A New View of the Heavy-Traffic Limit Theorem for Infinite-Server Queues

P. W. Glynn and W. Whitt

Advances in Applied Probability, Vol. 23, 188-209 (1991)

This paper presents a new approach for obtaining heavy-traffic limits for infinite-server queues and open networks of infinite-server queues. The key observationi s that infinite-serveqr ueues havingd eterministics ervicet imes can easily be analyzed in terms of the arrival counting process. A variant of the same idea applies when the service times take values in a finite set, so this is the key assumption. In addition to new proofs of established results, the paper contains several new results, including limits for the work-in-system process, limits for steady-state distributions, limits for open networks with general customer routes, and rates of convergence. The relatively tractable Gaussian limits are promising approximations for many-server queues and open networks of such queues, possibly with finite waiting rooms.