Parallel scheduling of multiclass M/M/m queues: Approximate and heavy-traffic optimization of achievable performance

Kevin D. Glazebrook and José Niño-Mora

Economics Working Papers from Department of Economics and Business, Universitat Pompeu Fabra

Abstract: 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 $c \mu$ 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 $c \mu$ rule for parallel scheduling.

Keywords: Multiclass queueing network; suboptimality bound; heavy-traffic optimality; parallel scheduling; achievable performance region; priority index rule; work decomposition laws (search for similar items in EconPapers)
JEL-codes: C60 C61 (search for similar items in EconPapers)
Date: 1997-02, Revised 1999-10
New Economics Papers: this item is included in nep-ind
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Persistent link: https://EconPapers.repec.org/RePEc:upf:upfgen:427

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