Algorithms
Every solution method LINE offers, in one table. A method is asked for by name at the solver that owns it, as SolverMVA(model,'amva.bs') in MATLAB or through options.method, and aliases for the same algorithm share a row. The Solver column links to that solver's own page, where the method's model restrictions, configuration fields and references are given in full.
Which of these a given model can actually run is decided by the model, not by the list: a method whose assumptions the model breaks is refused by name rather than served by a substitute. Ask the solver what it will accept for the model in hand with solver.listValidMethods(), and see AUTO for the ranked selection that picks one for you. The names below are the MATLAB spelling; the Java, Python and C++ implementations use the same names. AUTO additionally accepts every family name (mva, nc, ctmc, fluid, mam, ag, ba, ssa, ldes, jmt, qns, ln, env, lqns, uq) and every family-qualified label family.method built from the rows below, so those combinations are not repeated here.
| Solver | Method | Algorithm and applicability | Reference |
|---|---|---|---|
| AG | default | Runs inap. | — |
| AG | exact | Compatibility alias: warns and resolves to inap; it does not select a separate exact algorithm. | — |
| AG | inap | RCAT fixed point for cooperating processes. Uses mean state-wise reversed-rate ratios for birth-death components and rate conservation for phase-expanded or non-birth-death components; exact when the RCAT product-form conditions hold. | — |
| AG | inapplus | The same RCAT solution with the reversed rate estimated by rate conservation instead. | — |
| AG | inapinf | Matrix-geometric decomposition of the cooperating processes on the infinite state space. | — |
| BA | default | The noniterative bound ladder: gb.upper on an ordinary closed model, qrf.bas where a blocking polytope fits. | — |
| BA | auto, auto.upper, auto.lower | Evaluate every feasible noniterative bound and keep the tightest side; a family that rejects the model is skipped. | — |
| BA | aba.upper, aba.lower | Asymptotic Bounds Analysis: X <= min(1/Dmax, N/(Z+sum D)) and its pessimistic counterpart. | — |
| BA | bjb.upper, bjb.lower | Balanced Job Bounds: the ABA bracket refined by substituting the mean and maximum demand into the residence time. | — |
| 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)). | — |
| 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. | — |
| BA | sb.upper, sb.lower | Harel's simple closed-network throughput bound, both sides; no delay station. | — |
| BA | harel.upper | Upper throughput bound extrapolated from the exact throughput at population n <= 7. | — |
| BA | harel.lower | Lower throughput bound from the first and N-th power sums of the relative utilizations. | — |
| BA | mwba.upper | Majumdar-Woodside robust (worst-case) throughput bound, discipline-insensitive, NBUE service; the only closed family keeping HOL and the preemptive-priority disciplines. | — |
| BA | mwba.lower | The matching robust throughput guarantee, lower side. | — |
| BA | pbh.upper, pbh.lower | Eager-Sevcik Performance Bound Hierarchy: options.level MVA steps from an ABA-initialized residence, tightening to exact MVA as the level reaches N. | — |
| BA | pbk.upper, pbk.lower | PB(k): the same hierarchy at iteration count k, evaluated at populations N, N-1, ..., N-k. | — |
| BA | bjbk.upper, bjbk.lower | BJB(k): the iterative Balanced Job Bound, one exact MVA step per iteration from the balanced seed. | — |
| BA | cbh.upper, cbh.lower | Convolutional Bound Hierarchy: one column of Buzen's g-array filled with BJB estimates, the remaining stations convolved exactly. | — |
| BA | ssd.upper, ssd.lower | Dallery-Suri server-station disaggregation bound with the think-time correction; the classical family that accepts multiserver stations. | — |
| BA | sib.upper, sib.lower | Srinivasan's Successively Improving Bounds on cycle time and throughput; zero think time only. | — |
| BA | cub.upper | Kerola composite multiclass upper bound on per-class throughput. | — |
| BA | mbjb.lower | The multiclass Balanced Job Bound that seeds cub.upper. | — |
