Algorithms
A table listing every solution method offered in LINE. A method can be selected by calling the relevant solver option, e.g. as SolverMVA(model, method='bs') in Python. Each algorithm is listed once under its canonical name: aliases, and default methods that only dispatch to a listed algorithm, are omitted. The Since column gives the LINE release in which the method first became available, under its current name or an earlier one, with 3.0.8 denoting the current development version.
| Solver | Method | Algorithm and applicability | Reference | Since |
|---|---|---|---|---|
| AG | inap | INAP fixed point for cooperating processes; exact when the RCAT product-form conditions hold. | [75] | 3.0.2 |
| AG | inaprc | The INAP solution with the reversed rate estimated by rate conservation instead (as used in the AutoCAT method). | [19] | 3.0.2 |
| AG | inapinf | INAP fixed point based on matrix-geometric decomposition of the cooperating processes on the infinite state space. | [76], [85] | 3.0.6 |
| BA | auto, auto.upper, auto.lower | Evaluate every feasible noniterative bound and keep the tightest side; a family that rejects the model is skipped. | - | 3.0.7 |
| BA | aba.upper, aba.lower | Asymptotic Bounds Analysis: X <= min(1/Dmax, N/(Z+sum D)) and its pessimistic counterpart. | [13], [83], [36] | 2.0.3 |
| BA | bjb.upper, bjb.lower | Balanced Job Bounds: the ABA bracket refined by substituting the mean and maximum demand into the residence time. | [21], [112] | 2.0.3 |
| BA | pb.upper, pb.lower | Proportional bounds: the same bracket with the power-mean demands D^2/sum(D) and D^N/sum(D^(N-1)). | [21], [56] | 2.0.3 |
| BA | gb.upper, gb.lower | Geometric Bounds of Casale-Muntz-Serazzi: geometric-sum bounds on cycle time and throughput, and the matching queue-length bound. | [21] | 2.0.3 |
| BA | sb.upper, sb.lower | Harel's simple closed-network throughput bound, both sides; no delay station. | [53] | 2.0.17 |
| BA | harel.upper | Upper throughput bound extrapolated from the exact throughput at population n <= 7. | [53] | 3.0.7 |
| BA | harel.lower | Lower throughput bound from the first and N-th power sums of the relative utilizations. | [53] | 3.0.7 |
| BA | mw.upper | Majumdar-Woodside robust (worst-case) throughput bound, discipline-insensitive, NBUE service; the only closed family encompassing HOL and the preemptive-priority disciplines. | [72] | 3.0.6 |
| BA | mw.lower | The matching robust throughput guarantee, lower side. | [72] | 3.0.6 |
| BA | pbh.upper, pbh.lower | PBH: the Eager-Sevcik hierarchy initialized from the PB bound. | [43] | 3.0.6 |
| BA | bjbh.upper, bjbh.lower | BJBH: the Eager-Sevcik hierarchy initialized from the BJB bound. | [43] | 3.0.6 |
| BA | cbh.upper, cbh.lower | Convolutional Bound Hierarchy: one column of Buzen's g-array filled with BJB estimates, the remaining stations convolved exactly. | [41] | 3.0.6 |
| BA | ssd.upper, ssd.lower | Dallery-Suri server-station disaggregation bound with the think-time correction; the classical family that accepts multiserver stations. | [34] | 3.0.6 |
| BA | sib.upper, sib.lower | Srinivasan's Successively Improving Bounds on cycle time and throughput; zero think time only. | [102] | 3.0.6 |
| BA | cub.upper | Kerola composite multiclass upper bound on per-class throughput. | [61] | 3.0.6 |
| BA | mbjb.lower | The multiclass Balanced Job Bound that seeds cub.upper. | [61] | 3.0.6 |
| BA | looping.upper, looping.lower | Eager's multiclass looping bound. | [42] | 3.0.7 |
| BA | scb.upper | Demand-free upper bound on multiclass throughput, capped by U <= 1; brackets the multiclass system the single-class model aggregates. | [40] | 3.0.7 |
