On the M/G/1 queue by additional inputs

Abstract

A single-server queueing system is studied, the input into which consists of the sum of two independent stochastic processes. One of these is an ‘M/G' type input process, the other a much more general process which need not be Markov. There are two types of busy period, depending on which arrival process started the busy period. Stochastic monotonicity results are derived and it is found that under a stationarity-like condition the probability of being in a busy period which started with an ‘M/G' arrival is independent of time and is the same it would be with the ‘M/G' process as only input process. Also, distributional results are obtained for the virtual waiting-time process, and these results are used to reduce the study of a single-server queueing system with as input the sum of independent ‘M/G' and ‘GI/G' input streams to the study of a related GI/G/1 queueing system.The purpose of this paper is to pave the way for a study of an M/G/1 queueing system with periodic arrivals of additional work, and for optimal scheduling of maintenance processes in certain real-time computer systems.