On the eelationship of the transient behaviour of a general queueing model to its idle and busy period distributions

Abstract

A general queueing model is studied. The main limitation is that bulk arrivals and bulk services are not allowed. Simple relations between the transient state probabilities and the busy and idle period distributions are obtained. The LAPLACE Transform of the idle period distribution always follows from the transient solution. The same is true for one busy period distribution, when intervals between arrivals have negative exponential distributions. On the other hand the transient state probabilities can always be obtained directly from an investigation of a “busy cycle process”.