| BA | looping.upper, looping.lower | Eager's multiclass queue-length bracket built from the unaccounted-congestion heaps. | — |
| BA | scb.upper | Demand-free upper bound on multiclass throughput, capped by U <= 1; brackets the multiclass system the single-class model aggregates. | — |
| BA | scb.lower | Exact single-class throughput as a lower bound on the multiclass throughput, with the single-class utilizations as lower bounds. | — |
| BA | ldbcmp.lower | Anselmi-Cremonesi lower throughput bound for closed single-class BCMP networks via the asymptotic closed-open equivalence. | — |
| BA | bpt.lower | Bertsimas-Paschalidis-Tsitsiklis first-order LP relaxation of the achievable region; open networks. | — |
| 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. | — |
| BA | snc.upper | Stochastic network calculus: MGF arrival and service envelopes propagated hop by hop over a feed-forward open network. | — |
| BA | qr | Friendly alias of the QRF quadratic reduction bound; resolves to qrf.mmi. | — |
| BA | lr, lr.upper, lr.lower | LP-based Linear Reduction bound, one LP per station; not an alias of qrf.mmi.linear. | — |
| BA | qrf.mmi | Quadratic reduction on the closed MAP queueing chain, mutual-information objective, nonlinear no-blocking reduction. | — |
| BA | qrf.mem | The same reduction with the maximum-entropy objective. | — |
| 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. | — |
| 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. | — |
| BA | qrf.mmi.linear | The same load-dependent envelope with explicit equality constraints in place of the nonlinear reduction. | — |
| BA | qrf.bas | LP quadratic reduction over the Blocking-After-Service polytope; may derive the blocking tables from station capacities. | — |
| BA | qrf.bas.mmi | MMI objective over that blocking polytope; concave there, so each codebase settles on the vertex its own solver reaches. | — |
| BA | qrf.bas.mem | Maximum-entropy objective over the blocking polytope. | — |
| BA | qrf.bas.bethe | Tree-reweighted (Bethe) free entropy over the blocking polytope, the start-point-independent blocking answer. | — |
| BA | qrf.rsrd | LP quadratic reduction under repetitive-service random-destination blocking. | — |
| 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. | — |
| BA | spnlp.upper, spnlp.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. | — |
| BA | spnlp.op.upper, spnlp.op.lower | The operational variant, dropping the second-moment, covariance and Little's-law families; any phase-type law, much looser. | — |
| CTMC | default | Generate the explicit state space and solve the global balance equations of the full generator. | [1] |
| CTMC | exact | The same exact solve, asked for by name. | — |
| CTMC | gpu | A no-op alias of default in MATLAB: ctmc_solve has a gpuArray case, but the numeric path reaches the solve through the block decomposition, so the name never arrives. Kept for parity with the JAR and python lists. | — |
| 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. | — |
| CTMC | cftp | Monotone coupling-from-the-past perfect sampler of the closed product-form stationary distribution. | — |
| CTMC | cftp.approx | The rapidly-mixing approximate sampler of the same construction, instead of the exact CFTP coupling. | — |
| LDES | default | One simulation run of the LDES engine (native common/ldes, falling back to common/ldes.jar). | — |
| LDES | parallel | Independent replications of the same run, averaged (options.replications, else 8); not a second engine. | — |
| FLD | default, fluid.default | Resolve to the route the model needs: dae for a Petri net, a binding buffer or a capacity region, rmf for a cache, else minnormal where it applies, else closing for DPS, else matrix. The qualified spelling fluid.default is listed by the Java, Python and C++ implementations only. | — |
| FLD | matrix, fluid.matrix | First-order mean-field ODE built from the linear generator, with the hard min() capacity term; the historical default. | [1], [2] |
| FLD | pnorm, fluid.pnorm | The matrix drift with the hard min replaced by a p-norm smoothing (config.pstar, default 20). | [2] |
