The Annals of Applied Probability

Largest Weighted Delay First Scheduling: Large Deviations and Optimality

Kavita Ramanan and Alexander L. Stolyar

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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.

Article information

Ann. Appl. Probab., Volume 11, Number 1 (2001), 1-48.

First available in Project Euclid: 27 August 2001

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F10: Large deviations 90B12 60K25: Queueing theory [See also 68M20, 90B22]

queueing theory queueing delay large deviations rate function optimality fluid limit control scheduling quality of service (Qos) earliest deadline first (EDF) LWDF


Stolyar, Alexander L.; Ramanan, Kavita. Largest Weighted Delay First Scheduling: Large Deviations and Optimality. Ann. Appl. Probab. 11 (2001), no. 1, 1--48. doi:10.1214/aoap/998926986.

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