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Lookup NU author(s): Professor Kevin Glazebrook
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We address the problem of scheduling a multiclass M/M/m queue with Bernoulli feedback on m parallel servers to minimize time-average linear holding costs. We analyze the performance of a heuristic priority-index rule, which extends Klimov's optimal solution to the single-server case: servers select preemptively customers with larger Klimov indices. We present closed-form suboptimality bounds (approximate optimality) for Klimov's rule, which imply that its suboptimality gap is uniformly bounded above with respect to (i) external arrival rates, as long as they stay within system capacity; and (ii) the number of servers. It follows that its relative suboptimality gap vanishes in a heavy-traffic limit, as external arrival rates approach system capacity (heavy-traffic optimality). We obtain simpler expressions for the special no-feedback case, where the heuristic reduces to the classical cμ rule. Our analysis is based on comparing the expected cost of Klimov's rule to the value of a strong linear programming (LP) relaxation of the system's region of achievable performance of mean queue lengths. In order to obtain this relaxation, we derive and exploit a new set of work decomposition laws for the parallel-server system. We further report on the results of a computational study on the quality of the cμ rule for parallel scheduling.
Author(s): Glazebrook KD, Nino-Mora J
Publication type: Article
Publication status: Published
Journal: Operations Research
Year: 2001
Volume: 49
Issue: 4
Pages: 609-623
Print publication date: 01/07/2001
ISSN (print): 0030-364X
ISSN (electronic): 1526-5463
Publisher: Institute for Operations Research and the Management Sciences
URL: http://dx.doi.org/10.1287/opre.49.4.609.11225
DOI: 10.1287/opre.49.4.609.11225
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