LINE Solver (Python) Logo

Getting Started:

  • Installation
    • Requirements
    • Installing from PyPI
    • Dependencies
    • Verifying Installation
    • Optional Backends
  • Quick Start Guide
    • Creating a Simple Model
    • Choosing the Engine: lang='java' and lang='cpp'
    • Available Solvers
  • Solver Backends: lang='java', lang='cpp'
    • What each backend needs
      • lang='java'
      • lang='cpp'
    • What falls back, and what does not
    • See Also
  • Examples
    • Gallery Examples
      • Single Server Models
      • Multi-Server and Specialized Models
      • Network Models
    • Basic Examples
      • Open Queueing Networks
      • Closed Queueing Networks
      • Mixed Queueing Networks
      • Fork-Join Networks
      • Priority and Scheduling Models
      • Class Switching Models
      • Cache Models
      • Layered Queueing Networks
      • Stochastic Petri Nets
    • Advanced Examples
      • State Probabilities
      • State-Dependent Routing
      • Initial State Specification
      • Load-Dependent Services
      • Random Environment Models
      • Switchover Times
      • Reward Models
      • Layered Cache-Queueing Models
    • Further Example Areas
    • Notebooks Are Generated From the Scripts
    • Getting Started
    • Example Code Pattern

API Reference:

  • API Documentation
    • Core Modules
      • Network Models (line_solver.lang)
        • Main Classes
        • Node Classes
        • Job Class Classes
        • Routing and Structure
        • State Representation
      • Solvers (line_solver.solvers)
        • Base Solver Classes
        • Analytical Solvers
        • External Solver Wrappers
        • Specialized Solvers
        • Result Classes
        • Solver Configuration
      • Distributions (line_solver.distributions)
        • Base Distribution Classes
        • Continuous Distributions
        • Phase-Type Distributions
        • Markovian Arrival Processes
        • Discrete Distributions
        • Special Distributions
      • Layered Networks (line_solver.layered)
        • Main Classes
        • Cache Tasks
    • Cache Algorithms
      • cache_lrum_map_levelstats()
      • cache_t_lrum_map()
      • cache_ttl_lrum_map()
      • cache_erec()
      • cache_erec_aux()
      • cache_prob_erec()
      • cache_cost()
      • cache_cost_pathcheck()
      • cache_mva()
      • cache_spm_size()
      • cache_xi_iter()
      • cache_spm()
      • cache_prob_spm()
      • cache_prob_fpi()
      • cache_miss()
      • cache_xi_fp()
      • cache_miss_fpi()
      • cache_miss_spm()
      • cache_mva_miss()
      • cache_miss_asy()
      • cache_miss_rmf()
      • cache_rmf_lna()
      • cache_miss_sfifo_rmf()
      • cache_miss_fifo_rmf()
      • cache_is()
      • cache_prob_is()
      • cache_miss_is()
      • logmeanexp()
      • cache_t_hlru()
      • cache_ttl_hlru()
      • cache_ttl_lrua()
      • cache_rrm_meanfield_ode()
      • cache_rrm_meanfield()
      • cache_gamma_lp()
      • cache_gamma()
    • Loss Networks
      • lossn_erlangfp()
      • erlang_b()
      • erlang_c()
      • lossn_mci()
      • lossn_manjunath()
      • lossn_rec()
    • Layered Stochastic Networks
      • LayeredNetworkElement
        • LayeredNetworkElement.TASK
        • LayeredNetworkElement.ENTRY
        • LayeredNetworkElement.ACTIVITY
        • LayeredNetworkElement.PROCESSOR
        • LayeredNetworkElement.HOST
      • LayeredNetworkStruct
        • LayeredNetworkStruct.dag
        • LayeredNetworkStruct.mult
        • LayeredNetworkStruct.type
        • LayeredNetworkStruct.isref
      • kahn_topological_sort()
      • lsn_max_multiplicity()
    • Markov Chain Utilities
      • Markov Chain Analysis (line_solver.api.mc)
        • ctmc_solve()
        • ctmc_solve_reducible()
        • ctmc_solve_reducible_blkdecomp()
        • ctmc_sens()
        • ctmc_transient_sens()
        • ctmc_makeinfgen()
        • ctmc_transient()
        • ctmc_timeaverage()
        • ctmc_uniformization()
        • ctmc_foxglynn()
        • ctmc_foxglynn_weights()
        • ctmc_fau()
        • CtmcFauInfo
        • ctmc_gmres()
        • ctmc_gmres_multi()
        • ctmc_bicgstab()
        • ctmc_bicgstab_multi()
        • ctmc_randomization()
        • ctmc_stochcomp()
        • ctmc_timereverse()
        • ctmc_rand()
        • ctmc_simulate()
        • ctmc_isfeasible()
        • ctmc_ssg()
        • ctmc_ssg_reachability()
        • ctmc_memory_gate()
        • CtmcSsgResult
        • dtmc_solve()
        • dtmc_solve_reducible()
        • dtmc_makestochastic()
        • dtmc_isfeasible()
        • dtmc_simulate()
        • dtmc_rand()
        • dtmc_timereverse()
        • dtmc_stochcomp()
        • dtmc_stochcomp_full()
        • dtmc_transient()
        • dtmc_hitting_time()
        • ctmc_passage_ph()
        • ctmc_passage_lst()
        • ctmc_passage_moments()
        • ctmc_passage_time()
        • ctmc_hitting_time()
        • smp_passage_lst()