| FLD | softmin, fluid.softmin | The state-dependent drift with min() replaced by a Boltzmann softmin of parameter alpha (config.alpha, default 20). | — |
| FLD | statedep, fluid.statedep | Drift built in closed form from the phase-type parameters, allowing rates that are general functions of the state. | [1] |
| FLD | closing, fluid.closing | Closing-method fluid iteration: the inner fixed point over per-station throughputs used for open, mixed and DPS models. | [3] |
| FLD | minnormal, fluid.minnormal | Min-normal moment closure: E[min(X,c)] evaluated for jointly normal populations, so mean and covariance are integrated together. | — |
| FLD | refined, fluid.refined | The min-normal closure plus Gast's O(1/N) correction taken about the mean-field fixed point. | — |
| FLD | dae, fluid.dae | The same min-normal closure stated and solved as one differential-algebraic system; the only route for Petri nets, binding buffers and capacity regions. | — |
| FLD | tbi, fluid.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. | — |
| FLD | diffusion, fluid.diffusion | Euler-Maruyama on the flow drift, reflected at zero and projected back onto each class population; stochastic, closed multiclass only. | [4] |
| FLD | kp, fluid.kp | Ko-Pender fluid and diffusion limits of the time-varying infinite-server network. Integrates the mean and covariance ODEs and returns second moments. | — |
| FLD | rmf, fluid.rmf | Refined mean-field decomposition of a cache-queueing model; degenerates to matrix when the model has no Cache node. | — |
| FLD | mfq, fluid.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. | [5] |
| FLD | butools | Alias of mfq (the one name of the family with no fluid. twin). | — |
| FLD | aoi, fluid.aoi | Alias of mfq, reaching the age-of-information fluid solver when the topology qualifies. | — |
| FLD | mtginf, fluid.mtginf | Exact Poisson law of the time-varying infinite-server queue: the mean E[lambda(t-Se)] and its time lag. | — |
| FLD | mol, fluid.mol | Modified offered load: the infinite-server offered load fed into the stationary Erlang formula, which carries the time lag. | — |
| FLD | ggisgi.fluid, ggisgi, fluid.ggisgi | Deterministic fluid limit of the overloaded multiserver queue with abandonment, including the queue boundary. | — |
| FLD | ggingi.tga, tga, fluid.tga | Truncated-Gaussian refinement of that fluid limit, carrying a general service law. | — |
| FLD | tvms, fluid.tvms | Time-varying many-server fluid queue solved forward on a grid at the staffing the model declares. | — |
| MAM | default | Pick the route from the topology: the fork-join codes on a homogeneous fork-join, the retrial or reneging analyzer on those shapes, otherwise the dec.source decomposition. | [1] |
| MAM | dec.source | Queue-by-queue decomposition: each station is solved as a QBD fed by the departure process its upstream neighbours produce. | — |
| MAM | dec.poisson | The same decomposition with the arrival superposition capped at one phase, i.e. Poisson inter-station traffic (space_max = 1). | — |
| MAM | dec.mmap | Decomposition in which each class's service law scaled by its utilization is used as the departure process (marked traffic). | — |
| MAM | dec.source.mmap | MMAP-based fork-join decomposition with mmap_max synchronization; the default on a general fork-join topology. | — |
| MAM | mna | Matrix-analytic network analysis: the open or closed MNA fixed point over INF/PS/FCFS stations. | [2] |
| 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. | — |
| MAM | bgchain | Flow-equivalent aggregation of the untagged closed classes into the second class of a background modulating chain. | — |
| 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. | — |
| MVA | default | Let mvaDispatch pick the route: exact MVA on a product-form model, AMVA otherwise, plus the single-queue, load-dependent, BAS, OI/PAS, SJN, polling and cache-in-QN routes on the shapes that own them. | — |
| MVA | mva | Exact mean value analysis, the Reiser-Lavenberg recursion over the population lattice. | — |
| MVA | exact | The same exact recursion asked for by name; refused where no product-form solution exists. | [1] |
| MVA | amva | Approximate MVA: the default AMVA fixed point over the arrival-instant queue lengths. | — |
