Large deviations and the generalized processor sharing scheduling for a multiple-queue system

We establish asymptotic upper and lower bounds on the asymptotic decay rate of per-session 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. 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.