open/closed network with limited load dependence.
	pfqn_le.h
	Logistic expansion (LE) asymptotic approximation of the normalizing constant of a closed product-form network.
	pfqn_lekt.h
	The common corrected asymptotic expansion (LE-KT), computed on the cheaper side.
	pfqn_linearizer.h
	Chandy-Neuse Linearizer for single-server stations.
	pfqn_linearizerms.h
	Multiserver Linearizer (Krzesinski's Linearizer as described in Conway 1989, with De Souza e Silva and Muntz's presentation of the marginal-probability recursions).
	pfqn_linearizermx.h
	Linearizer for mixed open/closed queueing networks.
	pfqn_lldfun.h
	AMVA-QD limited-load-dependence function.
	pfqn_lldsingle.h
	Exact normalizing constant of a SINGLE-CLASS closed network whose stations are LIMITED load dependent, i.e.
	pfqn_looping.h
	Eager Looping bounds for closed multiclass product-form networks.
	pfqn_ls.h
	Logistic-sampling estimate of the normalizing constant of a closed product-form network.
	pfqn_manjunath.h
	Exact normalizing constant of a closed multiclass product-form network whose state space carries arbitrary linear integer constraints (Manjunath-Sikdar).
	pfqn_marie.h
	Marie's iterative aggregation-decomposition for closed networks with FCFS general (Coxian) service.
	pfqn_mc_common.h
	Randomness scaffolding shared by the Monte Carlo normalizing-constant estimators (pfqn_mci, pfqn_is, pfqn_ld_is, pfqn_oi_is, pfqn_pas_is, pfqn_ls, pfqn_mmsample2) and by the perfect sampler pfqn_cftp.
	pfqn_mci.h
	Monte Carlo Integration estimate of the normalizing constant of a closed product-form network (Ross, Wang and Yao; MonteQueue 2.0).
	pfqn_mcmc.h
	Chen-O'Cinneide REGULARIZATION: a Markov chain Monte Carlo estimator of the class throughputs X(r) = G(N-e_r)/G(N) and of the mean queue lengths Q(i,r) of a CLOSED multiclass product-form (BCMP, no type changes) network.
	pfqn_mcub.h
	Kerola's multiclass composite bound (Perf.
	pfqn_mmint2.h
	McKenna-Mitra integral form of the normalizing constant of a repairman model (one queueing station, R classes, per-class think time), in its three MATLAB quadratures.
	pfqn_mmsample2.h
	Sampled McKenna-Mitra integral form of the normalizing constant of a repairman (single-queue plus delay) model.
	pfqn_momlin.h
	Moment linearizer: approximate first and second queue-length moments of a large closed product-form network.
	pfqn_mu_ms.h
	Aggregate load-dependent rate of m identical c-server FCFS stations.
	pfqn_mushift.h
	Shift the load-dependent service-rate lattice of selected stations.
	pfqn_mva.h
	Exact Mean Value Analysis for closed product-form networks (Reiser and Lavenberg 1980).
	pfqn_mva_interval.h
	Exact interval-valued MVA for single-class closed product-form networks.
	pfqn_mvac.h
	MVAC: exact mean value analysis BY CHAIN of a closed multichain product-form network (Conway, de Souza e Silva and Lavenberg, IEEE Trans.
	pfqn_mvacld.h
	MVAC for networks with queue-length dependent (QLD) service centers, the Section V extension of Conway, de Souza e Silva and Lavenberg (1989).
	pfqn_mvajd.h
	Joint-dependent name of pfqn_mvaoi: the mean-value analysis of a closed network whose station rates read the whole per-class occupancy vector.
	pfqn_mvams.h
	Exact Mean Value Analysis for mixed open/closed networks with multiserver stations.
	pfqn_mvaoi.h
	Mean-value analysis of a closed network with order-independent (OI) stations, the composition-dependent generalization of Conditional MVA.
	pfqn_mvaoi_marg.h
	Exact marginal load-dependent MVA for a closed network of delay, load-independent and ANY number of order-independent (OI) stations.
	pfqn_mwrbb.h
	Majumdar-Woodside robust box bounds on the per-class throughput of a closed multiclass network with mixed scheduling disciplines (Perf.
	pfqn_nc.h
	Normalizing constant of a product-form queueing network: the dispatcher.
