API Documentation

This section provides detailed API documentation for all LINE Solver Python modules.

API Sections:

• Core Modules
  • Network Models (line_solver.lang)
  • Solvers (line_solver.solvers)
  • Distributions (line_solver.distributions)
  • Layered Networks (line_solver.layered)
• 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
  • LayeredNetworkStruct
  • kahn_topological_sort()
  • lsn_max_multiplicity()
• Markov Chain Utilities
  • Markov Chain Analysis (line_solver.api.mc)
• 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
  • LdqbdOptions
  • ldqbd_mphc()
  • ph_multisets()
  • MAPBMAP1Result
  • solver_mam_map_bmap_1()
  • BMAPMAP1Result
  • solver_mam_bmap_map_1()
  • QBDResult
  • QbdRapResult
  • 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
  • npfqn_traffic_merge()
  • npfqn_traffic_merge_cs()
  • npfqn_traffic_split_cs()
  • npfqn_sqd()
  • NpfqnSqdResult
  • npfqn_rqna_weight()
  • npfqn_traffic_rqt()
  • npfqn_bnd_bpt()
  • NpfqnBndBptResult
  • npfqn_bnd_bgt()
  • NpfqnBndBgtResult
  • npfqn_traffic_idc()
  • npfqn_traffic_split_rr()
  • npfqn_gtmtst_fluid()
  • npfqn_feedback_elim()
  • npfqn_dps_morrison()
  • NpfqnDpsMorrisonResult
• 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
  • 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
  • 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
  • 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
  • PfqnComomrmLdResult
  • PfqnFncResult
  • pfqn_unique()
  • pfqn_expand()
  • pfqn_combine_mi()
  • PfqnUniqueResult
  • 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
  • pfqn_mmint2()
  • pfqn_mmint2_gausslegendre()
  • pfqn_mmint2_gausslaguerre()
  • pfqn_mmsample2()
  • logsumexp()
  • pfqn_schmidt()
  • pfqn_schmidt_ext()
  • SchmidtResult
  • 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
  • pfqn_rd()
  • RdOptions
  • RdResult
  • pfqn_nre()
  • pfqn_nre_full()
  • PfqnNreResult
  • pfqn_nrl()
  • pfqn_nrp()
  • pfqn_lap()
  • laplaceapprox()
  • num_hess()
  • pfqn_cyclet_ofree()
  • pfqn_stdf()
  • pfqn_stdf_heur()
  • pfqn_cftp()
  • pfqn_mvasjn()
  • pfqn_amvasjn()
  • SjnOptions
• Queueing Systems
  • qsys_mapdc()
  • qsys_mapphc()
  • qsys_mmapgk1()
  • MmapGk1Result
  • MapPhcResult
  • 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
  • ph_to_map()
  • qsys_phph1()
  • qsys_mapph1()
  • qsys_mapm1()
  • qsys_mapmc()
  • qsys_mapmap1()
  • qsys_mapg1()
  • QueueType
  • BmapMatrix
  • PhDistribution
  • QbdStatespace
  • RetrialQueueResult
  • RetrialQueueAnalyzer
  • qsys_bmapphnn_retrial()
  • qsys_is_retrial()
  • RetrialInfo
  • RenegingInfo
  • 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
  • NetworkStruct
  • NodeType
  • SchedStrategy
  • RoutingStrategy
  • DropStrategy
  • sn_region_members()
  • sn_get_demands_chain()
  • SnGetDemandsResult
  • sn_deaggregate_chain_results()
  • SnDeaggregateResult
  • ProductFormParams
  • 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
  • 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)
• Utilities and Constants
  • Utility Functions (line_solver.utils)
  • Constants and Enumerations (line_solver.constants)
  • Example Gallery (line_solver.gallery)

Overview

• Core Modules - Networks, nodes, classes, distributions, solvers

• Cache Algorithms - Cache performance analysis

• Loss Networks - Analysis of networks with blocking

• Layered Stochastic Networks - Layered queueing network analysis

• Markov Chain Utilities - CTMC and DTMC analysis tools

• Matrix-Analytic Methods - QBD processes and matrix-analytic solutions

• Non-Product-Form Networks - Approximations for intractable queueing networks

• Polling Systems - Analysis of gated, exhaustive, and k-limited polling

• Product-Form Queueing Networks - MVA, convolution, and normalizing constant methods

• Queueing Systems - Single-station queueing system analysis

• Stochastic Network Utilities - Network analysis and transformation utilities

• Trace Analysis - Empirical trace characterisation and fitting

• Utilities and Constants - Helper functions, constants, and enumerations

Module Locations

Category	Python Path	Description
Cache API	line_solver.api.cache	Cache analysis algorithms
Constants	line_solver.constants	Enumerations and global constants
Core	line_solver.lang	Network, Node, and JobClass definitions
Distributions	line_solver.distributions	Exp, Erlang, PH, MAP, etc.
Layered Networks	line_solver.layered	LayeredNetwork, Task, Activity
LossN API	line_solver.api.lossn	Loss network algorithms
LSN API	line_solver.api.lsn	Layered stochastic network utilities
MAM API	line_solver.api.mam	Matrix-analytic methods
MC API	line_solver.api.mc	Markov chain analysis
NPFQN API	line_solver.api.npfqn	Non-product-form network approximations
PFQN API	line_solver.api.pfqn	Product-form queueing network algorithms
Polling API	line_solver.api.polling	Polling system algorithms
Qsys API	line_solver.api.qsys	Single queueing system formulas
SN API	line_solver.api.sn	Stochastic network utilities
Solvers	line_solver.solvers	MVA, CTMC, FLD, MAM, etc.
Trace API	line_solver.api.trace	Trace characterisation and fitting

License

BSD-3 License

Copyright (c) 2012-2026, QORE Lab, Imperial College London All rights reserved.