We establish asymptotic upper and lower bounds on the asymptotic decay rate of persession queue length tail distributions for a multiple-queue system where a single constant rate server services the queues using the generalized processor sharing (GPS) scheduling discipline. In the special case where there are only two queues, the upper and lower bounds match, yielding the optimal bound proved in . The dynamics of bandwidth sharing of a multiple-queue GPS system is captured using the notion of partial feasible sets, and the bounds are obtained using the sample-path large deviation principle. The results have implications in call admission control for high-speed communication networks.
Bibliographical noteFunding Information:
∗This work was done while the author was a graduate student in the Department of Computer Science, University of Massachusetts, under the support by the NSF under grants NCR-9116183 and CCR-9119922.
- Asymptotic decay rate
- Generalized processor sharing
- Large deviation principles
- Queue length tail distributions