Uncovering the topology of an infinite-server queueing network from population data

TL;DR

This paper introduces a method-of-moments approach for inferring parameters of an infinite-server queueing network from population data, demonstrating its consistency and accuracy through numerical experiments.

Contribution

It develops a novel statistical inference method for infinite-server queues, accommodating both parametric and non-parametric service-time models, with proven consistency.

Findings

Accurate parameter estimates achieved in simulations.

Method is effective even with many parameters.

Both parametric and non-parametric models are supported.

Abstract

This paper studies statistical inference in a network of infinite-server queues, with the aim of estimating the underlying parameters (routing matrix, arrival rates, parameters pertaining to the service times) using observations of the network population vector at Poisson time points. We propose a method-of-moments estimator and establish its consistency. The method relies on deriving the covariance structure of different nodes at different sampling epochs. Numerical experiments demonstrate that the method yields accurate estimates, even in settings with a large number of parameters. Two model variants are considered: one that assumes a known parametric form for the service-time distributions, and a model-free version that does not require such assumptions.