        • smp_passage_moments()
        • smp_passage_time()
        • CourtoisResult
        • KMSResult
        • TakahashiResult
        • ctmc_courtois()
        • ctmc_kms()
        • ctmc_takahashi()
        • ctmc_multi()
        • ctmc_saddlepoint()
    • Matrix-Analytic Methods
      • map_infgen()
      • map_piq()
      • map_prob()
      • map_pie()
      • map_lambda()
      • map_mean()
      • map_var()
      • map_scv()
      • map_moment()
      • map_scale()
      • map_normalize()
      • map_isfeasible()
      • exp_map()
      • erlang_map()
      • hyperexp_map()
      • map_exponential()
      • map_erlang()
      • map_hyperexp()
      • map_gamma()
      • map_sumind()
      • map_cdf()
      • map_pdf()
      • map_sample()
      • map_skew()
      • map_kurt()
      • map_acf()
      • map_acfc()
      • map_idc()
      • map_count_mean()
      • map_count_var()
      • map_count_idc()
      • map_varcount()
      • map_count_moment()
      • map_mmpp2()
      • map_gamma2()
      • map_rand()
      • map_randn()
      • map_renewal()
      • map_embedded()
      • map_sum()
      • map_super()
      • map_mixture()
      • map_max()
      • map_timereverse()
      • map_mark()
      • map_stochcomp()
      • map_kpc()
      • map_bernstein()
      • map_pntiter()
      • map_pntquad()
      • map2_fit()
      • map2_fit_idc()
      • map_joint()
      • map_issym()
      • map_feastol()
      • map_feasblock()
      • map_block()
      • map_largemap()
      • mmap_infgen()
      • mmap_normalize()
      • mmap_super_safe()
      • mmap_mark()
      • mmap_scale()
      • mmap_hide()
      • aph2_assemble()
      • aph2_fitall()
      • aph2_adjust()
      • aph2_fit()
      • aph2_fit_map()
      • aph2_fit_trace()
      • mmap_compress()
      • mmap_exponential()
      • mmap_issym()
      • mmap_isfeasible()
      • mmap_lambda()
      • mmap_count_lambda()
      • mmap_pie()
      • mmap_pc()
      • mmap_embedded()
      • mmap_sample()
      • mmap_rand()
      • mmap_timereverse()
      • mmap_sum()
      • mmap_super()
      • mmap_mixture()
      • mmap_max()
      • mmap_maps()
      • mmap_count_mean()
      • mmap_count_var()
      • mmap_count_moment()
      • mmap_count_idc()
      • mmap_count_mcov()
      • mmap_idc()
      • mmap_sigma()
      • mmap_sigma2()
      • mmap_forward_moment()
      • mmap_backward_moment()
      • mmap_cross_moment()
      • mmap_modulate()
      • ldqbd()
      • LdqbdResult
        • LdqbdResult.R
        • LdqbdResult.pi
        • LdqbdResult.pi_cells
      • LdqbdOptions
        • LdqbdOptions.epsilon
        • LdqbdOptions.max_iter
        • LdqbdOptions.verbose
      • ldqbd_mphc()
      • ph_multisets()
      • MAPBMAP1Result
        • MAPBMAP1Result.mean_queue_length
        • MAPBMAP1Result.utilization
        • MAPBMAP1Result.mean_response_time
        • MAPBMAP1Result.throughput
        • MAPBMAP1Result.pi
        • MAPBMAP1Result.R
        • MAPBMAP1Result.mean_batch_size
      • solver_mam_map_bmap_1()
      • BMAPMAP1Result
        • BMAPMAP1Result.mean_queue_length
        • BMAPMAP1Result.utilization
        • BMAPMAP1Result.mean_response_time
        • BMAPMAP1Result.throughput
        • BMAPMAP1Result.pi
        • BMAPMAP1Result.G
        • BMAPMAP1Result.mean_batch_size
      • solver_mam_bmap_map_1()
      • QBDResult
        • QBDResult.R
        • QBDResult.G
        • QBDResult.U
        • QBDResult.eta
      • QbdRapResult
        • QbdRapResult.levelProb
        • QbdRapResult.QN
        • QbdRapResult.R
        • QbdRapResult.G
        • QbdRapResult.U
        • QbdRapResult.spr
        • QbdRapResult.pqueue
        • QbdRapResult.pi0
      • qbd_R()
      • qbd_R_logred()
      • qbd_rg()
      • qbd_blocks_mapmap1()
      • qbd_bmapbmap1()
      • qbd_mapmap1()
      • qbd_rap()
      • qbd_rap_g()
      • qbd_raprap1()
      • qbd_setupdelayoff()
      • qbd_depproc_etaqa()
      • qbd_depproc_etaqa_ps()
      • qbd_depproc_jointmom()
      • map_ccdf_derivative()
      • map_jointpdf_derivative()
      • map_factorial_moment()
      • map_joint_moment()
      • map_m1ps_cdf_respt()
      • map_compute_R()
      • map_m1ps_h_recursive()
      • map_m1ps_sojourn()
      • mmdp_isfeasible()
      • hyperexp_fit_longtail()
    • Non-Product-Form Networks
      • npfqn_nonexp_approx()
      • NpfqnNonexpApproxResult
        • NpfqnNonexpApproxResult.ST
        • NpfqnNonexpApproxResult.gamma
        • NpfqnNonexpApproxResult.nservers
        • NpfqnNonexpApproxResult.rho
        • NpfqnNonexpApproxResult.scva
        • NpfqnNonexpApproxResult.scvs
        • NpfqnNonexpApproxResult.eta
      • npfqn_traffic_merge()
      • npfqn_traffic_merge_cs()
      • npfqn_traffic_split_cs()
      • npfqn_sqd()
      • NpfqnSqdResult
        • NpfqnSqdResult.X
        • NpfqnSqdResult.Q
        • NpfqnSqdResult.U
        • NpfqnSqdResult.R
      • npfqn_rqna_weight()
      • npfqn_traffic_rqt()
      • npfqn_bnd_bpt()
