Designing a Call Center with Impatient Customers
Manufacturing & Service Operations Management
Commissioned Paper: Telephone Call Centers: Tutorial, Review, and Research Prospects
Manufacturing & Service Operations Management
Call Centers with Impatient Customers: Many-Server Asymptotics of the M/M/n + G Queue
Queueing Systems: Theory and Applications
Fluid Models for Multiserver Queues with Abandonments
Operations Research
Queues with Many Servers and Impatient Customers
Mathematics of Operations Research
Diffusion approximations for open Jackson networks with reneging
Queueing Systems: Theory and Applications
Abandonment versus blocking in many-server queues: asymptotic optimality in the QED regime
Queueing Systems: Theory and Applications
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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 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 goes to infinity. These conditions include a minor assumption on the arrival processes that can be time-nonhomogeneous and a key assumption 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.