Dynamic Scheduling of a Multiclass Queue in the Halfin–Whitt Regime: A Computational Approach for High-Dimensional Problems
研究了电话呼叫中心中系统经理动态分配服务器给客户呼叫的问题，在Halfin–Whitt重流量机制下推导出近似扩散控制问题，并基于深度神经网络开发了计算方法，在高达500个客户类别的测试中表现优于或等于最佳基准。
We consider a multiclass queueing model of a telephone call center in which a system manager dynamically allocates available servers to customer calls. Calls can terminate through either service completion or customer abandonment, and the manager strives to minimize the expected total of holding costs plus abandonment costs over a finite horizon. Focusing on the Halfin–Whitt heavy traffic regime, we derive an approximating diffusion control problem and, building on earlier work by Beck et al. [Beck C, Becker S, Cheridito P, Jentzen A, Neufeld A (2021) Deep splitting method for parabolic PDEs. SIAM J. Sci. Comput. 43(5):A3135–A3154], develop a simulation-based computational method for solution of such problems, one that relies heavily on deep neural network technology. Using this computational method, we propose a policy for the original (prelimit) call center scheduling problem. Finally, the performance of this policy is assessed using test problems based on publicly available call center data. For the test problems considered so far, our policy does as well as or better than the best benchmark we could find. Moreover, our method is computationally feasible at least up to dimension 500, that is, for call centers with 500 or more distinct customer classes. This paper was accepted by David Simchi-Levi, stochastic models and simulation. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.03921 .