      • NpfqnBndBptResult
        • NpfqnBndBptResult.zlb
        • NpfqnBndBptResult.x
        • NpfqnBndBptResult.lambda_
        • NpfqnBndBptResult.rho
        • NpfqnBndBptResult.rho_station
        • NpfqnBndBptResult.nvars
        • NpfqnBndBptResult.nrows
      • npfqn_bnd_bgt()
      • NpfqnBndBgtResult
        • NpfqnBndBgtResult.Qub
        • NpfqnBndBgtResult.gamma
        • NpfqnBndBgtResult.Lmax
        • NpfqnBndBgtResult.L
        • NpfqnBndBgtResult.V
        • NpfqnBndBgtResult.B
        • NpfqnBndBgtResult.U
        • NpfqnBndBgtResult.tail_ratio
        • NpfqnBndBgtResult.tail_step
        • NpfqnBndBgtResult.rho
        • NpfqnBndBgtResult.rho_station
        • NpfqnBndBgtResult.scale
        • NpfqnBndBgtResult.class_type
        • NpfqnBndBgtResult.class_stage
        • NpfqnBndBgtResult.class_station
      • npfqn_traffic_idc()
      • npfqn_traffic_split_rr()
      • npfqn_gtmtst_fluid()
      • npfqn_feedback_elim()
      • npfqn_dps_morrison()
      • NpfqnDpsMorrisonResult
        • NpfqnDpsMorrisonResult.Q
        • NpfqnDpsMorrisonResult.R
        • NpfqnDpsMorrisonResult.X
        • NpfqnDpsMorrisonResult.Qlead
        • NpfqnDpsMorrisonResult.Rlead
        • NpfqnDpsMorrisonResult.sigma
        • NpfqnDpsMorrisonResult.W
        • NpfqnDpsMorrisonResult.rho
        • NpfqnDpsMorrisonResult.a
        • NpfqnDpsMorrisonResult.cB
        • NpfqnDpsMorrisonResult.cC
        • NpfqnDpsMorrisonResult.cD
        • NpfqnDpsMorrisonResult.cH
        • NpfqnDpsMorrisonResult.cI
        • NpfqnDpsMorrisonResult.cJ
        • NpfqnDpsMorrisonResult.cK
        • NpfqnDpsMorrisonResult.cL
        • NpfqnDpsMorrisonResult.cM
        • NpfqnDpsMorrisonResult.cQ
        • NpfqnDpsMorrisonResult.delta
        • NpfqnDpsMorrisonResult.cR
        • NpfqnDpsMorrisonResult.cS
        • NpfqnDpsMorrisonResult.cU
        • NpfqnDpsMorrisonResult.cA
        • NpfqnDpsMorrisonResult.cV
    • Polling Systems
      • polling_qsys_exhaustive()
      • polling_qsys_gated()
      • polling_qsys_1limited()
      • polling_qsys_decrementing()
    • Product-Form Queueing Networks
      • pfqn_mva()
      • pfqn_mva_ilock()
      • pfqn_mva_single_class()
      • pfqn_bs()
      • pfqn_cntol()
      • is_cntol()
      • pfqn_aql()
      • pfqn_sqni()
      • pfqn_qdlin()
      • pfqn_qli()
      • pfqn_fli()
      • pfqn_joint()
      • pfqn_jointmarg()
      • pfqn_ca()
      • pfqn_manjunath()
      • pfqn_is()
      • pfqn_nc()
      • pfqn_qlen_joint_moments()
      • pfqn_nc_resolved_method()
      • pfqn_panacea()
      • pfqn_panaceald()
      • pfqn_propfair()
      • pfqn_ls()
      • pfqn_mcmc()
      • PfqnMcmcResult
        • PfqnMcmcResult.X
        • PfqnMcmcResult.Q
        • PfqnMcmcResult.Xse
        • PfqnMcmcResult.Xlo
        • PfqnMcmcResult.Xhi
        • PfqnMcmcResult.Qse
        • PfqnMcmcResult.Qlo
        • PfqnMcmcResult.Qhi
        • PfqnMcmcResult.batches
        • PfqnMcmcResult.samples
        • PfqnMcmcResult.burnin
      • pfqn_clw()
      • pfqn_clw_lld()
      • pfqn_perm()
      • pfqn_qdamva()
      • pfqn_qsa()
      • pfqn_lcp()
      • pfqn_chow()
      • pfqn_looping()
      • pfqn_pam()
      • pfqn_clust()
      • pfqn_dmlin()
      • pfqn_linearizer()
      • pfqn_gflinearizer()
      • pfqn_egflinearizer()
      • pfqn_momlin()
      • PfqnMomlin
      • SchedStrategy
      • pfqn_sens()
      • PfqnSens
      • pfqn_sens_mva()
      • PfqnSensMva
      • pfqn_sens_ldmx_ec()
      • pfqn_sens_mvaldmx()
      • PfqnSensMvaldmx
      • pfqn_sens_mom()
      • PfqnSensMom
      • pfqn_sens_respt()
      • pfqn_busyp()
      • pfqn_busyp_multiclass()
      • pfqn_busyp_clw()
      • PfqnSensRespt
      • pfqn_respt_ps_moments()
      • PfqnResptPsMoments
      • pfqn_sens_linearizer()
      • PfqnSensLinearizer
      • pfqn_mvald()
      • pfqn_mvams()
      • pfqn_mvams_ilock()
      • pfqn_mvamx()
      • pfqn_xzabalow()
      • pfqn_xzabaup()
      • pfqn_qzgblow()
      • pfqn_qzgbup()
      • pfqn_xzgsblow()
      • pfqn_xzgsbup()
      • pfqn_mwrbb()
      • pfqn_harel_bounds()
      • pfqn_harel_lb()
      • pfqn_harel_ub()
      • pfqn_pbh()
      • pfqn_pbk()
      • pfqn_bjbk()
      • pfqn_cbh()
      • pfqn_mcub()
      • pfqn_ssd()
      • pfqn_sib()
      • pfqn_ldbcmp()
      • pfqn_scb()
      • pfqn_scbgap()
      • pfqn_usumbound()
      • pfqn_minclasses()
      • pfqn_explicit()
      • pfqn_explicit_ld()
      • pfqn_rgf()
      • pfqn_rgfmc()
      • pfqn_gerasimov()
      • pfqn_dnc()
      • pfqn_nintmva()
      • pfqn_mva_interval()
      • PfqnMvaIntervalResult
        • PfqnMvaIntervalResult.X
        • PfqnMvaIntervalResult.Q
        • PfqnMvaIntervalResult.U
        • PfqnMvaIntervalResult.R
        • PfqnMvaIntervalResult.Rtot
        • PfqnMvaIntervalResult.Qtot
      • pfqn_tay()
      • pfqn_scat()
      • pfqn_hst()
      • pfqn_marie()
      • pfqn_le()
      • pfqn_lekt()
      • pfqn_lekt_route()
      • pfqn_ble()
      • pfqn_aghq()