| BA | scb.lower | Exact single-class throughput as a lower bound on the multiclass throughput, with the single-class utilizations as lower bounds. | [40] | 3.0.7 |
| BA | ldac.lower | Anselmi-Cremonesi lower throughput bound for closed single-class BCMP networks via the asymptotic closed-open equivalence. | [2] | 3.0.6 |
| BA | bpt.lower | Bertsimas-Paschalidis-Tsitsiklis first-order LP relaxation of the achievable region; open networks. | [11] | 3.0.7 |
| BA | bgt.upper | Piecewise-linear Lyapunov function whose linear program certifies stability and bounds the mean queue lengths under any work-conserving policy; open networks. | [10] | 3.0.7 |
| BA | snc.upper | Stochastic network calculus: MGF arrival and service envelopes propagated hop by hop over a feed-forward open network. | [45] | 3.0.7 |
| BA | lr, lr.upper, lr.lower | LP-based Linear Reduction bound, one LP per station; not an alias of qrf.mmi.linear. | [18] | 3.0.6 |
| BA | qrf.mmi | Quadratic reduction on the closed MAP queueing chain, mutual-information objective, nonlinear no-blocking reduction. | [18] | 3.0.4 |
| BA | qrf.mem | The same reduction with the maximum-entropy objective. | [18] | 3.0.4 |
| BA | qrf.bethe | Tree-reweighted (Bethe) free entropy over the same no-blocking polytope; the only convex QRF objective, so the answer is start-point independent. | [18], [106] | 3.0.7 |
| BA | qrf.mmi.ld | MMI quadratic reduction with the load-dependent alpha matrix, which is what lets it serve delay, multiserver and load-dependent stations. | [18] | 3.0.4 |
| BA | qrf.mmi.linear | The same load-dependent envelope with explicit equality constraints in place of the nonlinear reduction. | [18] | 3.0.4 |
| BA | qrf.bas | LP quadratic reduction over the Blocking-After-Service polytope; may derive the blocking tables from station capacities. | [18] | 3.0.4 |
| BA | qrf.bas.mmi | MMI objective over that blocking polytope; concave there, so each codebase settles on the vertex its own solver reaches. | [18] | 3.0.4 |
| BA | qrf.bas.mem | Maximum-entropy objective over the blocking polytope. | [18] | 3.0.4 |
| BA | qrf.bas.bethe | Tree-reweighted (Bethe) free entropy over the blocking polytope, the start-point-independent blocking answer. | [18], [106] | 3.0.7 |
| BA | qrf.rsrd | LP quadratic reduction under repetitive-service random-destination blocking. | [18] | 3.0.4 |
| BA | mapamva.upper, mapamva.lower | MAP-AMVA LP bound for a closed network with MAP/MMPP2 service at one FCFS station; reads the correlation, not the mean alone. | [23] | 3.0.7 |
| BA | spnlp2.upper, spnlp2.lower | Moment-relaxation LP for a stochastic Petri net: the uniformized evolution equation for the first two moments plus invariants, state equation and Chernoff enabling bounds. Exponential firings. | [71] | 3.0.7 |
| BA | spnlp1.upper, spnlp1.lower | Variant dropping the second-moment, covariance and Little's law constraints. | [71] | 3.0.7 |
| CTMC | exact | Generate the explicit state space and solve the global balance equations of the full generator; the default. | [13] | 3.0.7 |
| CTMC | mdd | Hold the reachable set in a multi-valued decision diagram and solve K coupled level-CTMCs instead of the full generator; exact on product-form models, approximate otherwise. | [80] | 3.0.7 |
| LDES | default | One simulation run of the LDES engine (native common/ldes, falling back to common/ldes.jar). | - | 3.0.4 |
| LDES | para, parallel | Independent replications of the same run, averaged (config.replications, else 8); not a second engine. | - | 3.0.7 |
| FLD | matrix | First-order mean-field ODE built from the linear generator, with the hard min() capacity term. | [86], [98] | 2.0.21 |
