Bayesian Nonparametric Inference for M/G/1 Queueing Systems

TL;DR

This paper develops a Bayesian nonparametric method to infer characteristics of M/G/1 queueing systems, especially the waiting time distribution, using indirect inference via the Pollaczek-Khinchine transform formula.

Contribution

It introduces a novel Bayesian nonparametric approach for inference in M/G/1 queues, including posterior validation and separate inference of system observables.

Findings

Posterior consistency established for the estimator.

Posterior normality demonstrated for the inference.

Method enables inference of waiting time distribution from observed data.

Abstract

In this work, nonparametric statistical inference is provided for the continuous-time M/G/1 queueing model from a Bayesian point of view. The inference is based on observations of the inter-arrival and service times. Beside other characteristics of the system, particular interest is in the waiting time distribution which is not accessible in closed form. Thus, we use an indirect statistical approach by exploiting the Pollaczek-Khinchine transform formula for the Laplace transform of the waiting time distribution. Due to this, an estimator is defined and its frequentist validation in terms of posterior consistency and posterior normality is studied. It will turn out that we can hereby make inference for the observables separately and compose the results subsequently by suitable techniques.