      • pfqn_cub()
      • pfqn_mci()
      • pfqn_grnmol()
      • pfqn_le_fpi()
      • pfqn_le_fpiZ()
      • pfqn_le_hessian()
      • pfqn_le_hessianZ()
      • pfqn_ncld()
      • pfqn_ld_is()
      • pfqn_ncldmx()
      • PfqnNcldmxResult
        • PfqnNcldmxResult.G
        • PfqnNcldmxResult.lG
        • PfqnNcldmxResult.lGopen
        • PfqnNcldmxResult.method
        • PfqnNcldmxResult.XN
        • PfqnNcldmxResult.QN
      • pfqn_gld()
      • pfqn_gldsingle()
      • pfqn_lldsingle()
      • pfqn_lld()
      • pfqn_xia()
      • pfqn_mushift()
      • pfqn_comomrm_ld()
      • pfqn_fnc()
      • pfqn_ncoi()
      • pfqn_ncjd()
      • pfqn_clwoi()
      • pfqn_clwjd()
      • pfqn_oi_fnc()
      • pfqn_oi_insvc()
      • pfqn_pas_is()
      • pfqn_pas_nc()
      • pas_placement()
      • pas_swap2order()
      • pfqn_mvaoi()
      • pfqn_mvajd()
      • pfqn_mvaoi_marg()
      • PfqnNcResult
        • PfqnNcResult.G
        • PfqnNcResult.lG
        • PfqnNcResult.method
      • PfqnComomrmLdResult
        • PfqnComomrmLdResult.G
        • PfqnComomrmLdResult.lG
        • PfqnComomrmLdResult.prob
      • PfqnFncResult
        • PfqnFncResult.mu
        • PfqnFncResult.c
      • pfqn_unique()
      • pfqn_expand()
      • pfqn_combine_mi()
      • PfqnUniqueResult
        • PfqnUniqueResult.L_unique
        • PfqnUniqueResult.mu_unique
        • PfqnUniqueResult.gamma_unique
        • PfqnUniqueResult.mi
        • PfqnUniqueResult.mapping
      • pfqn_lldfun()
      • pfqn_mu_ms()
      • pfqn_nc_sanitize()
      • pfqn_cdfun()
      • pfqn_sdrcoeff()
      • pfqn_sdrprob()
      • pfqn_sdr()
      • pfqn_sdrvisits()
      • pfqn_sdrmva()
      • factln()
      • factln_vec()
      • softmin()
      • oner()
      • multichoose()
      • multichoosecon()
      • matchrow()
      • pfqn_comom()
      • pfqn_comomrm()
      • pfqn_comomrm_orig()
      • pfqn_comomrm_ms()
      • pfqn_procomom()
      • pfqn_procomom2()
      • ComomResult
        • ComomResult.lG
        • ComomResult.lGbasis
      • pfqn_mmint2()
      • pfqn_mmint2_gausslegendre()
      • pfqn_mmint2_gausslaguerre()
      • pfqn_mmsample2()
      • logsumexp()
      • pfqn_schmidt()
      • pfqn_schmidt_ext()
      • SchmidtResult
        • SchmidtResult.XN
        • SchmidtResult.QN
        • SchmidtResult.UN
        • SchmidtResult.CN
      • pprod()
      • hashpop()
      • pfqn_dac()
      • pfqn_recal()
      • pfqn_mvac()
      • pfqn_mvacld()
      • pfqn_mvaldmx()
      • pfqn_ldmx_ec()
      • pfqn_mvaldms()
      • pfqn_linearizerms()
      • pfqn_linearizermx()
      • pfqn_conwayms()
      • ljd_linearize()
      • infradius_h()
      • infradius_hnorm()
      • pfqn_kt()
      • pfqn_bkt()
      • pfqn_bk()
      • pfqn_bkue()
      • pfqn_bklc()
      • pfqn_ab_amva()
      • pfqn_ab_core()
      • AbAmvaResult
        • AbAmvaResult.QN
        • AbAmvaResult.UN
        • AbAmvaResult.RN
        • AbAmvaResult.CN
        • AbAmvaResult.XN
        • AbAmvaResult.totiter
      • pfqn_rd()
      • RdOptions
        • RdOptions.tol
        • RdOptions.method
      • RdResult
        • RdResult.lGN
        • RdResult.Cgamma
      • pfqn_nre()
      • pfqn_nre_full()
      • PfqnNreResult
        • PfqnNreResult.lG
        • PfqnNreResult.G
        • PfqnNreResult.lGs
        • PfqnNreResult.vsad
      • pfqn_nrl()
      • pfqn_nrp()
      • pfqn_lap()
      • laplaceapprox()
      • num_hess()
      • pfqn_cyclet_ofree()
      • pfqn_stdf()
      • pfqn_stdf_heur()
      • pfqn_cftp()
      • pfqn_mvasjn()
      • pfqn_amvasjn()
      • SjnOptions
        • SjnOptions.ns
        • SjnOptions.lfactor
        • SjnOptions.prio
        • SjnOptions.tol
        • SjnOptions.iter_max
        • SjnOptions.umax
        • SjnOptions.validate()
    • Queueing Systems
      • qsys_mapdc()
      • qsys_mapphc()
      • qsys_mmapgk1()
      • MmapGk1Result
        • MmapGk1Result.lambdas
        • MmapGk1Result.arrivalRate
        • MmapGk1Result.utilization
        • MmapGk1Result.idleVector
        • MmapGk1Result.waitLST
        • MmapGk1Result.waitMoments
        • MmapGk1Result.meanWaitingTime
        • MmapGk1Result.meanSojournTime
        • MmapGk1Result.meanQueueLength
        • MmapGk1Result.waitCDF
        • MmapGk1Result.waitPoints
        • MmapGk1Result.analyzer
      • MapPhcResult
        • MapPhcResult.meanQueueLength
        • MapPhcResult.meanWaitingTime
        • MapPhcResult.meanSojournTime
        • MapPhcResult.utilization
        • MapPhcResult.queueLengthDist
        • MapPhcResult.waitingTimeMoments
        • MapPhcResult.waitingTimeCCDF
        • MapPhcResult.waitingTimePoints
        • MapPhcResult.probWait
        • MapPhcResult.phaseCount
        • MapPhcResult.analyzer
      • qsys_mapd1()
      • qsys_mdc_crommelin()
      • qsys_dmc()
      • qsys_phm1()
      • qsys_phmc()
      • qsys_bmapm1()
      • qsys_mm1_ps()
      • qsys_mg1_ps()
      • qsys_mm1()
      • qsys_mmk()
      • qsys_mmck()