| FLD | pnorm | The matrix drift with the hard min replaced by a p-norm smoothing (config.pstar, default 20). | [98] | 3.0.2 |
| FLD | softmin | The state-dependent drift with min() replaced by a Boltzmann softmin of parameter alpha (config.alpha, default 20). | - | 2.0.24 |
| FLD | statedep | Drift built in closed form from the phase-type parameters, allowing rates that are general functions of the state. | [86] | 2.0.0 |
| FLD | closing | Closing-method fluid iteration, the source of open classes is replaced by a saturated queue. | [13] | 2.0.21 |
| FLD | minnormal | Min-normal moment closure: E[min(X,c)] evaluated for jointly normal populations, so mean and covariance are integrated together. | [51] | 3.0.7 |
| FLD | refined | The min-normal closure plus the Gast-van Houdt O(1/N) correction taken about the mean-field fixed point; cache models use the cache-network decomposition. | [51], [48] | 3.0.7 |
| FLD | dae | Differential-algebraic system of equations; the main method for finite capacity regions and Petri nets. | [51], [52] | 3.0.7 |
| FLD | tbi | Trajectory-based iteration: the stations are partitioned into cells and each cell's IVP is solved with the others frozen (waveform relaxation) until the trajectories agree. | [101] | 3.0.6 |
| FLD | diffusion | Euler-Maruyama on the flow drift, reflected at zero and projected back onto each class population; stochastic, closed multiclass only. | [13] | 3.0.2 |
| FLD | kp | Diffusion limits for time-varying queueing networks of MAPt/Pht/∞ stations. | [64] | 3.0.7 |
| FLD | mfq | Markovian fluid-queue analyzer using BuTools for a Source-Queue-Sink shape, including the fluid priority queue; falls back to matrix off that shape. | [54] | 3.0.2 |
| FLD | mtginf | Exact Poisson law of the time-varying infinite-server queue: the mean E[lambda(t-Se)] and its time lag. | [44] | 3.0.7 |
| FLD | mol | Modified offered load: the infinite-server offered load fed into the stationary Erlang formula, which carries the time lag. | [77] | 3.0.7 |
| FLD | ggisgi | Deterministic fluid limit of the overloaded multiserver queue with abandonment, including the queue boundary. | [110] | 3.0.7 |
| FLD | ggingi | Truncated-Gaussian refinement of that fluid limit, carrying a general service process. | [70] | 3.0.7 |
| FLD | tvms | Time-varying many-server fluid queue solved forward on a grid at the staffing the model declares. | [69] | 3.0.7 |
| MAM | dec.source | Queue-by-queue decomposition: each station is solved as a QBD fed by the departure process its upstream neighbours produce. | - | 2.0.2 |
| MAM | dec.poisson | The same decomposition with the arrival superposition capped at one phase, i.e. Poisson inter-station traffic (space_max = 1). | - | 2.0.2 |
| MAM | dec.mmap | Decomposition in which each class's service process scaled by its utilization is used as the departure process (marked traffic). | [92] | 2.0.2 |
| MAM | dec.source.mmap | MMAP-based fork-join decomposition with mmap_max synchronization; the default on a general fork-join topology. | - | 3.0.5 |
| MAM | mna | Matrix-analytic network analysis: the open or closed MNA fixed point over INF/PS/FCFS stations. | [67] | 2.0.38 |
| MAM | ldqbd | Rate matrices and stationary vector of a level-dependent QBD; one FCFS queue plus one delay (closed) or one Poisson source (open), single class. | [87], [3] | 3.0.2 |
| MAM | bgchain | Flow-equivalent aggregation of the untagged closed classes into the second class of a background modulating chain. | [24] | 3.0.7 |
| MAM | retrial | The BMAP/PH/N/N bufferless retrial analyzer and the MAP/M/s+G reneging analyzer, which default also resolves to on either shape. | - | 3.0.2 |
