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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.PROCESSOR
        • LayeredNetworkElement.HOST
        • LayeredNetworkElement.TASK
        • LayeredNetworkElement.ENTRY
        • LayeredNetworkElement.ACTIVITY
        • LayeredNetworkElement.CALL
      • LayeredNetworkStruct
        • LayeredNetworkStruct.dag
        • LayeredNetworkStruct.mult
        • LayeredNetworkStruct.type
        • LayeredNetworkStruct.isref
        • LayeredNetworkStruct.arrival
        • LayeredNetworkStruct.hassetup
        • LayeredNetworkStruct.repl
        • LayeredNetworkStruct.parent
      • kahn_topological_sort()
      • lsn_max_multiplicity()
    • Markov Chain Utilities
      • Markov Chain Analysis (line_solver.api.mc)
        • ctmc_solve()
        • ctmc_makeinfgen()
    • Matrix-Analytic Methods
      • map_lambda()
      • mmap_super_safe()
      • mmap_compress()
      • ldqbd()
      • LdqbdOptions
        • LdqbdOptions.epsilon
        • LdqbdOptions.max_iter
        • LdqbdOptions.verbose
      • ldqbd_mphc()
    • Non-Product-Form Networks
    • Polling Systems
      • polling_qsys_exhaustive()
      • polling_qsys_gated()
      • polling_qsys_1limited()
      • polling_qsys_decrementing()
    • Product-Form Queueing Networks
    • Queueing Systems
    • Stochastic Network Utilities
      • 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.classspawn
        • NetworkStruct.isslc
        • NetworkStruct.issignal
        • NetworkStruct.signaltarget
        • NetworkStruct.signaltype
        • NetworkStruct.syncreply
        • NetworkStruct.replyblock
        • NetworkStruct.immfeed
        • NetworkStruct.signalremdist
        • NetworkStruct.arrivalbatch
        • 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.regionlincon
        • NetworkStruct.sync
        • NetworkStruct.gsync
        • NetworkStruct.nodeparam
        • NetworkStruct.routingweights
        • NetworkStruct.reward
        • NetworkStruct.rtorig
        • NetworkStruct.rt_visits
        • 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.batchRejectProb
        • 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.PSJF
        • SchedStrategy.FB
        • SchedStrategy.LAS
        • SchedStrategy.LRPT
        • SchedStrategy.FCFSPI
        • SchedStrategy.fromString()
        • SchedStrategy.fromLINEString()
        • SchedStrategy.toID()
        • SchedStrategy.to_feature()
      • RoutingStrategy
        • RoutingStrategy.SQ
        • RoutingStrategy.SDR
        • RoutingStrategy.to_feature()
      • DropStrategy
        • DropStrategy.WAITQ
        • DropStrategy.DROP
        • DropStrategy.BAS
        • DropStrategy.BBS
        • DropStrategy.BlockingBeforeService
        • DropStrategy.RSRD
        • DropStrategy.ReServiceOnRejection
        • DropStrategy.RETRIAL
        • DropStrategy.Retrial
        • DropStrategy.RETRIAL_WITH_LIMIT
        • DropStrategy.RetrialWithLimit
      • sn_get_demands_chain()
      • sn_deaggregate_chain_results()
      • sn_rt_stations()
      • sn_get_arvr_from_tput()
      • sn_is_closed_model()
      • sn_is_open_model()
    • 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)
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