TITLE: Customer abandonment in many-server queues

SPEAKER: Shuangchi He

ABSTRACT:

We first study G/G/n+GI queues in which customer patience times are independent, identically distributed following a general distribution. We prove that, under some conditions, a deterministic relationship holds asymptotically between the abandonment-count and the queue-length processes under the diffusion scaling, when the number of servers goes to infinity. Using this relationship, we prove that for critically loaded G/Ph/n+GI queues with phase-type service times, a pair of diffusion-scaled customer-count and server-allocation processes, properly centered, converges in distribution to a continuous Markov process. We also develop a numerical algorithm based on the finite-element method to compute the steady-state distribution of the diffusion limits of the queue-length process in the G/Ph/n+GI queues.

Joint work with Jim Dai and Tolga Tezcan.