      • qsys_mg1()
      • qsys_gm1()
      • qsys_mminf()
      • qsys_mginf()
      • qsys_mmcc_retrial_fp()
      • qsys_gig1_rq()
      • qsys_gigk_rqt()
      • qsys_gig1_rqt()
      • qsys_gigk_rqt_gamma()
      • qsys_gig1_approx_allencunneen()
      • qsys_gig1_approx_kingman()
      • qsys_gig1_approx_marchal()
      • qsys_gig1_approx_whitt()
      • qsys_gig1_approx_heyman()
      • qsys_gig1_approx_kobayashi()
      • qsys_gig1_approx_klb()
      • qsys_gig1_approx_gelenbe()
      • qsys_gig1_approx_kimura()
      • qsys_gig1_approx_myskja()
      • qsys_gig1_approx_myskja2()
      • qsys_gg1()
      • qsys_gig1_lbnd()
      • qsys_gigk_approx()
      • qsys_gigk_approx_cosmetatos()
      • qsys_gigk_approx_whitt()
      • qsys_gig1_ubnd_kingman()
      • qsys_gigk_approx_kingman()
      • qsys_mg1_prio()
      • qsys_mm1_dps()
      • qsys_mg1_srpt()
      • qsys_mg1_fb()
      • qsys_mg1_lrpt()
      • qsys_mg1_psjf()
      • qsys_mg1_setf()
      • qsys_mm1k_loss()
      • qsys_mg1k_loss()
      • qsys_mg1k_loss_mgs()
      • qsys_mxm1()
      • qsys_mapg1k()
      • qsys_mmapg1k()
      • qsys_mapg1k_perflow()
      • QueueResult
        • QueueResult.meanQueueLength
        • QueueResult.meanWaitingTime
        • QueueResult.meanSojournTime
        • QueueResult.utilization
        • QueueResult.queueLengthDist
        • QueueResult.queueLengthMoments
        • QueueResult.sojournTimeMoments
        • QueueResult.analyzer
      • ph_to_map()
      • qsys_phph1()
      • qsys_mapph1()
      • qsys_mapm1()
      • qsys_mapmc()
      • qsys_mapmap1()
      • qsys_mapg1()
      • QueueType
        • QueueType.STANDARD
        • QueueType.RETRIAL
        • QueueType.RENEGING
        • QueueType.RETRIAL_RENEGING
      • BmapMatrix
        • BmapMatrix.D0
        • BmapMatrix.D_batch
        • BmapMatrix.__post_init__()
        • BmapMatrix.arrival_rate
        • BmapMatrix.fundamental_arrival_rate
      • PhDistribution
        • PhDistribution.beta
        • PhDistribution.S
        • PhDistribution.__post_init__()
        • PhDistribution.mean
        • PhDistribution.mean_squared
        • PhDistribution.scv
      • QbdStatespace
        • QbdStatespace.A0
        • QbdStatespace.A1
        • QbdStatespace.A2
        • QbdStatespace.B0
        • QbdStatespace.max_level
        • QbdStatespace.__post_init__()
        • QbdStatespace.get_state_index()
        • QbdStatespace.get_level_phase()
        • QbdStatespace.binomial_state_dimension
      • RetrialQueueResult
        • RetrialQueueResult.queue_type
        • RetrialQueueResult.L_orbit
        • RetrialQueueResult.N_server
        • RetrialQueueResult.utilization
        • RetrialQueueResult.throughput
        • RetrialQueueResult.P_idle
        • RetrialQueueResult.P_empty_orbit
        • RetrialQueueResult.stationary_dist
        • RetrialQueueResult.truncation_level
        • RetrialQueueResult.trunc_error
        • RetrialQueueResult.converged
        • RetrialQueueResult.iterations
        • RetrialQueueResult.error
        • RetrialQueueResult.analyzer
      • RetrialQueueAnalyzer
        • RetrialQueueAnalyzer.__init__()
        • RetrialQueueAnalyzer.detect_queue_type()
        • RetrialQueueAnalyzer.extract_bmap()
        • RetrialQueueAnalyzer.extract_ph_service()
        • RetrialQueueAnalyzer.extract_retrial_parameters()
        • RetrialQueueAnalyzer.build_qbd_statespace()
        • RetrialQueueAnalyzer.analyze()
      • qsys_bmapphnn_retrial()
      • qsys_is_retrial()
      • RetrialInfo
        • RetrialInfo.is_retrial
        • RetrialInfo.station_idx
        • RetrialInfo.node_idx
        • RetrialInfo.source_idx
        • RetrialInfo.class_idx
        • RetrialInfo.error_msg
        • RetrialInfo.N
        • RetrialInfo.alpha
        • RetrialInfo.gamma
        • RetrialInfo.p
        • RetrialInfo.R
      • RenegingInfo
        • RenegingInfo.is_reneging
        • RenegingInfo.source_idx
        • RenegingInfo.queue_idx
        • RenegingInfo.class_idx
        • RenegingInfo.n_servers
        • RenegingInfo.service_rate
        • RenegingInfo.error_msg
      • detect_reneging_topology()
      • has_reneging_patience()
      • extract_bmap_matrices()
      • extract_ph_params()
      • convert_patience_to_regimes()
      • solver_mam_retrial()
      • qsys_ldps_workload()
      • qsys_lindley_moment()
      • qsys_mm1_lindley()
      • qsys_hh1_lindley()
      • qsys_mm1_tandem_lindley()
      • qsys_tandem_lindley()
      • qsys_tandem_ub_ciucu()
      • qsys_mgisrgi_whitt()
      • qsys_erlanga()
      • qsys_ggisgi_fluid()
      • qsys_mmk_qed()
      • qsys_mmk_qed_alpha()
      • qsys_mmk_qed_staffing()
      • qsys_mtginf()
      • qsys_gig1_bnds_extremal()
      • qsys_gtmtst_fluid()
      • qsys_ggnm_diffusion()
      • qsys_ggingi_tga()
      • qsys_mtgs0_mol()
      • erlang_b()
      • erlang_c()
      • qsys_maxima_twomoment()
    • Stochastic Network Utilities
      • sn_gd_balance()
      • MatrixArray