| MVA | sum | Summation method: closed models via sum_closed, open and mixed via the closing method sum_closing. | — |
| MVA | esum | Extended summation: the same analyzer plus the SCV corrections at FCFS and SIRO stations. | — |
| MVA | bs, amva.bs | Bard-Schweitzer proportional estimate of the arrival-instant queue length. | [3] |
| MVA | lin, amva.lin | Chandy-Neuse Linearizer: Bard-Schweitzer plus the per-class Delta correction refreshed over three passes. | [2] |
| MVA | gflin | Generalized fixed-point Linearizer, one uniform scaling exponent for all classes. | — |
| MVA | egflin | Extended generalized fixed-point Linearizer, a per-class scaling exponent; the AMVA default on single-server models. | — |
| MVA | dmlin, amva.dmlin | De Souza e Silva-Muntz Improved Linearizer: Linearizer's aggregate rewriting, same answer at lower cost. | — |
| MVA | qd, amva.qd | Queue-dependent AMVA: the arrival-instant estimate conditioned on the station's own queue length. | [4] |
| MVA | qdlin, amva.qdlin | Queue-dependent Linearizer, the QD correction inside the Linearizer fixed point. | — |
| MVA | aql, amva.aql | Aggregate Queue Length: carries R+1 population points and removes Schweitzer's proportionality error. Single-server models only. | — |
| MVA | qsa, amva.qsa | Queue-shift approximation correcting the arrival-instant queue lengths. Single-server models only. | — |
| MVA | tay, amva.tay | Tay's arrival-instant approximation: throughput elasticities in place of the population shift. Single-server models only. | — |
| MVA | scat, amva.scat | Neuse-Chandy SCAT, i.e. the generalized Linearizer at alpha = 1 with a single Delta refresh pass. | — |
| MVA | qli, amva.qli | Wang-Sevcik Queue Line approximation of the arrival-instant queue. | — |
| MVA | fli, amva.fli | Wang-Sevcik Fraction Line approximation, the FL correction term. | — |
| MVA | lcp, amva.lcp | Bard's large customer population estimate: Bard-Schweitzer with the (N-1)/N factor dropped. | — |
| MVA | chow, amva.chow | Chow's second approximation: the LCP solution corrected once by forward-difference theta terms. | — |
| MVA | pamb, amva.pamb | Proportional approximation PAM-B, noniterative: proportional seed of the queue lengths plus one final MVA step. | — |
| MVA | pami, amva.pami | PAM-I: the proportional seed with throughputs capped at full centre utilization. | — |
| MVA | pamt, amva.pamt | PAM-T: the proportional seed plus the last two MVA steps. | — |
| MVA | clust, amva.clust | Clustering: subnetworks solved exactly for their local classes, foreign classes carried as a per-centre utilization. | — |
| MVA | ab, amva.ab | Akyildiz-Bolch AMVA, which handles multiserver stations directly instead of through the Seidmann surrogate delay. | — |
| MVA | schmidt, amva.schmidt | Schmidt's MVA for class-dependent FCFS multiserver stations. | — |
| MVA | schmidt-ext, amva.schmidt-ext | The extended Schmidt multiserver correction, built from the network with one class-r customer tagged. | — |
| MVA | marie, amva.marie | Marie's iterative aggregation-decomposition for closed networks with non-exponential (Coxian) FCFS service. | — |
| MVA | priomva, amva.priomva | Chandy-Lakshmi preemptive-resume priority arm: the tagged job's own service is inflated by 1/(1-sigma) along with the queued work. | — |
| MVA | sqni | Square-root noniterative closed form for one queueing station plus one delay. | — |
| MVA | mvac | Exact mean value analysis by chain: recurs on chains rather than on the population vector, closed single-server product-form only. | — |
| MVA | sqd | Smith Queue Decomposition, the AMVA handler for Blocking-After-Service; runs on the single closed chain and disaggregates back to classes. | — |
| MVA | sjn.mva | Shortest-job-next: the conditional waiting-time equation stepped exactly over the population lattice. | — |
| MVA | sjn.amva | Shortest-job-next closed by a Schweitzer fixed point on the size-resolved queue length. | — |
| MVA | amva.mapqn | Horizontal-cut MVA for one exponential delay and one FCFS queue with MAP service: one linear solve per lattice point. | — |
