The Effect of Customer Abandonment on Queueing System Approximation and Control
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Date: 05-12-2009
Start Time:
1:00pm
End Time: 2:00pm
Speaker: Amy Ward, Marshall School of Business: University of Southern California
Location: 303 Mudd
ABSTRACT
Although many standard queueing models assume that customers are infinitely patient while waiting for service, it is often the case that such an assumption is not reasonable. In particular, impatient customers faced with long waiting times often evidence their frustration by abandoning the system before completing service. We show that customer abandonments can have a significant impact on both the approximation and control of queueing systems, even when the percentage of customers abandoning is small, by studying several simple, but representative models.
Specifically, we first observe that, in a GI/GI/1 queue with customer abandonments, there is a trade-off between turning away a customer and having him wait in queue but possibly abandon before receiving his service. We develop an admission control policy for this system that minimizes expected infinite horizon discounted cost. This is interesting from a methodological standpoint because the problem does not admit a so-called pathwise solution.
Next, we consider the effect of customer abandonment on the optimal control policy in the parallel server system known as N-system1. Specifically, we show that the inclusion of customer abandonments in the model fundamentally changes the asymptotically optimal policy proposed in Bell and Williams (2001). The asymptotically optimal policy we propose requires that classes sometimes be prioritized in a non-greedy manner, and so cannot be characterized as a generalization of the cµ-rule.
References:
Reed and Ward. 2008. Approximating the GI/GI/1+GI Queue with a Nonlinear Drift Diffusion: Hazard Rate Scaling in Heavy Traffic. Mathematics of Operations Research 33 (3), 606-644.
Ward and Kumar. 2008. Asymptotically Optimal Admission Control of a Queue with Impatient Customers. Mathematics of Operations Research 33 (1), 167-202.
Ghamami and Ward. 2009. Dynamic Scheduling of an N-System with Customer Abandonments. Working Paper.
1 The N-system consists of two customer classes and two servers. Server 1 is dedicated, and serves only one customer class. Server 2 can serve either customer class. Each time server 2 finishes processing a customer, and there are customers in both buffers, there is a real-time control decision concerning which class server 2 should serve next.
BIO
Amy R Ward is an assistant Professor in the Information and Operations Management Department at the Marshall School of Business at USC. Prior to joining USC, she was an assistant Professor in the Industrial and Systems Engineering Department at Georgia Tech. She earned her PhD from Stanford in 2001, in Management Science and Engineering. Her research interests include: probability and stochastic processes; manufacturing and service system applications; and queueing.