Comparing a Scheduled Process with an Analogous Poisson Process

Abstract

The generating function of a queue in which n arrivals occur at fixed times, of equal intervals apart, and in which the service times are independently and identically distributed exponentially is derived in recursive form. The state probabilities are calculated explicitly for n = 1. An analogous recursion formula for the generating function of a related Poisson process is used to estimate whether the scheduled process may be approximated by a Poisson one. In no instance is the approximation a good one.