Simulation Optimization for Queues with Heavy-Tailed Service Times

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 to more 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.