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1 results

  • A new view of the heavy-traffic limit theorem for infinite-server queues

  • Peter W. Glynn, Ward Whitt
  • Journal:
    Advances in Applied Probability / Volume 23 / Issue 1 / March 1991
    Published online by Cambridge University Press:
    01 July 2016, pp. 188-209
    Print publication:
    March 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 observation is that infinite-server queues having deterministic service times 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.