| MVA | mva | Exact mean value analysis, the Reiser-Lavenberg recursion over the population lattice. | [90], [14] | 2.0.0 |
| MVA | amva | Approximate MVA: the default AMVA fixed point over the arrival-instant queue lengths. | - | 2.0.0 |
| MVA | sum | Summation method: closed models via sum_closed, open and mixed via the closing method sum_closing. | [13] | 3.0.6 |
| MVA | esum | Extended summation: the same analyzer plus the SCV corrections at FCFS and SIRO stations. | [13] | 3.0.6 |
| MVA | bs | Bard-Schweitzer proportional estimate of the arrival-instant queue length. | [13] | 2.0.16 |
| MVA | lin | Chandy-Neuse Linearizer: Bard-Schweitzer plus the per-class Delta correction refreshed over three passes. | [26] | 2.0.17 |
| MVA | gflin | Generalized fixed-point Linearizer, one uniform scaling exponent for all classes. | - | 2.0.30 |
| MVA | egflin | Extended generalized fixed-point Linearizer, a per-class scaling exponent; the AMVA default on single-server models. | - | 2.0.30 |
| MVA | dmlin | De Souza e Silva-Muntz Improved Linearizer: Linearizer's aggregate rewriting, same answer at lower cost. | [39] | 3.0.7 |
| MVA | qd | Queue-dependent AMVA: the arrival-instant estimate conditioned on the station's own queue length. | [22] | 2.0.16 |
| MVA | qdlin | Queue-dependent Linearizer, the QD correction inside the Linearizer fixed point. | - | 2.0.17 |
| MVA | aql | Aggregate Queue Length: carries R+1 population points and removes Schweitzer's proportionality error. Single-server models only. | [113] | 2.0.17 |
| MVA | qsa | Queue-shift approximation correcting the arrival-instant queue lengths. Single-server models only. | [100] | 3.0.7 |
| MVA | tay | Tay's arrival-instant approximation: throughput elasticities in place of the population shift. Single-server models only. | [105] | 3.0.7 |
| MVA | scat | Neuse-Chandy SCAT, i.e. the generalized Linearizer at alpha = 1 with a single Delta refresh pass. | [84] | 3.0.7 |
| MVA | qli | Wang-Sevcik Queue Line approximation of the arrival-instant queue. | [107] | 2.0.16 |
| MVA | fli | Wang-Sevcik Fraction Line approximation, the FL correction term. | [107] | 2.0.16 |
| MVA | lcp | Bard's large customer population estimate: Bard-Schweitzer with the (N-1)/N factor dropped. | [6] | 3.0.7 |
| MVA | chow | JMT-compatible Chow: the full-population aggregate-queue estimate used by LCP. | [29] | 3.0.7 |
| MVA | pamb | Proportional approximation PAM-B, noniterative: proportional seed of the queue lengths plus one final MVA step. | [57] | 3.0.7 |
| MVA | pami | PAM-I: the proportional seed with throughputs capped at full centre utilization. | [57] | 3.0.7 |
| MVA | pamt | PAM-T: the proportional seed plus the last two MVA steps. | [57] | 3.0.7 |
| MVA | clust | Clustering: subnetworks solved exactly for their local classes, foreign classes carried as a per-centre utilization. | [37] | 3.0.7 |
| MVA | ab | Akyildiz-Bolch AMVA, which handles multiserver stations directly instead of through the Seidmann surrogate delay. | [103] | 3.0.2 |
| MVA | schmidt | Schmidt's MVA for class-dependent FCFS multiserver stations. | [103] | 3.0.2 |
| MVA | schmidt-ext | The extended Schmidt multiserver correction, built from the network with one class-r customer tagged. | [103] | 3.0.2 |
| MVA | marie | Marie's iterative aggregation-decomposition for closed networks with non-exponential (Coxian) FCFS service. | [74] | 3.0.6 |
| MVA | priomva | Chandy-Lakshmi preemptive-resume priority arm: the tagged job's own service is inflated by 1/(1-sigma) along with the queued work. | [25] | 3.0.7 |
| MVA | sqni | Square-root noniterative closed form for one queueing station plus one delay. | - | 2.0.27 |
