🤖 AI Summary
This work addresses real-time dynamic scheduling in large-scale multi-class call centers, modeled under the Halfin-Whitt heavy-traffic regime to minimize the expected total cost—arising from customer waiting and abandonment—over a finite horizon. We propose the first deep neural network-based simulation optimization framework that approximates high-dimensional (up to 500 classes) queueing systems as diffusion control problems and optimizes policies via end-to-end training. Our method integrates stochastic optimal control theory, diffusion approximations of queueing dynamics, and simulation-based policy gradient estimation. Experiments on real-world data demonstrate that our approach significantly outperforms existing benchmarks while exhibiting strong scalability—overcoming the longstanding dimensionality bottleneck in high-dimensional queueing control.
📝 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.