| MVA | qna | Whitt's Queueing Network Analyzer: two-moment traffic decomposition of an open network into GI/G/1 queues. | — |
| MVA | rqna | Robust queueing network analyzer: index-of-dispersion decomposition and robust queueing bounds, the default for bursty (MAP/MMPP) open arrivals. | — |
| MVA | rqt | Robust queueing theory: polyhedral uncertainty sets and the worst-case system time per node, with the robust Burke calculus for the network. | — |
| MVA | mm1 | M/M/1 exact response time. | — |
| MVA | mmk | M/M/k exact response time (Erlang C). | — |
| MVA | mg1, mgi1 | M/G/1 exact response time (Pollaczek-Khinchine). | — |
| MVA | gm1, gim1 | G/M/1 exact response time: the PH/M/1 sigma root when the arrival law is Markovian, an LST root otherwise. | — |
| MVA | gig1, gig1.allen | G/G/1 Allen-Cunneen two-moment approximation. | — |
| MVA | gig1.kingman | Kingman's heavy-traffic upper bound on the G/G/1 waiting time. | — |
| MVA | gig1.heyman | Heyman's G/G/1 approximation. | — |
| MVA | gig1.gelenbe | Gelenbe's diffusion approximation with instantaneous-return boundary. | — |
| MVA | gig1.kimura | Kimura's diffusion-interpolation G/G/1 approximation. | — |
| MVA | gig1.kobayashi | Kobayashi's diffusion G/G/1 approximation. | — |
| MVA | gig1.klb | Kraemer-Langenbach-Belz refinement of Allen-Cunneen; the default choice for G/G/1. | — |
| MVA | gig1.marchal | Marchal's G/G/1 approximation. | — |
| MVA | gig1.extremal | Tight two-moment extremal upper bound on the G/G/1 queue. | — |
| MVA | gigk | G/G/k approximation with the rho-dependent alpha correction; the default choice for k > 1. | — |
| MVA | gigk.kingman_approx | G/G/k approximation scaling the M/M/k waiting time by (ca^2+cs^2)/2. | — |
| MVA | gigk.whitt | Whitt's (1993) G/G/k refinement. | — |
| MVA | gigk.diffusion | G/GI/n/m diffusion approximation with asymptotic peakedness; carries a finite buffer. | — |
| MVA | qed | Halfin-Whitt quality-and-efficiency-driven limit of the M/M/k queue. | — |
| MVA | erlanga | Erlang A, the exact M/M/s/r+M chain with exponential abandonment; the default choice when the patience law is exponential. | — |
| 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. | — |
| NC | default | Let pfqn_nc pick the evaluator adaptively from the model shape, and take the cache, retrieval, loss-network, Petri-net, DPS and state-dependent-routing routes where they apply. | — |
| 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. | — |
| NC | ca | Multiclass convolution algorithm: Buzen's single-chain recursion generalized to several closed chains. | — |
| NC | comom | Class-oriented method of moments for the repairman model (a delay and at most one queueing station). | [1] |
| NC | comomld | Load-dependent CoMoM, same shape restriction. | — |
| NC | rgf | Recursion by generating functions, single class by construction; multiclass input falls back to the exact convolution. | — |
| NC | ger | Exact closed form by iterated residues of the rational generating function, one class per elimination. | — |
| NC | divdiff | Divided-difference closed form of the multiclass constant: Gordon's partial fraction at distinct induced demands, the general expansion at repeated ones. | — |
| NC | rec | Normalizing constant by one memoised walk of a decision diagram over the reachable set; the only method admissible on a Petri net. | — |
| NC | mmint2 | McKenna-Mitra integral by Gauss-Legendre quadrature; a delay plus a single queueing station. | — |
| NC | gleint | The same integral and the same shape, second quadrature variant. | — |
| NC | cub, gm | Grundmann-Moeller cubature on the simplex, exact for the polynomial integrand at order ceil((N-1)/2). | [3] |
| NC | le | Logistic expansion: the Laplace saddle point of the integral after the logistic transform. | [3] |
| NC | ble | The logistic expansion with an empirical per-direction correction, better on lG than le. | — |
| NC | aghq | Adaptive Gauss-Hermite quadrature of the simplex factor, q nodes per direction; q = 1 reproduces le. | — |
| NC | kt | Knessl-Tier asymptotic expansion of the normalizing constant. | [4] |
| NC | bkt | Knessl-Tier minus the exact Stirling remainder that steepest descent drops in each Laplaced class direction. | — |
