HEAVY TRAFFIC ASYMPTOTICS FOR A GATED, INFINITE-SERVER QUEUE WITH UNIFORM SERVICE TIMES

The authors consider a gated, infinite-server queue with uniform servi ce times. Using perturbation methods they construct asymptotic formula s for the probability that k customers are served during a stage. The authors assume that the Poisson arrival rate lambda is large and consi der the two space scales k = lambda + 0(root lambda) and k = 0(lambda) . This leads to very simple approximations to the probability distribu tion, which are shown to be in excellent agreement with numerical resu lts.