Scheduling in Parallel Finite Buffer Systems: Optimal Decisions under Delayed Feedback

Scheduling decisions in parallel queuing systems arise as a fundamental problem, underlying the dimensioning and operation of many computing and communication systems, such as job routing in data center clusters, multipath communication, and Big Data systems. In essence, the scheduler maps each arriving job to one of the possibly heterogeneous servers while aiming at an optimization goal such as load balancing, low average delay or low loss rate. One main difficulty in finding optimal scheduling decisions here is that the scheduler only partially observes the impact of its decisions, e.g., through the delayed acknowledgements of the served jobs. In this paper, we provide a partially observable (PO) model that captures the scheduling decisions in parallel queuing systems under limited information of delayed acknowledgements. We present a simulation model for this PO system to find a near-optimal scheduling policy in real-time using a scalable Monte Carlo tree search algorithm. We numerically show that the resulting policy outperforms other limited information scheduling strategies such as variants of Join-the-Most-Observations and has comparable performance to full information strategies like: Join-the-Shortest-Queue, Join-the- Shortest-Queue(d) and Shortest-Expected-Delay. Finally, we show how our approach can optimise the real-time parallel processing by using network data provided by Kaggle.