Demonstration of effective UCB-based routing in skill-based queues on real-world data

This paper is about optimally controlling skill-based queueing systems such as data centers, cloud computing networks, and service systems. By means of a case study using a real-world data set, we investigate the practical implementation of a recently developed reinforcement learning algorithm for optimal customer routing. Our experiments show that the algorithm efficiently learns and adapts to changing environments and outperforms static benchmark policies, indicating its potential for live implementation. We also augment the real-world applicability of this algorithm by introducing a new heuristic routing rule to reduce delays. Moreover, we show that the algorithm can optimize for multiple objectives: next to payoff maximization, secondary objectives such as server load fairness and customer waiting time reduction can be incorporated. Tuning parameters are used for balancing inherent performance trade--offs. Lastly, we investigate the sensitivity to estimation errors and parameter tuning, providing valuable insights for implementing adaptive routing algorithms in complex real-world queueing systems.

Learning payoffs while routing in skill-based queues

Motivated by applications in service systems, we consider queueing systems where each customer must be handled by a server with the right skill set. We focus on optimizing the routing of customers to servers in order to maximize the total payoff of customer--server matches. In addition, customer--server dependent payoff parameters are assumed to be unknown a priori. We construct a machine learning algorithm that adaptively learns the payoff parameters while maximizing the total payoff and prove that it achieves polylogarithmic regret. Moreover, we show that the algorithm is asymptotically optimal up to logarithmic terms by deriving a regret lower bound. The algorithm leverages the basic feasible solutions of a static linear program as the action space. The regret analysis overcomes the complex interplay between queueing and learning by analyzing the convergence of the queue length process to its stationary behavior. We also demonstrate the performance of the algorithm numerically, and have included an experiment with time-varying parameters highlighting the potential of the algorithm in non-static environments.