Delay analysis for discrete-time queueing-systems with multiple randomly interrupted servers

This paper analyzes the performance of discrete-time multiserver queues, subjected to random server interruptions. The arrival process is general independent. The numbers of available servers from slot to slot are modelled as a set of random variables. These are assumed to be independent, identically distributed. Under these assumptions, an expression for the probability generating function of the delay is derived. From this function the first two moments of the delay are obtained. The result is shown to agree with Little's theorem. In addition, an analytic approximation for the tail probabilities of both delay and system contents is presented. A numerical example is included to illustrate the analysis.