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MARGINAL PRODUCTIVITY INDEX POLICIES FOR SCHEDULING A Multiclass Delay/losssensitive Queue
, 2005
"... We address the problem of scheduling a multiclass M/M/1 queue with a finite dedicated buffer for each class. Some classes are delaysensitive, modeling realtime traffic (e.g. voice, video), whereas others are losssensitive, modeling nonrealtime traffic (e.g. data). Different levels of tolerance t ..."
Abstract

Cited by 7 (5 self)
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We address the problem of scheduling a multiclass M/M/1 queue with a finite dedicated buffer for each class. Some classes are delaysensitive, modeling realtime traffic (e.g. voice, video), whereas others are losssensitive, modeling nonrealtime traffic (e.g. data). Different levels of tolerance to delay and loss are modeled by appropriate linear holding cost and rejection cost rates. The goal is to design wellgrounded and tractable scheduling policies which nearly minimize the discounted or longrun average expected cost objective. We develop new dynamic index policies, prescribing to give higher service priority to classes with larger index values, where the priority index of a class measures the marginal productivity of work at its current state. To construct the indices, we deploy the theory of marginal productivity indices (MPIs) and PCLindexability we have introduced in recent work, and further introduce significant extensions to such theory motivated by phenomena observed in the model of concern. The MPI policies are shown to furnish new, insightful structural results, and to exhibit a nearly optimal performance in a computational study.
Structural results on a batch acceptance problem for capacitated queues
 Mathematical Methods of Operations Research
"... The purpose of this paper is to investigate the structural properties of the optimal batch acceptance policy in a Markovian queueing problem where different classes of customers arrive in batches and the buffer capacity is finite. We prove that the optimal policy can possess certain monotonicity pro ..."
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Cited by 7 (3 self)
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The purpose of this paper is to investigate the structural properties of the optimal batch acceptance policy in a Markovian queueing problem where different classes of customers arrive in batches and the buffer capacity is finite. We prove that the optimal policy can possess certain monotonicity properties under the assumptions of a singleserver and constant batch sizes. Even though our proof cannot be extended to cases where either one of the assumptions is relaxed, we numerically observe that the optimal policy can still possess the same properties when only the singleserver assumption is relaxed. Finally, we present counter examples that show the nonmonotone structure of the optimal policy when the constant batch size assumption is relaxed. 1