Queues in Reliability

Abstract

Queuing models can be useful in solving many complex reliability problems. Component failures are usually interpreted as the arrival of customers and the repair or replacement of failed components is typically associated with the service facility. A distinctive characteristic of queues in reliability is that requests for service are usually generated by a finite customer population because, in general, there are a limited number of units, e.g., machines which can fail, and when they are all in the system, being repaired or waiting for repair, no more can arrive. Thus the arrivals do not form a renewal process as they may depend on the number of units in the system. This is an essential difference from typical queuing systems, where the population of potential arrivals can be considered to be effectively limitless. This article gives an overview of the main queuing models used in reliability which are illustrated using the classical machine repairmen model. Some statistical methods to estimate the main quantities of interest in a queue are also discussed.