The “W” network and the dynamic control of unreliable flexible servers

Soroush Saghafian, Mark Van Oyen and Bora Kolfal

IISE Transactions, 2011, vol. 43, issue 12, 893-907

Abstract: 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 cμ 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 cμ rule. Extensive numerical tests show that LEWC performs well in comparison with four key policies: optimal, LQ, cμ, and generalized cμ (Gcμ). The stability of the LEWC, LQ, and Gcμ policies is proved. [Supplementary materials are available for this article. Go to the publisher's online edition of IIE Transactions for additional appendices (detailed proofs, additional analyses, data sets, etc.).]

Date: 2011
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DOI: 10.1080/0740817X.2011.575678

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