Auxiliary Variables for Bayesian Inference in Multi-Class Queueing Networks

TL;DR

This paper introduces a flexible Bayesian inference method for multi-class queueing networks, addressing missing data and complex service dynamics, validated on synthetic and real hospital data.

Contribution

It presents a novel slice sampling approach for parameter inference in multi-class Markovian queue networks with switching and diverse service disciplines.

Findings

Effective inference with missing data demonstrated on synthetic datasets.

Successful application to real hospital service data.

Method overcomes prior restrictions on service rates.

Abstract

Queue networks describe complex stochastic systems of both theoretical and practical interest. They provide the means to assess alterations, diagnose poor performance and evaluate robustness across sets of interconnected resources. In the present paper, we focus on the underlying continuous-time Markov chains induced by these networks, and we present a flexible method for drawing parameter inference in multi-class Markovian cases with switching and different service disciplines. The approach is directed towards the inferential problem with missing data and introduces a slice sampling technique with mappings to the measurable space of task transitions between service stations. The method deals with time and tractability issues, can handle prior system knowledge and overcomes common restrictions on service rates across existing inferential frameworks. Finally, the proposed algorithm is validated on synthetic data and applied to a real data set, obtained from a service delivery tasking tool implemented in two university hospitals.