Backlogged Bandits: Cost-Effective Learning for Utility Maximization in Queueing Networks

Bipartite queueing networks with unknown statistics, where jobs are routed to and queued at servers and yield server-dependent utilities upon completion, model a wide range of problems in communications and related research areas (e.g., call routing in call centers, task assignment in crowdsourcing, job dispatching to cloud servers). The utility maximization problem in bipartite queueing networks with unknown statistics is a bandit learning problem where the delayed semi-bandit feedback depends on the server queueing delay. In this paper, we propose an efficient algorithm that overcomes the technical shortcomings of the state-of-the-art and achieves square root regret, queue length, and feedback delay. Our approach also accommodates additional constraints, such as quality of service, fairness, and budgeted cost constraints, with constant expected peak violation and zero expected violation after a fixed timeslot. Empirically, our algorithm's regret is competitive with the state-of-the-art for some problem instances and outperforms it in others, with much lower delay and constraint violation.