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February 2001 Largest Weighted Delay First Scheduling: Large Deviations and Optimality
Kavita Ramanan, Alexander L. Stolyar
Ann. Appl. Probab. 11(1): 1-48 (February 2001). DOI: 10.1214/aoap/998926986


We consider a single server system with N input flows. We assume that each flow has stationary increments and satisfies a sample path large deviation principle, and that the system is stable. We introduce the largest weighted delay first (LWDF) queueing discipline associated with any given weight vector α=(α1,...,αN). We show that under the LWDF discipline the sequence of scaled stationary distributions of the delay \(\hat{w}_{i}\) of each flow satisfies a large deviation principle with the rate function given by a finite- dimensional optimization problem. We also prove that the LWDF discipline is optimal in the sense that it maximizes the quantity $$\min_{i= 1,\space ...,\space N}\left[α_i \lim_{n\to\infty}\frac{−1}{n}\log P(\hat{w}_i>n)\right],$$ within a large class of work conserving disciplines.


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Kavita Ramanan. Alexander L. Stolyar. "Largest Weighted Delay First Scheduling: Large Deviations and Optimality." Ann. Appl. Probab. 11 (1) 1 - 48, February 2001.


Published: February 2001
First available in Project Euclid: 27 August 2001

zbMATH: 1024.60012
MathSciNet: MR1825459
Digital Object Identifier: 10.1214/aoap/998926986

Primary: 60F10 , 60K25 , 90B12

Keywords: (EDF) , (Qos) , control , earliest deadline first , fluid limit , large deviations , LWDF , optimality , quality of service , queueing delay , Queueing theory , Rate function , scheduling

Rights: Copyright © 2001 Institute of Mathematical Statistics


Vol.11 • No. 1 • February 2001
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