	pfqn_nc_sanitize.h
	Preprocessing shared by the normalizing-constant solvers: drop the classes that cannot contribute, rescale the demands per class, and order the classes so that the zero-think-time ones come first.
	pfqn_ncjd.h
	Joint-dependent name of pfqn_ncoi: the balance-function convolution of a closed network whose station rates read the whole per-class occupancy vector.
	pfqn_ncld.h
	Normalizing constant of a LOAD-DEPENDENT closed network: the dispatcher.
	pfqn_ncldmx.h
	Normalizing constant of a MIXED open/closed network with limited load dependence.
	pfqn_ncoi.h
	Normalizing constant of a closed network of ORDER-INDEPENDENT (OI) / pass-and-swap stations with empty swap graph, plus one aggregated delay.
	pfqn_nintmva.h
	Mean value analysis at a nonintegral population (fractional-base aMVA).
	pfqn_nre.h
	Norlund-Rice inversion of the normalizing constant on a SADDLE-TILTED contour, with a second-order Edgeworth correction.
	pfqn_nrl.h
	Norlund-Rice inversion of the normalizing constant, in its logistic (NRL) and probit (NRP) substitutions.
	pfqn_oi_fnc.h
	Order-independent (OI) functional server: the balance function Psi and the rate mu_f of an auxiliary station whose insertion turns the mean of a queue-dependent function into a ratio of normalizing constants.
	pfqn_oi_insvc.h
	Conditional mean number of IN-SERVICE jobs per class at an order-independent station.
	pfqn_oi_is.h
	Importance-sampling estimate of the normalizing constant of a closed two-station order-independent (OI) tandem.
	pfqn_pam.h
	Hsieh-Lam Proportional Approximation Methods (PAMB / PAMI / PAMT).
	pfqn_panacea.h
	PANACEA normal-usage asymptotic expansion of the normalizing constant (Ramakrishnan and Mitra, BSTJ 61(10):2849-2872, 1982).
	pfqn_panaceald.h
	PANACEA normal-usage asymptotic expansion for LOAD-DEPENDENT closed networks (Mitra and McKenna, JACM 33(3):568-592, 1986).
	pfqn_pas_is.h
	Importance-sampling estimate of the normalizing constant of a single communicating class of a cyclic two-station pass-and-swap (P&S) network with swap graph H.
	pfqn_pas_nc.h
	Normalizing constant G_C of one communicating class of a closed PASS-AND-SWAP (P&S) network, plus one aggregated delay.
	pfqn_pbh.h
	Performance Bound Hierarchy (Eager and Sevcik 1983, ACM TOCS 1(2):99-115) for single-class closed product-form networks, and the two iterative families that are defined in terms of it.
	pfqn_perm.h
	Permanent of a matrix with repeated columns, by Ryser's formula.
	pfqn_pff_delay.h
	Product-form factor of a delay station.
	pfqn_procomom.h
	ProCoMoM: marginal queue-length probabilities of a closed multiclass product-form network by the class-oriented method of moments.
	pfqn_propfair.h
	Proportionally fair allocation estimate of the normalizing constant (Schweitzer 1979; Walton, "Proportional fairness and its relationship with multi-class queueing networks", 2009).
	pfqn_qdamva.h
	QD-AMVA: queue-dependent approximate mean value analysis.
	pfqn_qdlin.h
	QD-LIN: the Linearizer arm of AMVA-LD, on a plain demand matrix.
	pfqn_qlen_joint_moments.h
	Joint moments of the queue-length vector of a closed product-form network, obtained from normalizing constants.
	pfqn_qsa.h
	Queue-Shift Approximation (QSA) for closed product-form networks.
	pfqn_qzgblow.h
	Geometric-bound lower bound on the queue length at station i.
	pfqn_qzgbup.h
	Geometric-bound upper bound on the queue length at station i.
	pfqn_rd.h
	Reduction heuristic (RD) for the normalizing constant of a closed LOAD-DEPENDENT product-form network.
	pfqn_recal.h
	RECAL (REcursive CALculation) for the exact normalizing constant of a closed product-form network (Conway and Georganas 1986).
	pfqn_respt_ps_moments.h
	Sojourn-time moments at the processor-sharing station of a closed terminal-driven system (Mitra and Morrison 1983).
