TITLE:  Performance Bounds for Large Scale Queueing Systems

SPEAKER:  David Goldberg

ABSTRACT:

Parallel server queues arise in many applications, ranging from call centers to national security and health care. Understanding how these systems behave when the number of servers is large and the service distribution is non-Markovian is a difficult problem. In this talk, we resolve several open questions related to a certain heavy traffic scaling regime (Halfin-Whitt) for parallel server queues, which has recently been used in the modeling of call centers. In particular, we derive the asymptotics of the steady-state queue length for a very general class of service distributions. We also bound the large deviations behavior of the limiting steady-state queue length, and prove that the associated critical exponent takes a particularly simple form in certain cases. Our main proof technique involves bounding the multiserver queue between two simpler systems. These systems exhibit an interesting duality, and yield bounds of a very general nature, which may be useful in answering a range of questions related to the modeling and optimization of queues.