Optimal Control of Service Systems with Heterogeneous Servers and Priority Customers

• 成果类型: Article
• 署名作者: Chen, David; Chen, Ruoran; Wang, Rowan; Wang, Xuan
• 署名单位: The Chinese University of Hong Kong, Shenzhen; Southwest Jiaotong University; Southern University of Science & Technology; Hong Kong University of Science & Technology
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.2023.01228
• 发表日期: 2025
• 关键词: queueing system; optimal control; heterogeneous servers; priority customers

摘要

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 workconserving 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.