ENV (Environment/Blending Solver)
Methods · Configuration · Shared options · All solvers
The ENV solver analyzes queueing systems operating in random environments with multiple operational stages. The solver uses stage-dependent analysis where system parameters vary according to the current environmental state. Performance metrics are computed as ensemble averages over all environmental stages, enabling modeling of systems subject to external conditions or failures.
Methods
The method names and defaults below describe the MATLAB interface. Aliases share a row; model-specific restrictions and backend differences are noted. Use solver.listValidMethods() to inspect the names available for your model.
| Method | Algorithm and applicability |
|---|---|
default | Alias of meanfield. |
meanfield | Mean-field coupling of the stages: only the marginal means cross an environment switch. |
mean | Alias of meanfield, naming what crosses a switch rather than the limit it comes from. |
meancov | The same coupling carrying a covariance beside the mean, seeding the next stage through config.init_qlen/init_qcov. |
blend | Alias of default/meanfield since 2026-09-13; it named statevec before then. |
statevec | State-vector coupling: the whole joint distribution crosses a switch (CTMC or MAM stage solvers, finite timespan). |
statedep | Coupling in which the environment transition depends on the state it leaves. |
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. |
avg | Closed-form fast-environment limit: the stages are averaged instead of iterated. |
dec | Closed-form slow-environment limit: the stages are decoupled and solved separately. |
Configuration options
The solver-specific fields below belong to options.config. Set them on an options struct, for example opt.config.name = value, and pass that struct to the solver constructor. See shared solver options for all top-level fields, shared configuration, defaults and usage. Options apply only to the methods and model features that consume them.
Relevant top-level options: iter_max, timespan, init_sol.
ENV defaults to iter_max=100. Configure each stage solver separately. The meancov coupling passes init_qlen and init_qcov to compatible fluid stage solvers. statevec requires CTMC or MAM stages and a finite time horizon. Use config.da for decomposition selection; decomp is a docstring name, not a field read by the code.
| Option | Default | Description and values |
|---|---|---|
da | 'courtois' | Decomposition-aggregation algorithm for the coupled CTMC: 'courtois', 'kms' (Koury-McAllister-Stewart), 'takahashi', 'multi' (multigrid). |
da_iter | 10 | Iterations of the kms and takahashi variants. |
decomp | see da | The name the ctmc_decompose docstring uses for the same selector; the code reads da. |
env_alpha | 0.01 | Coupling threshold of the beam search that partitions an environment of more than 10 stages. |
Example
This example demonstrates the ENV solver for queueing systems operating in random environments with multiple operational stages. The unique feature of ENV is its ability to analyze systems where parameters vary according to environmental states, computing ensemble averages over all stages.
% Create a simple M/M/1 queue operating in multiple environmental stages
model = Network('ENV Example');
source = Source(model, 'Source');
queue = Queue(model, 'Queue', SchedStrategy.FCFS);
sink = Sink(model, 'Sink');
jobclass = OpenClass(model, 'Class1');
source.setArrival(jobclass, Exp(0.8));
queue.setService(jobclass, Exp(1.0));
P = model.initRoutingMatrix();
P.set(jobclass, jobclass, source, queue, 1.0);
P.set(jobclass, jobclass, queue, sink, 1.0);
model.link(P);
% Solve with environment-aware analysis
ENV(model).avgTable()Output:
ENV analysis [method: default; type: approximate, deterministic; lang: matlab; env: 2025a] completed in 0.08s. Station JobClass QLen Util RespT ResidT ArvR Tput Queue Class1 4 0.8 5 1 0.8 0.8 Ensemble averaged over environmental stages.
// Create a simple M/M/1 queue operating in multiple environmental stages
Network model = new Network("ENV Example");
Source source = new Source(model, "Source");
Queue queue = new Queue(model, "Queue", SchedStrategy.FCFS);
Sink sink = new Sink(model, "Sink");
OpenClass jobclass = new OpenClass(model, "Class1");
source.setArrival(jobclass, new Exp(0.8));
queue.setService(jobclass, new Exp(1.0));
RoutingMatrix P = model.initRoutingMatrix();
P.set(jobclass, jobclass, source, queue, 1.0);
P.set(jobclass, jobclass, queue, sink, 1.0);
model.link(P);
// Solve with environment-aware analysis
new ENV(model).avgTable.print();Output:
ENV analysis [method: default; type: approximate, deterministic; lang: java; env: 17.0.9] completed.
Station JobClass QLen Util RespT ResidT ArvR Tput
Queue Class1 4 0.8 5 1 0.8 0.8
Ensemble averaged over environmental stages.
# Create a simple M/M/1 queue operating in multiple environmental stages
from line_solver import *
model = Network("ENV Example")
source = Source(model, "Source")
queue = Queue(model, "Queue", SchedStrategy.FCFS)
sink = Sink(model, "Sink")
jobclass = OpenClass(model, "Class1")
source.set_arrival(jobclass, Exp(0.8))
queue.set_service(jobclass, Exp(1.0))
P = model.init_routing_matrix()
P.set(jobclass, jobclass, source, queue, 1.0)
P.set(jobclass, jobclass, queue, sink, 1.0)
model.link(P)
# Solve with environment-aware analysis
print(ENV(model).avg_table)Output:
ENV analysis [method: default; type: approximate, deterministic; lang: python; env: 3.13.7] completed.
Station JobClass QLen Util RespT ResidT ArvR Tput
Queue Class1 4 0.8 5 1 0.8 0.8
Ensemble averaged over environmental stages.