Heavy traffic asymptotics for a gated, infinite-server queue with uniform service times

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 is large and consider the two space scales and . This leads to very simple approximations to the probability distribution, which are shown to be in excellent agreement with numerical results.