Optimally Scheduling Heterogeneous Impatient Customers
Manufacturing & Service Operations Management, Forthcoming
35 Pages Posted: 15 Jun 2020 Last revised: 10 Jan 2023
Date Written: May 20, 2020
Problem Definition: We study scheduling multi-class impatient customers in parallel server queueing systems. At the time of arrival, customers are identified as being one of many classes, where the class represents the service time and patience time distributions, as well as cost characteristics. From the system's perspective, customers of the same class at time of arrival get differentiated on their residual patience time as they wait in queue. We leverage this property and propose two novel and easy-to-implement multi-class scheduling policies.
Academic/Practical Relevance: Scheduling multi-class impatient customers is an important and challenging topic, especially when customers' patience times are non-exponential. In these contexts even for customers of the same class, processing them under the First Come First Served (FCFS) policy is suboptimal. This is due to the fact that at time of arrival, the system only knows the overall patience distribution from which a customer's patience value is drawn, and as time elapses, the estimate of the customer's residual patience time can be further updated. For non-exponential patience distributions, such an update indeed reveals additional information and using this information to implement within-class prioritization can lead to additional benefits relative to the FCFS policy.
Methodology: We use fluid approximations to analyze the multi-class scheduling problem with ideas borrowed from convex optimization. These approximations are known to perform well for large systems and we use simulations to validate our proposed policies for small systems.
Results: We propose a multi-class time-in-queue policy that prioritizes both across customer classes, and within each class using a simple rule, and further show that most of the gains of such a policy can be achieved by deviating from within-class FCFS for at most one customer class. In addition, for systems with exponential patience times, our policy reduces to a simple priority-based policy, which we prove is asymptotically optimal for Markovian systems with an optimality gap that does not grow with system scale.
Managerial Implications: Our work provides managers ways of improving quality of service to manage parallel server queueing systems. We propose easy-to-implement policies that perform well relative to reasonable benchmarks. Our work also adds to the academic literature on multi-class queueing systems by demonstrating the joint benefits of cross-class and within-class prioritization.
Keywords: multi-class queues, stochastic control, optimization, priority, approximations
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