TITLE: Customer Abandonment in Critically Loaded Many-Server Queues

SPEAKER: Shuangchi He

ABSTRACT:

We study G/G/n+GI queues in which customer patience times are independent, identically distributed following a general distribution. When a customer's waiting time in queue exceeds his patience time, the customer abandons the system without service. For the performance of such a system, we focus on the abandonment-count process and the queue length process. Assume the system is operated in many-server heavy traffic. We prove that, under some conditions, a deterministic relationship among the two stochastic possesses holds asymptotically under the diffusion-scaling when the number of server n to infty. The key assumption is that the diffusion-scaled queue length process is stochastically bounded. We also establish a comparison result that allows one to check the stochastic boundedness by studying a corresponding system without customer abandonment.