A parallel server queueing system in the so-called Halfin-Whitt (Quality- and Efficiency-Driven) heavy traffic regime has been actively studied recently as a model of large scale call centers.

Very little is known about the behavior of this system for generally (non-exponentially) distributed service times (call durations). We will discuss the behavior of this system in the steady-state when the service times havelattice-valued distribution. We characterize the limiting queue length and waiting time distributions in terms of the stationary distribution of some explicitly constructed Markov chain. As a consequence, the "correct" scaling behavior of this system is established. Then we obtain an explicit expression for the decay rate of the queue length and waiting time distribution, which has a very simple representation in terms of three parameters: the amount of spare capacity and the coefficients of variation of interarrival and service times.

No background on queueing theory is expected and some connections with an ongoing project on management of Cisco workgroups will be discussed.

Joint work with Petar Momcilovic, University of Michigan.