TITLE: Parallel server queueing systems in the heavy traffic regime

SPEAKER: David Gamarnik

ABSTRACT:

A parallel server queueing system model is used in a variety of applications including computer networks, call centers and health care management. Understanding the behavior of this system in the heavy traffic setting when the number of servers is large is a very challenging problem. While a lot is known in the special case of exponentially distributed processing times, starting with
the classical work of Halfin and Whitt in 1980, far less is known in the non-exponential case. This is unfortunate since the real life data, for example the number of days spent by patients in a hospital, often suggests distributions far from exponential.

We will present a recent progress in understanding the steady state behavior of a parallel server queueing system when the processing time distribution is arbitrary. Specifically, we establish that the basic performance measures for this queueing model have the same scaling as for the special case of exponential processing times. Then we obtain a surprisingly simple and explicit upper bound on the limiting tail distribution of the queue length. In special cases we establish the tightness of this bound.

Joint work with Petar Momcilovic (University of Michigan) and David Goldberg (MIT).