The "w" network and the dynamic control of unreliable flexible servers

This article addresses the problem of effectively assigning partially flexible resources to various jobs in Markovian parallel queueing systems with heterogeneous and unreliable servers. Attention is focused on a structure forming a W and it is found that this design is highly efficient; it requires only a small amount of cross-training but often performs almost as well as a fully cross-trained system. It is shown that (even allowing disruptions) a version of the c rule, which prioritizes serving the fixed task before the shared, is optimal under some conditions. Since the optimal policy is complex in general, a powerful and yet simple control policy is developed. This policy (which is implementable in any parallel queueing system) defines a simple measure of workload costs and assigns each server to the queue with the Largest Expected Workload Cost (LEWC). Thus, it effectively combines the intuition underlying two widely used policies: (i) the load-balancing objective in serving the Longest Queue (LQ); and (ii) the greedy cost minimization emphasis of the c rule. Extensive numerical tests show that LEWC performs well in comparison with four key policies: optimal, LQ, c, and generalized c (Gc). The stability of the LEWC, LQ, and Gc policies is proved.