Parallel server queueing systems in the heavy traffic regime
<-- Return to the list
Date: 04-21-2009
Start Time:
1:00pm
End Time: 2:00pm
Speaker: David Gamarnik, Massachusetts Institute of Technology
Location: 303 Mudd
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 holding 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 in the heavy traffic regime when the holding time distribution is arbitrary. Specifically, we obtain a surprisingly simple upper bound on the limiting tail distribution of the queue length in terms of the stochastic primitives of the model. In special cases we establish the tightness of this bound.
Joint work with Petar Momcilovic (University of Michigan) and David Goldberg (MIT).
BIO
David Gamarnik is an associate professor of operations research at the Sloan School of Management, MIT. He received B.A. in mathematics from New York University in 1993 and Ph.D. in operations research from MIT in 1998. Since then he worked as a research staff member in the Department of Mathematical Sciences, IBM Research, before joining the Operations Research and Statistics group in the Sloan School of Management in 2005. His research interests include applied probability and stochastic processes, queueing theory, theory of random combinatorial structures and algorithms, combinatorial optimization, statistical learning theory and various applications. He is a recipient of the Erlang Prize from the INFORMS Applied Probability Society and IBM Faculty Partnership Award.
He is an associate editor of Annals of Applied Probability and Operations Research journals.