## The Annals of Applied Probability

### Largest Weighted Delay First Scheduling: Large Deviations and Optimality

#### Abstract

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

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

Dates
First available in Project Euclid: 27 August 2001

https://projecteuclid.org/euclid.aoap/998926986

Digital Object Identifier
doi:10.1214/aoap/998926986

Mathematical Reviews number (MathSciNet)
MR1825459

Zentralblatt MATH identifier
1024.60012

#### Citation

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. https://projecteuclid.org/euclid.aoap/998926986