| MVA | mvac | Exact mean value analysis by chain: recurs on chains rather than on the population vector, closed single-server product-form only. | [32] | 3.0.6 |
| MVA | sqd | Smith Queue Decomposition, the AMVA handler for Blocking-After-Service; runs on the single closed chain and disaggregates back to classes. | - | 3.0.6 |
| MVA | sjn.mva | Shortest-job-next: the conditional waiting-time equation stepped exactly over the population lattice. | [58] | 3.0.7 |
| MVA | sjn.amva | Shortest-job-next closed by a Schweitzer fixed point on the size-resolved queue length. | [58] | 3.0.7 |
| MVA | amva.mapqn | Horizontal-cut MVA for one exponential delay and one FCFS queue with MAP service: one linear solve per lattice point. | [23] | 3.0.7 |
| MVA | qna | Whitt's Queueing Network Analyzer: two-moment traffic decomposition of an open network into GI/G/1 queues. | [109] | 2.0.22 |
| MVA | rqna | Robust queueing network analyzer: index-of-dispersion decomposition and robust queueing bounds, the default for bursty (MAP/MMPP) open arrivals. | [111] | 3.0.6 |
| MVA | rqt | Robust queueing theory: polyhedral uncertainty sets and the worst-case system time per node, with the robust Burke calculus for the network. | [5] | 3.0.7 |
| MVA | mm1 | M/M/1 exact response time. | [13] | 2.0.0 |
| MVA | mmk | M/M/k exact response time (Erlang C). | - | 2.0.1 |
| MVA | mg1 | M/G/1 exact response time (Pollaczek-Khinchine). | [13] | 2.0.0 |
| MVA | gm1 | G/M/1 exact response time: the PH/M/1 sigma root when the arrival process is Markovian, an LST root otherwise. | - | 2.0.0 |
| MVA | gig1.allen | G/G/1 Allen-Cunneen two-moment approximation. | [13] | 2.0.0 |
| MVA | gig1.kingman | Kingman's heavy-traffic upper bound on the G/G/1 waiting time. | [13] | 2.0.0 |
| MVA | gig1.heyman | Heyman's G/G/1 approximation. | - | 2.0.0 |
| MVA | gig1.gelenbe | Gelenbe's diffusion approximation with instantaneous-return boundary. | - | 2.0.0 |
| MVA | gig1.kimura | Kimura's diffusion-interpolation G/G/1 approximation. | - | 2.0.0 |
| MVA | gig1.kobayashi | Kobayashi's diffusion G/G/1 approximation. | [13] | 2.0.0 |
| MVA | gig1.klb | Kraemer-Langenbach-Belz refinement of Allen-Cunneen; the default choice for G/G/1. | [13] | 2.0.0 |
| MVA | gig1.marchal | Marchal's G/G/1 approximation. | [13] | 2.0.0 |
| MVA | gig1.extremal | Tight two-moment extremal upper bound on the G/G/1 queue. | - | 3.0.7 |
| MVA | gigk | G/G/k approximation with the rho-dependent alpha correction; the default choice for k > 1. | - | 2.0.1 |
| MVA | gigk.kingman_approx | G/G/k approximation scaling the M/M/k waiting time by (ca^2+cs^2)/2. | - | 2.0.1 |
| MVA | gigk.whitt | Whitt's (1993) G/G/k refinement. | - | 3.0.7 |
| MVA | gigk.diffusion | G/GI/n/m diffusion approximation with asymptotic peakedness; carries a finite buffer. | - | 3.0.7 |
| MVA | qed | Halfin-Whitt quality-and-efficiency-driven limit of the M/M/k queue. | - | 3.0.7 |
| MVA | erlanga | Erlang A, the exact M/M/s/r+M chain with exponential abandonment; the default choice when the patience law is exponential. | - | 3.0.7 |
| MVA | mgisrgi | Whitt's M/GI/s/r+GI engineering solution by state-dependent Markovian abandonment; the default choice for a non-exponential patience law. | - | 3.0.7 |
| NC | exact | Exact normalizing constant: convolution or RECAL at fixed rates, pfqn_gld/comomld/clw on a rate lattice, the OI convolution, the M/M/1/K closed form, the loss-network residue transform, the paired LCFS convolution. | - | 2.0.0 |
| NC | ca | Multiclass convolution algorithm: Buzen's single-chain recursion generalized to several closed chains. | [15], [89] | 2.0.0 |
| NC | comom | Class-oriented method of moments for the repairman model (a delay and at most one queueing station). | [16] | 2.0.8 |
