UQ (Uncertainty Quantification)

The UQ solver is a meta-solver for uncertainty quantification, exposed through the Posterior class. It attaches a Prior distribution to one or more uncertain model parameters, repeatedly evaluates the model with an inner back-end solver under alternative parameter values, and aggregates the outcomes into a posterior distribution of the chosen performance metrics. This enables propagation of parameter uncertainty through a queueing model without re-implementing the underlying analytical or simulation loop. See Tutorial 12: Posterior Analysis for a complete walkthrough.

MethodAlgorithmReference
defaultPosterior analysis by evaluation of the model over the prior support—

Example

This example propagates uncertainty in the service rate of an M/M/1 queue. A Prior distribution over a set of exponential service alternatives is attached to the queue, and Posterior runs an inner MVA solver once per alternative, aggregating the results into prior-weighted mean performance metrics.

% Build an M/M/1 model with an uncertain service rate
model = Network('UncertainServiceModel');
source = Source(model, 'Source');
queue  = Queue(model, 'Queue', SchedStrategy.FCFS);
sink   = Sink(model, 'Sink');
jobClass = OpenClass(model, 'Jobs');
source.setArrival(jobClass, Exp(0.5));

% Prior over service-rate alternatives
serviceRates = linspace(0.7, 2.5, 30);
priorProbs = exp(-0.5 * ((serviceRates - 1.3) / 0.4).^2);
priorProbs = priorProbs / sum(priorProbs);
alternatives = arrayfun(@(r) Exp(r), serviceRates, 'UniformOutput', false);
queue.setService(jobClass, Prior(alternatives, priorProbs));

model.link(Network.serialRouting(source, queue, sink));

% Run the UQ meta-solver over an MVA back-end
post = Posterior(model, @SolverMVA);
post.getAvgTable()   % prior-weighted means

Output:

Posterior analysis [back-end: MVA, alternatives: 30] completed.

  Station     JobClass     QLen     Util     RespT     Tput
  Queue         Jobs       0.62     0.38     1.24      0.50
// Build an M/M/1 model with an uncertain service rate
Network model = new Network("UncertainServiceModel");
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, "Jobs", 0);
source.setArrival(jobClass, new Exp(0.5));

// Prior over service-rate alternatives
int numAlternatives = 30;
List<Distribution> alternatives = new ArrayList<>();
double[] priorProbs = new double[numAlternatives];
double sum = 0.0;
for (int i = 0; i < numAlternatives; i++) {
    double rate = 0.7 + (2.5 - 0.7) * i / (double) (numAlternatives - 1);
    alternatives.add(new Exp(rate));
    double z = (rate - 1.3) / 0.4;
    priorProbs[i] = Math.exp(-0.5 * z * z);
    sum += priorProbs[i];
}
for (int i = 0; i < numAlternatives; i++) priorProbs[i] /= sum;
queue.setService(jobClass, new Prior(alternatives, priorProbs));

model.link(Network.serialRouting(source, queue, sink));

// Run the UQ meta-solver over an MVA back-end
Posterior post = new Posterior(model, m -> new MVA(m));
post.getAvgTable().print();   // prior-weighted means

Output:

Posterior analysis [back-end: MVA, alternatives: 30] completed.

  Station     JobClass     QLen     Util     RespT     Tput
  Queue         Jobs       0.62     0.38     1.24      0.50
from line_solver import *
import numpy as np

# Build an M/M/1 model with an uncertain service rate
model = Network('UncertainServiceModel')
source = Source(model, 'Source')
queue  = Queue(model, 'Queue', SchedStrategy.FCFS)
sink   = Sink(model, 'Sink')
jobClass = OpenClass(model, 'Jobs')
source.setArrival(jobClass, Exp(0.5))

# Prior over service-rate alternatives
service_rates = np.linspace(0.7, 2.5, 30)
prior_probs = np.exp(-0.5 * ((service_rates - 1.3) / 0.4) ** 2)
prior_probs = prior_probs / np.sum(prior_probs)
alternatives = [Exp(rate) for rate in service_rates]
queue.setService(jobClass, Prior(alternatives, prior_probs.tolist()))

model.link(Network.serial_routing([source, queue, sink]))

# Run the UQ meta-solver over an MVA back-end
post = Posterior(model, MVA)
print(post.get_avg_table())   # prior-weighted means

Output:

Posterior analysis [back-end: MVA, alternatives: 30] completed.

  Station     JobClass     QLen     Util     RespT     Tput
  Queue         Jobs       0.62     0.38     1.24      0.50
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