Large Deviations for the Infinite Server Queue in Heavy Traffic
P. W. Glynn
In Stochastic Networks, Vol. 71 of Mathematics and its Applications [F. P. Kelly, R. J. Williams, eds.], 387-395 (1995)
In this paper, we establish large deviations approximations to the tail probabilities of the queue-length r.v. in an infinite-server queue in heavy traffic. These large deviations approximations complement the existing Gaussian approximations developed for such systems using weak convergence theory of function spaces. We also describe a simulation-based algorithm for numerical computing such tail probabilities that take advantage of the large deviations theory developed here.