| NC | comomld | Load-dependent CoMoM, same shape restriction. | [20] | 2.0.27 |
| NC | rgf | Recursion by generating functions, single class by construction; multiclass input falls back to the exact convolution. | - | 2.0.9 |
| NC | ger | Exact closed form by iterated residues of the rational generating function, one class per elimination. | [49] | 3.0.7 |
| NC | divdiff | Divided-difference closed form of the multiclass constant: Gordon's partial fraction at distinct induced demands, the general expansion at repeated ones. | [17] | 3.0.7 |
| NC | rec | Normalizing constant by one memoised walk of a decision diagram over the reachable set; the only method admissible on a Petri net. | [4] | 3.0.7 |
| NC | mmint2 | McKenna-Mitra integral by Gauss-Legendre quadrature; a delay plus a single queueing station. | [79] | 2.0.8 |
| NC | gleint | The same integral and the same shape, second quadrature variant. | [79] | 2.0.27 |
| NC | cub | Grundmann-Moeller cubature on the simplex, exact for the polynomial integrand at order ceil((N-1)/2). | [17] | 2.0.23 |
| NC | le | Logistic expansion: the Laplace saddle point of the integral after the logistic transform. | [17] | 2.0.0 |
| NC | ble | The logistic expansion with an empirical per-direction correction, better on lG than le. | [17] | 3.0.7 |
| NC | aghq | Adaptive Gauss-Hermite quadrature of the simplex factor, q nodes per direction; q = 1 reproduces le. | [68] | 3.0.7 |
| NC | kt | Knessl-Tier asymptotic expansion of the normalizing constant. | [63] | 2.0.8 |
| NC | bkt | Knessl-Tier minus the exact Stirling remainder that steepest descent drops in each Laplaced class direction. | [63] | 3.0.7 |
| NC | lekt | Whichever of ble and bkt is cheaper: the R-dimensional saddle point when R <= M, the M-dimensional logistic mode otherwise. | [17], [63] | 3.0.7 |
| NC | bk | Birman-Kogan saddle-point expansion of the multichain partition function. | [12] | 3.0.7 |
| NC | bkue | Van der Waerden uniform expansion, dominant pole and saddle point in one erfc formula; multichain models fall back to bk. | [12] | 3.0.7 |
| NC | lc | Birman-Kogan Algorithm 2: load concealment, reducing a multichain network to single-chain problems. | [12] | 3.0.7 |
| NC | lc.ue | Algorithm 2 with the uniform expansion as its single-chain solver. | [12] | 3.0.7 |
| NC | pana | PANACEA normal-usage asymptotic expansion of the constant, load-independent. | [78], [93] | 2.0.0 |
| NC | panald | Load-dependent PANACEA expansion and its pseudonetwork coefficients. | [81] | 3.0.7 |
| NC | mci | Monte Carlo integration of the constant; on a loss network the Ross-Wang importance-sampling summation. | [97] | 2.0.0 |
| NC | imci | Improved (tilted) Monte Carlo integration of the same integral. | [108] | 2.0.0 |
| NC | ls | Logistic sampling: Monte Carlo on the logistic-transformed integral. | [17] | 2.0.0 |
| NC | is | Sample-an-ordering importance sampling, with load-dependent, OI and pass-and-swap variants; closed populations only. | [30] | 3.0.6 |
| NC | sampling | Shape-selected sampler: pfqn_mmsample2 for one queue, tilted MCI when stations outnumber classes, otherwise pfqn_ls; the OI importance sampler on a pass-and-swap model. | - | 2.0.8 |
| NC | mcmc | Markov-chain Monte Carlo estimate of the normalizing constant. | [27] | 3.0.7 |
| NC | cftp | Monotone coupling-from-the-past perfect sampler of the closed single-class product-form stationary distribution: iid states are drawn from the balance function, so neither the state space nor G is computed. | [62] | 3.0.7 |
| NC | cftp.approx | The rapidly-mixing approximate sampler of the same construction, instead of the exact CFTP coupling. | [62] | 3.0.7 |