        • MatrixArray.__new__()
        • MatrixArray.__array_finalize__()
        • MatrixArray.__getitem__()
        • MatrixArray.__setitem__()
        • MatrixArray.get()
        • MatrixArray.set()
      • NetworkStruct
        • NetworkStruct.nstations
        • NetworkStruct.nstateful
        • NetworkStruct.nnodes
        • NetworkStruct.nclasses
        • NetworkStruct.nchains
        • NetworkStruct.nclosedjobs
        • NetworkStruct.njobs
        • NetworkStruct.nservers
        • NetworkStruct.cap
        • NetworkStruct.classcap
        • NetworkStruct.rates
        • NetworkStruct.scv
        • NetworkStruct.phases
        • NetworkStruct.phasessz
        • NetworkStruct.phaseshift
        • NetworkStruct.visits
        • NetworkStruct.nodevisits
        • NetworkStruct.inchain
        • NetworkStruct.chains
        • NetworkStruct.refstat
        • NetworkStruct.refclass
        • NetworkStruct.sched
        • NetworkStruct.schedparam
        • NetworkStruct.routing
        • NetworkStruct.rt
        • NetworkStruct.rtnodes
        • NetworkStruct.nodetype
        • NetworkStruct.isstation
        • NetworkStruct.isstateful
        • NetworkStruct.isstatedep
        • NetworkStruct.sdr
        • NetworkStruct.hassetup
        • NetworkStruct.nodeToStation
        • NetworkStruct.nodeToStateful
        • NetworkStruct.stationToNode
        • NetworkStruct.stationToStateful
        • NetworkStruct.statefulToNode
        • NetworkStruct.statefulToStation
        • NetworkStruct.state
        • NetworkStruct.stateprior
        • NetworkStruct.space
        • NetworkStruct.lldscaling
        • NetworkStruct.cdscaling
        • NetworkStruct.cdscalingpeak
        • NetworkStruct.jdscaling
        • NetworkStruct.jdscalingpeak
        • NetworkStruct.gdscaling
        • NetworkStruct.gdscalingpeak
        • NetworkStruct.gdscalingcutoff
        • NetworkStruct.classprio
        • NetworkStruct.classdeadline
        • NetworkStruct.isslc
        • NetworkStruct.issignal
        • NetworkStruct.signaltarget
        • NetworkStruct.signaltype
        • NetworkStruct.syncreply
        • NetworkStruct.replyblock
        • NetworkStruct.immfeed
        • NetworkStruct.signalremdist
        • NetworkStruct.signalrempolicy
        • NetworkStruct.iscatastrophe
        • NetworkStruct.connmatrix
        • NetworkStruct.nodenames
        • NetworkStruct.classnames
        • NetworkStruct.mu
        • NetworkStruct.phi
        • NetworkStruct.proc
        • NetworkStruct.isph
        • NetworkStruct.pie
        • NetworkStruct.procid
        • NetworkStruct.lst
        • NetworkStruct.fj
        • NetworkStruct.fjsync
        • NetworkStruct.fjclassmap
        • NetworkStruct.isfjaugmented
        • NetworkStruct.fjauxclass
        • NetworkStruct.droprule
        • NetworkStruct.nregions
        • NetworkStruct.region
        • NetworkStruct.regionrule
        • NetworkStruct.regionweight
        • NetworkStruct.regionsz
        • NetworkStruct.regionmaxmem
        • NetworkStruct.regionmembers
        • NetworkStruct.sync
        • NetworkStruct.gsync
        • NetworkStruct.nodeparam
        • NetworkStruct.routingweights
        • NetworkStruct.reward
        • NetworkStruct.rtorig
        • NetworkStruct.csmask
        • NetworkStruct.nvars
        • NetworkStruct.isbasblocking
        • NetworkStruct.isbasdestination
        • NetworkStruct.impatienceType
        • NetworkStruct.impatienceMu
        • NetworkStruct.impatienceClass
        • NetworkStruct.impatiencePhi
        • NetworkStruct.impatiencePhases
        • NetworkStruct.impatienceProc
        • NetworkStruct.impatiencePie
        • NetworkStruct.impatienceDist
        • NetworkStruct.balkingStrategy
        • NetworkStruct.balkingThresholds
        • NetworkStruct.retrialType
        • NetworkStruct.retrialMu
        • NetworkStruct.retrialPhi
        • NetworkStruct.retrialProc
        • NetworkStruct.retrialMaxAttempts
        • NetworkStruct.retrialPolicy
        • NetworkStruct.orbitMaxJobs
        • NetworkStruct.orbitImpatience
        • NetworkStruct.hasbreakdown
        • NetworkStruct.breakdownMu
        • NetworkStruct.repairMu
        • NetworkStruct.breakdownProc
        • NetworkStruct.repairProc
        • NetworkStruct.downServiceRates
        • NetworkStruct.varsparam
        • NetworkStruct.markidx
        • NetworkStruct.__setattr__()
        • NetworkStruct.__post_init__()
        • NetworkStruct.validate()
        • NetworkStruct.is_valid()
        • NetworkStruct.get_chain_population()
        • NetworkStruct.is_closed_chain()
        • NetworkStruct.is_open_chain()
        • NetworkStruct.get_station_indices()
        • NetworkStruct.get_stateful_indices()
        • NetworkStruct.get_scheduling_at_station()
        • NetworkStruct.has_multi_server()
        • NetworkStruct.has_load_dependence()
        • NetworkStruct.has_class_dependence()
        • NetworkStruct.has_joint_dependence()
        • NetworkStruct.has_open_classes()
