Optimally Scheduling Heterogeneous Impatient Customers

34 Pages Posted: 15 Jun 2020

Date Written: May 20, 2020

Abstract

We study the question of scheduling impatient customers in parallel server queuing systems. At the time of arrival, customers can be identified as one of many classes, where the class represents the service time and patience time distributions, and cost characteristics. From the system's perspective, customers that are of the same type at time of arrival get further differentiated on their residual patience time as they wait in the system. This is due to the fact that at time of arrival, the system only knows the overall patience distribution from which the customer's patience value is drawn, and as time elapses, this estimate can be further updated for customers who are still in the system using the information that the customer has not yet abandoned. For non-exponential patience distributions, such an update indeed reveals additional information. In this paper, we use a fluid approach to characterize the cost-minimizing policy that schedules customers on two dimensions of heterogeneity: class and time-in-queue information. We propose a multi-class time-in-queue policy that prioritizes both across customer classes, and within each customer class using a simple rule, and further we show that most of the gains of such a policy can be achieved by deviating from within-class First Come First Serve (FCFS) for at most one customer class. Finally, for systems with exponential abandonment times, our policy reduces to a simple priority-based policy, which we prove to be asymptotically optimal with an optimality gap that does not grow with system scale.

Keywords: multi-class queues, stochastic control, optimization, priority, approximations

Suggested Citation

Bassamboo, Achal and Randhawa, Ramandeep S. and Wu, Chenguang (Allen), Optimally Scheduling Heterogeneous Impatient Customers (May 20, 2020). Available at SSRN: https://ssrn.com/abstract=3605961 or http://dx.doi.org/10.2139/ssrn.3605961

Achal Bassamboo

Northwestern University - Department of Managerial Economics and Decision Sciences (MEDS) ( email )

2001 Sheridan Road
Evanston, IL 60208
United States

Ramandeep S. Randhawa

University of Southern California ( email )

Marshall School of Business
BRI 401, 3670 Trousdale Parkway
Los Angeles, CA 90089
United States

Chenguang (Allen) Wu (Contact Author)

Hong Kong University of Science and Technology ( email )

Room 5559C, Academic Building
HongKong University of Science and Technology
Hong Kong
Hong Kong

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