Scheduling Queues with Simultaneous and Heterogeneous Requirements from Multiple Types of Servers

We study the scheduling of a new class of multi-class multi-pool queueing systems where different classes of customers have heterogeneous – in terms of the type and amount – resource requirements. In particular, a customer may require different numbers of servers from different server pools to be allocated simultaneously in order to be served. We apply stochastic simulation to study properties of the model and identify two types of server idleness: avoidable and unavoidable idleness, which play important, but different, roles in dictating system performance, and need to be carefully managed in scheduling. To minimize the long-run average holding cost, we propose a generalization of the cµ-rule, called Generalized Idle-Aware (GIA) cµ-rule. We provide insights into how to set the hyper parameters of the GIA cµ-rule. We also demonstrate that, with properly chosen hyper parameters, the GIA cµ-rule achieves superior and robust performance compared to reasonable benchmarks.