        • NetworkStruct.has_closed_classes()
        • NetworkStruct.get_total_population()
        • NetworkStruct.get_open_class_indices()
        • NetworkStruct.get_closed_class_indices()
        • NetworkStruct.copy()
        • NetworkStruct.__repr__()
        • NetworkStruct.obj
      • NodeType
        • NodeType.SOURCE
        • NodeType.SINK
        • NodeType.QUEUE
        • NodeType.DELAY
        • NodeType.JOIN
        • NodeType.CACHE
        • NodeType.ROUTER
        • NodeType.CLASSSWITCH
        • NodeType.PLACE
        • NodeType.TRANSITION
        • NodeType.LOGGER
        • NodeType.FINITE_CAPACITY_REGION
        • NodeType.toText()
      • SchedStrategy
        • SchedStrategy.LCFSPI
        • SchedStrategy.HOL
        • SchedStrategy.LPS
        • SchedStrategy.SETF
        • SchedStrategy.FCFSPR
        • SchedStrategy.EDF
        • SchedStrategy.JOIN
        • SchedStrategy.EDD
        • SchedStrategy.SRPT
        • SchedStrategy.SRPTPRIO
        • SchedStrategy.LCFSPRIO
        • SchedStrategy.LCFSPRPRIO
        • SchedStrategy.LCFSPIPRIO
        • SchedStrategy.FCFSPRPRIO
        • SchedStrategy.FCFSPIPRIO
        • SchedStrategy.FSP
        • SchedStrategy.PAS
        • SchedStrategy.OI
        • SchedStrategy.FCFSPI
      • RoutingStrategy
        • RoutingStrategy.SQ
        • RoutingStrategy.SDR
      • DropStrategy
        • DropStrategy.WAITQ
        • DropStrategy.DROP
        • DropStrategy.BAS
        • DropStrategy.BBS
        • DropStrategy.RSRD
        • DropStrategy.RETRIAL
        • DropStrategy.RETRIAL_WITH_LIMIT
      • sn_region_members()
      • sn_get_demands_chain()
      • SnGetDemandsResult
        • SnGetDemandsResult.Lchain
        • SnGetDemandsResult.STchain
        • SnGetDemandsResult.Vchain
        • SnGetDemandsResult.alpha
        • SnGetDemandsResult.Nchain
        • SnGetDemandsResult.SCVchain
        • SnGetDemandsResult.refstatchain
      • sn_deaggregate_chain_results()
      • SnDeaggregateResult
        • SnDeaggregateResult.Q
        • SnDeaggregateResult.U
        • SnDeaggregateResult.R
        • SnDeaggregateResult.T
        • SnDeaggregateResult.C
        • SnDeaggregateResult.X
      • ProductFormParams
        • ProductFormParams.lam
        • ProductFormParams.D
        • ProductFormParams.N
        • ProductFormParams.Z
        • ProductFormParams.mu
        • ProductFormParams.S
        • ProductFormParams.V
      • sn_get_product_form_params()
      • sn_get_residt_from_respt()
      • sn_get_state_aggr()
      • sn_set_arrival()
      • sn_set_service()
      • sn_set_servers()
      • sn_set_population()
      • sn_set_priority()
      • sn_set_routing()
      • sn_refresh_visits()
      • sn_refresh_cacheqn_visits()
      • sn_set_fork_fanout()
      • sn_set_service_batch()
      • sn_nonmarkov_toph()
      • sn_rt_stations()
      • ChainParams
        • ChainParams.lambda_vec
        • ChainParams.D
        • ChainParams.N
        • ChainParams.Z
        • ChainParams.mu
        • ChainParams.S
        • ChainParams.V
      • sn_pn_firing_rates()
      • sn_pn_avg_rates()
      • sn_get_arvr_from_tput()
      • sn_map_modulation()
      • sn_get_node_arvr_from_tput()
      • sn_get_node_tput_from_tput()
      • sn_get_product_form_chain_params()
      • sn_set_routing_prob()
      • sn_is_closed_model()
      • sn_is_open_model()
      • sn_is_mixed_model()
      • sn_is_population_model()
      • sn_has_closed_classes()
      • sn_has_open_classes()
      • sn_has_mixed_classes()
      • sn_has_single_class()
      • sn_has_multi_class()
      • sn_has_multiple_closed_classes()
      • sn_has_single_chain()
      • sn_has_multi_chain()
      • sn_has_fcfs()
      • sn_has_ps()
      • sn_has_inf()
      • sn_has_lcfs()
      • sn_has_lcfspr()
      • sn_has_lcfs_pr()
      • sn_has_lcfs_pi()
      • sn_has_siro()
      • sn_has_dps()
      • sn_has_dps_prio()
      • sn_has_gps()
      • sn_has_gps_prio()
      • sn_has_ps_prio()
      • sn_has_hol()
      • sn_has_lps()
      • sn_has_setf()
      • sn_has_sept()
      • sn_has_lept()
      • sn_has_sjf()
      • sn_has_ljf()
      • sn_has_polling()
      • sn_has_homogeneous_scheduling()
      • sn_has_multi_class_fcfs()
      • sn_has_multi_class_heter_fcfs()
      • sn_has_multi_class_heter_exp_fcfs()
      • sn_has_multi_server()
      • sn_has_load_dependence()
      • sn_has_fork_join()
      • sn_has_immfeed()
      • sn_has_priorities()
      • sn_has_class_switching()
      • sn_has_quorum_join()
      • sn_has_fractional_populations()
      • sn_has_sd_routing()
      • sn_has_blocking()
      • sn_compat_rate()
      • sn_compat_peak()
      • sn_compat_scaling()
      • sn_is_mm1k_loss()
      • sn_has_product_form()
      • sn_has_bursty_arrival()
      • sn_has_product_form_not_het_fcfs()
      • sn_has_product_form_except_multi_class_heter_exp_fcfs()
      • sn_is_state_valid()
      • sn_fj_visits_spn()
      • sn_print()
