Bayesian Analysis of Stochastic Process Models

7

Queueing analysis

7.1 Introduction

Many real-life situations such as customers shopping at a supermarket or patients waiting for a heart transplant involve the arrival of clients who must then wait to be served. As more clients arrive, in many cases a queue is formed. Queueing theory deals with the analysis of such systems. This chapter examines Bayesian inference and prediction for some of the most important queueing systems, as well as some typical decision-making problems in queueing systems such as the selection of the number of servers.

The chapter is laid out as follows. In Section 7.2, we introduce the basic outline of a queueing system and some of the most important characteristics. Then, in Section 7.3, we outline some of the most important queueing models. General aspects of Bayesian inference for queueing systems are briefly commented in Section 7.4 and then, inference for the M/M/1 system is examined in Section 7.5. Inference for non-Markovian systems is considered in Section 7.6. Decision problems for queueing systems are analyzed in Section 7.7 and then, a case study on hospital bed optimization is carried out in Section 7.8. The chapter finishes with a discussion in Section 7.9.

7.2 Basic queueing concepts

Formally, a queueing system is a structure in which clients arrive according to some arrival process and wait if necessary before receiving service from one or more servers. When a client arrives, he or she will be attended if there are free servers. Otherwise, ...