Customer Abandonment in Many-Server Queues

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. We prove that, under some conditions, a deterministic relationship between the two stochastic processes holds asymptotically under the diffusion scaling when the number of servers n → ∞. The key assumption is that the sequence of diffusion-scaled queue-length processes, indexed by n, is stochastically bounded. We also establish a comparison result that allows one to verify the stochastic boundedness by studying a corresponding sequence of systems without customer abandonment.

• Type: Journal
• Year: 2010
• Where: MOR
• Authors: J. G. Dai, Shuangchi He
• Keywords: Customer, General Distribution, MOR 2010, Patience Time