      • sn_print_routing_matrix()
      • sn_refresh_process_fields()
      • sn_is_phasetype()
      • sn_rtnodes_to_rtorig()
      • sn_interlock_chain()
      • sn_patience_handles()
      • sn_arrival_rate_fun()
    • Trace Analysis
      • Trace Utilities (line_solver.api.trace)
        • trace_mean()
        • trace_var()
        • trace_scv()
        • trace_acf()
        • trace_gamma()
        • trace_iat2counts()
        • trace_idi()
        • trace_idc()
        • trace_pmf()
        • trace_shuffle()
        • trace_joint()
        • trace_iat2bins()
        • trace_summary()
        • trace_bicov()
        • mtrace_mean()
        • mtrace_var()
        • mtrace_count()
        • mtrace_sigma()
        • mtrace_sigma2()
        • mtrace_cross_moment()
        • mtrace_forward_moment()
        • mtrace_backward_moment()
        • mtrace_cov()
        • mtrace_pc()
        • mtrace_summary()
        • mtrace_split()
        • mtrace_merge()
        • mtrace_joint()
        • mtrace_moment()
        • mtrace_moment_simple()
        • mtrace_bootstrap()
        • mtrace_iat2counts()
    • Utilities and Constants
      • Utility Functions (line_solver.utils)
        • tget()
        • circul()
        • IndexedTable
      • Constants and Enumerations (line_solver.constants)
        • Scheduling Strategies
        • Distribution and Process Types
        • Node Types
        • Job Class Types
        • Routing Strategies
        • Service Strategies
        • Solver Types
        • Metric Types
        • Drop and Replacement Strategies
        • Join Strategies
        • Layered Network Types
        • Polling Types
        • Event and Timing Types
        • Verbose Level
        • Global Constants
      • Example Gallery (line_solver.gallery)
        • gallery_aphm1()
        • gallery_coxm1()
        • gallery_detm1()
        • gallery_erlm1()
        • gallery_erlm1ps()
        • gallery_gamm1()
        • gallery_hyperlk()
        • gallery_hypm1()
        • gallery_mhyp1()
        • gallery_merl1()
        • gallery_mm1()
        • gallery_mm1_linear()
        • gallery_mm1_tandem()
        • gallery_mmk()
        • gallery_mpar1()
        • gallery_parm1()
        • gallery_um1()
        • gallery_cqn()
        • gallery_mm1_feedback()
        • gallery_mm1_prio()
        • gallery_mm1_multiclass()
        • gallery_mapm1()
        • gallery_dm1()
        • gallery_erldk()
        • gallery_erlerl1()
        • gallery_erlerl1_reentrant()
        • gallery_erlm1_ps()
        • gallery_erlm1_reentrant()
        • gallery_hyperl1_feedback()
        • gallery_hyperl1_reentrant()
        • gallery_hyphyp1_linear()
        • gallery_hyphyp1_reentrant()
        • gallery_hyphyp1_tandem()
        • gallery_hypm1_reentrant()
        • gallery_lukumar_reentrant()
        • gallery_mapmk()
        • gallery_mdk()
        • gallery_merl1_linear()
        • gallery_merl1_reentrant()
        • gallery_merl1_tandem()
        • gallery_merlk()
        • gallery_mhyp1_linear()
        • gallery_mhyp1_reentrant()
        • gallery_mhyp1_tandem()
        • gallery_mhypk()
        • gallery_mm1_ps()
        • gallery_mm1_ps_feedback()
        • gallery_mm1_ps_multiclass()
        • gallery_mm1_ps_reentrant()
        • gallery_mm1_reentrant()
        • gallery_mm1_tandem_multiclass()
        • gallery_cqn_multiclass()
        • gallery_repairmen()
        • gallery_mmap1()
        • gallery_mmap1_multiclass()
        • gallery_mmapk()
        • gallery_replayerm1()
        • gallery_multitier()
        • gallery_multitier_storage()
        • gallery_fj_open()
        • gallery_fj_closed()
        • gallery_fj_quorum()
        • gallery_cache_lru()
        • gallery_cache_routing()
        • gallery_lqn_basic()
        • gallery_lqn_workflows()
        • gallery_mm1k()
        • gallery_fcr()
        • gallery_renv_breakdown()
        • gallery_qn_random()
        • gallery_lqn_random()
    • Overview
    • Module Locations
    • License
  • Reference
    • Scheduling Strategies
    • Distribution Types
    • Node Types

Additional Reference:

  • Solver Reference
    • Common NetworkSolver Methods
      • Steady-State Average Metrics
        • Basic Performance Metrics
        • Specialized Average Methods
        • Chain-Based Metrics
      • State Probability Methods
      • Distribution Methods
      • Transient Analysis Methods
      • Sample Path Methods
      • Solver Options
    • Individual Solvers
      • AUTO Solver
      • CTMC Solver
      • FLD Solver
      • JMT Solver
      • LN Solver
      • LQNS Solver
      • MAM Solver
      • MVA Solver
      • NC Solver
      • SSA Solver
      • LDES Solver
    • Solver Compatibility Matrix
    • See Also
  • Choosing the Right Solver
    • Selection Guidelines
    • Performance Considerations
    • Choosing the Engine
    • See Also
LINE Solver (Python)
  • Search

© Copyright 2025, Imperial College London.

Built with Sphinx using a theme provided by Read the Docs.