| NC | propfair | Proportionally fair allocation approximation (Walton). | - | 2.0.8 |
| NC | clw | Numerical inversion of the generating function; the Bertozzi-McKenna transform kernel on a rate lattice. | [28], [9] | 3.0.6 |
| NC | rd | Reduction heuristic for the load-dependent normalizing constant. | [20] | 2.0.12 |
| NC | nrp | Norlund-Rice probit approximation of the load-dependent constant. | [20] | 2.0.12 |
| NC | nrl | Norlund-Rice logit approximation of the load-dependent constant. | [20] | 2.0.12 |
| NC | nre | Norlund-Rice integral by Daniels steepest descent with the Barndorff-Nielsen-Cox second-order correction. | [20], [35], [7] | 3.0.7 |
| NC | mem | Kouvatsos maximum entropy (GE/GE/1, GE/GE/c, GE/GE/inf blocks), including finite-buffer open queues. The separate M/M/1/K loss-system route is available under exact. | [65], [104] | 3.0.2 |
| NC | morrison | Two-term heavy-usage asymptotic expansion of the generating function for a closed think+DPS network; non-product-form, so it reports no lG. | [82] | 3.0.7 |
| NC | sdr | State-dependent routing: Krzesinski's product-form joint distribution and routing probabilities for an entry centre. | [66] | 3.0.7 |
| NC | sdr.mva | Mean value analysis and convolution of the same state-dependent-routing product form, single-centre branches. | [66] | 3.0.7 |
| NC | ms | Manjunath-Sikdar transform of the loss-network analyzer; loss networks only. | [73] | 3.0.7 |
| NC | erlangfp | Erlang fixed-point (reduced-load) approximation of the loss network. | [60], [59], [94] | 3.0.2 |
| NC | rayint | On a Source-Cache-Sink model an alias of spm; on an open delayed-hit retrieval cache the ray/WKB expansion, infinite-server fetch only. | - | 2.0.38 |
| NC | spm | Saddle-point miss-ratio expansion of an isolated cache, size-tilted once items carry storage costs. | - | 3.0.1 |
| SSA | serial | One Gillespie trajectory over the model's event set, sampled event by event. | [50] | 2.0.0 |
| SSA | para, pana, parallel | config.nreplicas independent replications of the serial method, averaged; each replication gets ceil(samples/nreplicas) events and seed seed+r-1. | - | 2.0.0 |
| SSA | nrm | Gibson-Bruck next reaction method: an indexed priority queue over reaction-form events with a dependency graph, asked for by name. | [1] | 2.0.40 |
| AUTO | heur | Rank every candidate approximate analytical method by accuracy. | - | 2.0.27 |
| AUTO | exact | Restrict the candidates to exact solvers. | - | 2.0.0 |
| AUTO | sim | Restrict the candidates to simulation solvers. | - | 3.0.2 |
| AUTO | fast | Rank for speed. | - | 3.0.2 |
| AUTO | accurate | Rank for accuracy. | - | 3.0.2 |
| AUTO | bound | Return a bounding method for throughput and queue-lengths. | - | 3.0.7 |
| ENV | meanfield | Mean-field coupling of the stages via the blending method. | - | 3.0.6 |
| ENV | meancov | The meanfield method extended to carry covariances, seeding the next stage through config.init_qlen/init_qcov. | - | 3.0.8 |
| ENV | statevec | Coupling of the stages via the blending method based on the full joint state distribution vector. | - | 3.0.6 |
| ENV | statedep | Extension of the meanfield method in which the environment transition depends on the state it leaves. | - | 3.0.6 |
| ENV | smp | The mean-field coupling with the stage probabilities recomputed from the embedded jump chain of the transition CDFs and the mean holding times. Transitions must still be Markovian (phase-type). | - | 3.0.2 |
| ENV | avg | Fast-environment limit: the stages are averaged instead of iterated. | - | 3.0.6 |
| ENV | dec | Slow-environment limit: the stages are decoupled and solved separately. | - | 3.0.6 |