	pfqn_rgf.h
	Recursion by Generating Functions (RGF) for the normalizing constant of a SINGLE-CLASS closed product-form network with replicated stations.
	pfqn_rgfmc.h
	Multiclass Recursion by Generating Functions (RGF), with think times.
	pfqn_scat.h
	Neuse-Chandy SCAT (Self-Correcting Approximation Technique) approximate MVA.
	pfqn_scb.h
	Dowdy-Carlson-Krantz-Tripathi (1992) single-class bounds of multi-class queueing networks, J.
	pfqn_schmidt.h
	Schmidt's MVA for closed networks with general scheduling disciplines and class-dependent multiserver FCFS stations.
	pfqn_schmidt_ext.h
	Extended Schmidt MVA with queue-aware alpha corrections.
	pfqn_sdr.h
	Product-form state-dependent routing.
	pfqn_sens.h
	Exact analytic derivatives of the mean performance measures {X,Q,U,R} of a closed product-form (BCMP) network with respect to the demands L(i,r) and the think times Z(r).
	pfqn_sens_ldmx_ec.h
	Effective capacity terms of the mixed load-dependent MVA of Bruell-Balbo-Afshari, together with their exact derivatives with respect to the open-class load Lo(i) of each station.
	pfqn_sens_linearizer.h
	Approximate moments E[Q_i], Var[Q_i], Cov[Q_i,Q_j], E[Q_i^2] and E[Q_i^3] of the per-station total queue lengths of a closed product-form network, by the LINEARIZER-2 / LINEARIZER-3 algorithms of Strelen (Performance Evaluation 11:127-142, 1990, Section 5).
	pfqn_sens_mom.h
	Exact moments E[Q], Var[Q], E[Q^2] and E[Q^3] of the grouped queue lengths of a closed product-form network, by second-order differentiation of the MVA recursion.
	pfqn_sens_mva.h
	Exact per-station queue-length variances and covariances of a closed product-form network, by the MVA-like moment recursion of de Souza e Silva and Muntz (IEEE TC 37(9):1125-1129, 1988, Corollary 1).
	pfqn_sens_mvaldmx.h
	Exact queue-length variances and covariances of a mixed open/closed product-form network with limited load dependence, the load-dependent and mixed counterpart of pfqn_sens_mva.
	pfqn_sens_respt.h
	Exact raw moments E[W^t], t = 1..3, of the sojourn time of a job at an FCFS b-server center of a closed product-form network.
	pfqn_sib.h
	Successively Improving Bounds (Srinivasan 1985/1987) on the cycle time and throughput of a single-class closed product-form network.
	pfqn_simplex.h
	Shared machinery for closures of the simplex factor of the McKenna-Mitra integral, used by pfqn_aghq.h.
	pfqn_sjn.h
	Closed networks with non-preemptive shortest-job-next (SJN/SJF) stations.
	pfqn_sqni.h
	Square-root non-iterative (SQNI) approximation for a single queueing station with per-class delay.
	pfqn_ssd.h
	Server-Station Disaggregation bounds for a multiserver closed network (Dallery and Suri, SIGMETRICS 1986).
	pfqn_stdf.h
	Sojourn-time distribution at multiserver FCFS stations of a closed product-form network (J.
	pfqn_stdf_heur.h
	Heuristic sojourn-time distribution at multiserver FCFS stations, a variant of J.
	pfqn_tay.h
	Tay's arrival-instant approximate MVA.
	pfqn_unique.h
	Station consolidation and its inverse: merge identical demand rows into one station with a multiplicity, and expand per-station results back.
	pfqn_wangsevcik.h
	Two approximate MVA schemes: Queue-Line and Fraction-Line.
	pfqn_xia.h
	Xia's asymptotic approximation of the normalizing constant of a load-dependent (multiserver) closed network.
	pfqn_xzabalow.h
	Asymptotic-bound-analysis lower bound on throughput.
	pfqn_xzabaup.h
	Asymptotic-bound-analysis upper bound on throughput.
	pfqn_xzgsblow.h
	Geometric-square-root bound, lower bound on throughput.
	pfqn_xzgsbup.h
	Geometric-square-root bound, upper bound on throughput.