Optimal Control of Service Systems with Heterogeneous Servers and Priority Customers

David Chen (), Ruoran Chen (), Rowan Wang () and Xuan Wang ()
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David Chen: Shenzhen Finance Institute, School of Management and Economics, The Chinese University of Hong Kong, Shenzhen, Shenzhen 518172, China
Ruoran Chen: School of Economics and Management, Southwest Jiaotong University, Chengdu 610031, China
Rowan Wang: SUSTech Business School, Southern University of Science and Technology, Shenzhen 518055, China
Xuan Wang: School of Business and Management, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

Management Science, 2025, vol. 71, issue 8, 6559-6579

Abstract: We study service systems with parallel servers and random customer arrivals and focus on the waiting cost of customers. Using a Markov decision process (MDP) modeling approach, we analytically characterize the structures of the optimal dynamic server assignment policies for two important systems, one consisting of multiple homogeneous servers and two classes of customers and the other consisting of two heterogeneous servers and multiple classes of customers. Based on the obtained results, we propose a threshold-type heuristic policy for the generalized system consisting of multiple heterogeneous servers and multiple classes of customers. To design such a heuristic policy, we first develop techniques for the performance evaluation of general threshold-type policies with any given threshold values. We then construct a path to search for the optimal threshold values. We compare the performance of the best threshold-type heuristic policy with that of the optimal policy and show that our proposed heuristic policy is computationally efficient yet generates great performance. To derive additional managerial insights, we compare the system under our threshold-type dynamic server assignment policy with other commonly seen and simple systems, such as the dedicated system and the work-conserving flexible priority system. The clear performance advantage observed from extensive numerical experiments demonstrates the importance and usefulness of dynamic server assignment control for systems serving multiple classes of customer arrivals. Finally, we extend our analysis to incorporate customer-dependent service rates and sojourn-time minimization performance metrics.

Keywords: queueing system; optimal control; heterogeneous servers; priority customers (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:71:y:2025:i:8:p:6559-6579

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