Letter to the Editor—Some Results for the Bulk-Arrival Infinite-Server Poisson Queue

Abstract

An infinite server queue is considered in which an arrival is actually a group (of random size) of customers. A generating function for the time-dependent queue length is obtained, and used to show that the limiting distribution is compound Poisson. It is also shown that the regression of queue length at time t on the initial length is linear, and from this an expression for the autocorrelation function is deduced.