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On the optimality and the asymptotic optimality of the smallest weighted available buffer policy

Part of: Special processes Stochastic systems and control

Published online by Cambridge University Press:  01 July 2016

Duan-Shin Lee
Duan-Shin Lee*
Affiliation:
National Tsing Hua University
*
∗ Postal address: Department of Computer Science, National Tsing Hua University, Hsinchu, Taiwan 300. Email address: lds@cs.nthu.edu.tw
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Abstract

A major design challenge of Asynchronous Transfer Mode (ATM) networks is to efficiently provide the quality of service (QOS) specified by users with different demands. We classify sources so that sources in one class join the same buffer and have the same requirement for the ATM cell loss ratio. It is important to search for the service discipline that minimizes the accumulated cell loss under the constraint that the cell loss ratios of the sources are proportional to their QOS requirements. In this paper we consider a model that has N finite buffers and a single server. Buffer i, of size Bi, is assigned a positive number wi. The server serves from one of the non-empty buffers whose indices are equal to argmin wi(Bi-Qi), where Qi is the queue length of buffer i. This scheduling policy is called the smallest weighted available buffer policy (SWAB). We show that in a completely symmetric setting, the SWAB policy minimizes the discounted expected loss of cells under some technical conditions. For asymmetric models, we show that the accumulated loss of cells of the SWAB service discipline is asymptotically optimal under heavy traffic conditions in the diffusion limit. Finally, we obtain the expression of wi so that the cell loss ratios of the sources in the diffusion limit are proportional to their QOS requirements.

Keywords

Smallest weighted available buffer scheduling disciplineoptimal controlMarkov decision processweak convergenceheavy trafficreflected Brownian motionquality of serviceATM networks

MSC classification

Primary: 60K25: Queueing theory
Secondary: 93E20: Optimal stochastic control
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 31 , Issue 4 , December 1999 , pp. 1118 - 1150
Copyright
Copyright © Applied Probability Trust 1999 

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Footnotes

Part of the work was done when the author was affiliated with C&C Research Lab, NEC USA, NJ, USA.

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