Optimal Policies for Multi-server Non-preemptive Priority Queues
Queueing Systems: Theory and Applications
Dynamic Routing in Large-Scale Service Systems with Heterogeneous Servers
Queueing Systems: Theory and Applications
Mathematics of Operations Research
Fair Dynamic Routing in Large-Scale Heterogeneous-Server Systems
Operations Research
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We address the problem of scheduling a multiclassM/M/m queue with Bernoulli feedback onm 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 itsrelative 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脗µ 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 ofwork decomposition laws for the parallel-server system. We further report on the results of a computational study on the quality of the c脗µ rule for parallel scheduling.