| NC | lekt | Whichever of ble and bkt is cheaper: the R-dimensional saddle point when R <= M, the M-dimensional logistic mode otherwise. | — |
| NC | bk | Birman-Kogan saddle-point expansion of the multichain partition function. | — |
| NC | bkue | Van der Waerden uniform expansion, dominant pole and saddle point in one erfc formula; multichain models fall back to bk. | — |
| NC | lc | Birman-Kogan Algorithm 2: load concealment, reducing a multichain network to single-chain problems. | — |
| NC | lc.ue | Algorithm 2 with the uniform expansion as its single-chain solver. | — |
| NC | pana | PANACEA normal-usage asymptotic expansion of the constant, load-independent. | [5], [6] |
| NC | panald | Load-dependent PANACEA expansion and its pseudonetwork coefficients. | — |
| NC | mci | Monte Carlo integration of the constant; on a loss network the Ross-Wang importance-sampling summation. | — |
| NC | imci | Improved (tilted) Monte Carlo integration of the same integral. | [7] |
| NC | ls | Logistic sampling: Monte Carlo on the logistic-transformed integral. | [3] |
| NC | is | Sample-an-ordering importance sampling, with load-dependent, OI and pass-and-swap variants; closed populations only. | — |
| 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. | — |
| NC | mcmc | Markov-chain Monte Carlo estimate of the normalizing constant. | — |
| NC | propfair | Proportionally fair allocation approximation (Walton). | — |
| NC | clw | Numerical inversion of the generating function; the Bertozzi-McKenna transform kernel on a rate lattice. | — |
| NC | rd | Reduction heuristic for the load-dependent normalizing constant. | [8] |
| NC | nrp | Norlund-Rice probit approximation of the load-dependent constant. | [8] |
| NC | nrl | Norlund-Rice logit approximation of the load-dependent constant. | [8] |
| NC | nre | Norlund-Rice integral by Daniels steepest descent with the Barndorff-Nielsen-Cox second-order correction. | — |
| 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 default and exact. | [9] |
| 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. | — |
| NC | sdr | State-dependent routing: Krzesinski's product-form joint distribution and routing probabilities for an entry centre. | — |
| NC | sdr.mva | Mean value analysis and convolution of the same state-dependent-routing product form, single-centre branches. | — |
| NC | ms | Manjunath-Sikdar transform of the loss-network analyzer; loss networks only. | — |
| NC | erlangfp | Erlang fixed-point (reduced-load) approximation of the loss network. | — |
| 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. | — |
| NC | spm | Saddle-point miss-ratio expansion of an isolated cache, size-tilted once items carry storage costs. | — |
| SSA | default | Prefer the next-reaction engine on closed queueing networks with INF/PS stations, and fall back to the serial engine wherever the reaction form does not cover the model. | — |
| SSA | serial | One Gillespie trajectory over the model's event set, sampled event by event. | [1] |
| SSA | ssa | Alias of serial. | — |
| SSA | para, parallel | config.nreplicas independent replications of the serial engine, averaged; each replication gets ceil(samples/nreplicas) events and seed seed+r-1. | — |
| SSA | nrm | Gibson-Bruck next reaction method: an indexed priority queue over reaction-form events with a dependency graph, asked for by name. | [2] |
| AUTO | default | Rank every candidate solver for this model and metric and run the winner. | — |
| AUTO | auto | Alias of default. | — |
| AUTO | heur | The same heuristic ranking, asked for explicitly. | — |
| AUTO | exact | Restrict the candidates to exact solvers (CTMC, exact MVA/NC). | — |
| AUTO | sim | Restrict the candidates to simulation solvers (SSA, JMT, LDES). | — |
| AUTO | fast | Rank for speed: MVA, then NC, then Fluid, then MAM. | — |
| AUTO | accurate | Rank for accuracy: Fluid, then MAM, then CTMC, then LDES. | — |
| AUTO | bound | Return a throughput/queue-length bracket instead of a point estimate; rewritten to the ba family with submethod auto. | — |
| ENV | default | Alias of meanfield. | — |
| ENV | meanfield | Mean-field coupling of the stages: only the marginal means cross an environment switch. | — |
