Bounds, approximations and applications for a two-queue GPS system

In this paper we study the performance of a multiplexer using the Generalized Processor Sharing (GPS) scheduling to serve Markov Modulated Fluid Sources (MMFSs). We focus on a two-queue GPS system serving two classes of sources. By using a bounding approach combined with an approximation approach and by taking advantage of the specific structure of MMFSs, we are able to derive a lower bound and an upper bound approximation on queue length distributions for each class of the GPS system. Numerical investigations show that the lower bound and the upper bound approximation are very accurate. Hence our work greatly improves the earlier results on GPS scheduling in [15, 17] which are obtained for a more general stochastic model. Application of our performance bounds to call admission control and bandwidth sharing is also illustrated, and a comparison with FIFO and strict priority in different scenarios is presented. We show that the flexibility provided by GPS does not provide much better performance than FIFO and priority when the classes only have loss requirements. However, this flexibility provides better performance when the classes exhibit delay requirements as well as loss requirements.