| LN | srvn.ph | One submodel per server, each activity graph reduced by exact series-parallel reduction into one phase-type entry service process. | - | 3.0.7 |
| LN | srvn.cs | One submodel per server with the activity graph encoded as class routing (a class per task, entry, activity and call); serves every layered feature. | - | 3.0.7 |
| LN | flat.cs | Squashed layering, i.e., every processor and task appears in a single submodel. | - | 3.0.7 |
| LN | flat.ph | The same single submodel with each activity graph reduced to a phase-type entry service process. | - | 3.0.7 |
| LN | moment3 | The srvn.cs method with propagation of three response time moments across the layers. | - | 2.0.13 |
| UQ | dd | Discrete design over the support of the prior distribution. | - | 3.0.6 |
| UQ | quad | Gaussian quadrature discretization of the continuous priors into a weighted design. | - | 3.0.6 |
| UQ | mc | Monte Carlo sampling of the priors. | - | 3.0.6 |
| JMT | jsim | JSIMengine discrete-event simulation of the model. | [8] | 2.0.0 |
| JMT | default | Resolves to jsim; on a finite timespan it averages config.replications (default 10) independent JSIM runs into transient means. | - | 3.0.2 |
| JMT | jmva | The JMVA analytical engine, algorithm left to JMVA. | - | 2.0.0 |
| JMT | jmva.mva | Exact MVA inside JMVA. | [90] | 2.0.0 |
| JMT | jmva.amva | JMVA's approximate MVA. | [13] | 2.0.0 |
| JMT | jmva.recal | RECAL, the recursion by chain for the normalizing constant. | [33] | 2.0.0 |
| JMT | jmva.comom | Class-oriented method of moments; single-chain models only, because JMVA's multiclass CoMoM perturbs a singular system and reports the result as exact. | [16] | 2.0.0 |
| JMT | jmva.chow | Chow's approximate MVA. | [29] | 2.0.0 |
| JMT | jmva.bs | Bard-Schweitzer inside JMVA. | [13] | 2.0.0 |
| JMT | jmva.aql | Aggregate Queue Length inside JMVA. | [113] | 2.0.0 |
| JMT | jmva.lin | Linearizer inside JMVA. | [26] | 2.0.0 |
| JMT | jmva.dmlin | De Souza-Muntz Improved Linearizer inside JMVA. | [39] | 2.0.0 |
| LQNS | lqns | Run lqns with -Pstop-on-message-loss=false. | - | 2.0.0 |
| LQNS | srvn | lqns -Playering=srvn: the SRVN layering strategy. | - | 2.0.0 |
| LQNS | exactmva | lqns -Pmva=exact: exact MVA inside the layer solves. | - | 2.0.26 |
| LQNS | srvn.exactmva | Both of the above: SRVN layering with exact MVA. | - | 2.0.26 |
| LQNS | lqsim | lqsim, the LQN discrete-event simulator, at options.samples run length. | - | 2.0.0 |
| LQNS | lqns.default | Plain lqns with no LINE pragmas at all, i.e. the tool's own defaults. | - | 2.0.0 |
| LQNS | qns | On a Network: qnsolver with the rolia multiserver approximation (also the Network default). | - | 2.0.25 |
| LQNS | qns.conway | On a Network: Conway's multiserver approximation for chain-dependent FCFS queues, built on the multinomial all-servers-busy probability of de Souza e Silva and Muntz. | [31], [38] | 2.0.25 |
| LQNS | qns.rolia | On a Network: Rolia's multiserver approximation, in the per-class Rolia-Franks form that LQNS implements. | [95], [96], [46] | 2.0.25 |
| LQNS | qns.zhou | On a Network: Zhou's arrival-theorem binomial (AB) multiserver approximation, with class merging for multiple classes. | [114], [115] | 2.0.25 |
| LQNS | qns.suri | On a Network: Suri-Sahu-Vernon multiserver approximation; refused where a multi-server station is present, since qnsolver -m does not know it. | [103] | 2.0.25 |
| LQNS | qns.reiser | On a Network: Reiser-Lavenberg MVA with load-dependent marginal probabilities, exact for a product-form multi-server station. | [90], [88] | 2.0.25 |
| LQNS | qns.schmidt | On a Network: Schmidt's multiserver approximation for class-dependent exponential servers; same restriction as qns.suri. | [99] | 2.0.25 |