Dynamic Scheduling of a Multiclass Queue in the Halfin-Whitt Regime: A Computational Approach for High-Dimensional Problems
Baris Ata, Ebru Kasikaralar
TL;DR
This paper develops a diffusion-approximation framework for dynamic, multiclass queueing with nonstationary data in the Halfin-Whitt regime and solves the resulting high-dimensional Brownian control problem using a novel deep splitting neural-network method. By translating the HJB PDE into a sequence of tractable subproblems solved backward in time with neural approximations of the value function and its gradient, the authors produce a data-driven scheduling policy that performs competitively with or better than state-of-the-art benchmarks, even in problems with up to 500 classes. The methodology is validated on13 data-driven test problems derived from US Bank call-center data, showcasing the approach’s scalability, computational feasibility, and practical impact for large-scale call centers. The work contributes a computationally feasible pathway to diffusion-controlled policies in high dimensions, bridging stochastic control theory, deep learning, and real-world operations management.
Abstract
We consider a multi-class 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. (2021), 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 (pre-limit) 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.