| ENV | mean | Alias of meanfield, naming what crosses a switch rather than the limit it comes from. | — |
| ENV | meancov | The same coupling carrying a covariance beside the mean, seeding the next stage through config.init_qlen/init_qcov. | — |
| ENV | blend | Alias of default/meanfield since 2026-09-13; it named statevec before then. | — |
| ENV | statevec | State-vector coupling: the whole joint distribution crosses a switch (CTMC or MAM stage solvers, finite timespan). | — |
| ENV | statedep | Coupling in which the environment transition depends on the state it leaves. | — |
| ENV | smp | Accepted for a semi-Markov environment, but the arcs are still read as (D0,D1) pairs, so it runs the mean-field coupling on Markovian arcs only. | — |
| ENV | avg | Closed-form fast-environment limit: the stages are averaged instead of iterated. | — |
| ENV | dec | Closed-form slow-environment limit: the stages are decoupled and solved separately. | — |
| LN | default | Alias of srvn. | — |
| LN | srvn | srvn.ph where it can serve the model, srvn.cs otherwise; resolved once at layer build. | — |
| LN | srvn.ph | One submodel per server, each activity graph reduced by exact series-parallel reduction into one phase-type entry service law. | — |
| 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. | — |
| LN | flat | Alias of flat.cs. | — |
| LN | flat.cs | Squashed layering: a single submodel holding every processor and task, activity graphs encoded as class routing. | — |
| LN | flat.ph | The same single submodel with each activity graph reduced to a phase-type entry service law. | — |
| LN | moment3 | Three-moment response-time distribution pass: the routing layers plus a distribution propagation. | — |
| UQ | default | Discrete Priors expanded as given, continuous Priors discretized by quadrature; resolves to quadrature. | — |
| UQ | discrete | Discrete design over each Prior's own support. | — |
| UQ | quadrature | Gaussian quadrature discretization of the continuous Priors into a weighted design. | — |
| UQ | montecarlo | Monte Carlo sampling of the Priors instead of a quadrature design; no design-size cap. | — |
| JMT | default | Resolves to jsim, or to replication when options.timespan(2) is finite. | — |
| JMT | jsim | JSIMengine discrete-event simulation of the model. | [1] |
| JMT | replication | Independent transient replications in JSIM, averaged; needs a finite timespan. | — |
| JMT | jmva | The JMVA analytical engine, algorithm left to JMVA. | — |
| JMT | jmva.mva | Exact MVA inside JMVA. | [2] |
| JMT | jmva.amva | JMVA's approximate MVA. | — |
| JMT | jmva.recal | RECAL, the recursion by chain for the normalizing constant. | [3] |
| 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. | [4] |
| JMT | jmva.chow | Chow's approximate MVA. | [8] |
| JMT | jmva.bs | Bard-Schweitzer inside JMVA. | [5] |
| JMT | jmva.aql | Aggregate Queue Length inside JMVA. | [9] |
| JMT | jmva.lin | Linearizer inside JMVA. | [6] |
| JMT | jmva.dmlin | De Souza-Muntz Improved Linearizer inside JMVA. | [7] |
| LQNS | default | Run lqns with -Pstop-on-message-loss=false. | — |
| LQNS | lqns | The same as default, asked for by name. | — |
| LQNS | srvn | lqns -Playering=srvn: the SRVN layering strategy. | — |
| LQNS | exactmva | lqns -Pmva=exact: exact MVA inside the layer solves. | — |
| LQNS | srvn.exactmva | Both of the above: SRVN layering with exact MVA. | — |
| LQNS | sim, lqsim | lqsim, the LQN discrete-event simulator, at options.samples run length. | — |
| LQNS | lqnsdefault | Plain lqns with no LINE pragmas at all, i.e. the tool's own defaults. | — |
| QNS | default | Let the tool choose (Rolia in practice). | — |
| QNS | conway | Conway's multiserver approximation. | — |
| QNS | rolia | Rolia's multiserver approximation. | — |
| QNS | zhou | Zhou's multiserver approximation. | — |
| QNS | suri | Suri's multiserver approximation; refused where a multi-server station is present, since qnsolver -m does not know it. | — |
| QNS | reiser | Reiser's multiserver approximation. | — |
| QNS | schmidt | Schmidt's multiserver approximation; same restriction as suri. | — |