Heavy Traffic Asymptotics for a Gated, Infinite-Server Queue with Uniform Service Times

Abstract

The authors consider a gated, infinite-server queue with uniform service times. Using perturbation methods they construct asymptotic formulas for the probability that k customers are served during a stage. The authors assume that the Poisson arrival rate $\lambda $ is large and consider the two space scales $k = \lambda + O( {\sqrt \lambda } )$ and$k = O( \lambda )$. This leads to very simple approximations to the probability distribution, which are shown to be in excellent agreement with numerical results.