DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:** Weining Kang, UMBC

**Title: ***
Performance Analysis of Many-server Queues with Reneging
*

**Abstract:**
Motivated by problems of current relevance for call centers,
we consider a queuing system with a single pool of N identical servers
that process incoming customers who have generally distributed service
requirements, and abandon the queue if their waiting time exceeds
their so-called patience time. We derive a first-order approximation
of this system and study its asymptotic behavior, as the number of
servers goes to infinity. We also establish existence of stationary
distributions of the state descriptor of such a system. Moreover,
under the uniqueness assumption on the invariant state of the
associated fluid model solution, we show that, as the number of
servers goes to infinity, the sequence of stationary distributions for
the fluid scaled system state descriptors converges to the unique
invariant state. At last, we show some counterexamples when the
uniqueness assumption fails to hold.

**Time:** Friday, April 9, 2010, 1:30-2:30 p.m.

**Place:** Science and Tech I, Room 242

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491