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 lambda is large and consider the two space scales k = lambda + 0(root lambda) and k = 0(lambda). This leads to very simple approximations to the probability distribution, which are shown to be in excellent agreement with numerical results.