Contribution to unreliable M/M/1/M queueing systems modelling

Abstract

In the queueing theory we usually assume that a server breakdown can not occur (see for example in [1], [2], [3] or [4]). In other words a utility server works without failures. But in practice this assumption is not correct, the server is often a technical device and every technical device can be broken. During the breakdown the server can not work which means that the consideration of server failures has got an effect on performance measures of studied queueing system. We can say that queueing models with unreliable servers are more closely to a reality than models with reliable servers. On the other hand unreliable queueing models are more complicated. This paper presents two models of Markov queueing systems with an unreliable server.