Journal of the Operations Research Society of China ›› 2025, Vol. 13 ›› Issue (3): 810-836.doi: 10.1007/s40305-024-00562-z

Previous Articles     Next Articles

Simulation Optimization for Queues with Heavy-Tailed Service Times

Gui-Yu Hong, Xin-Yun Chen   

  1. School of Data Science, The Chinese University of Hong Kong, Shenzhen 518172, Guangdong, China
  • Received:2023-09-01 Revised:2024-08-29 Online:2025-09-30 Published:2025-09-16
  • Contact: Xin-Yun Chen E-mail:chenxinyun@cuhk.edu.cn
  • Supported by:
    The project is funded by Science, Technology and Innovation Commission of Shenzhen Munici pality(No. RCYX20210609103124047), the National Natural Science Foundation of China (Nos. 72171205 and 72394361) and Guangdong Provincial Key Laboratory of Mathematical Foundations for Artificial Intelligence (No. 2023B1212010001).

Abstract: We develop a gradient-based simulation optimization algorithm, dabbed KWiQ-H, for joint pricing and staffing problems in single-server queues with heavy-tailed service time distributions. Our algorithm is designed based on the well-known Kiefer-Wolfowitz algorithm so that it is applicable tomore general and practical settings where customer’s behavior is unknown to service providers in prior. We first establish a convergence result for KWiQ-H when the service times have a finite fifth moment. Then, we show that under a stronger condition with a finite seventh moment, KWiQ-H could achieve sample complexity with the same asymptotic order as in the case when service times are light-tailed in Chen et al. (Oper Res, 2023). Complementing the theoretic results, we carry out comprehensive numerical experiments to test the efficiency and robustness of KWiQ-H in a variety of model settings.

Key words: Queues, Kiefer-Wolfowitz, Heavy-tail effect, Pricing and staffing

CLC Number: