Bandwidth allocation for fluid input generalized processor sharing servers

Generalized processor sharing (GPS) service policy is a scheduling algorithm to allocate the bandwidth of a queueing system with multi-class input traffic. Simulating the GPS system in realistic traffic environments requires a large amount of time. Thus, fluid simulation is useful because it requires much less time. We analyze the bandwidth allocation for fluid simulation in GPS servers, in which the traffic into the server is treated as fluid. Three properties which characterize GPS servers with fluid input are discussed. We show that there exists a unique bandwidth allocation with the properties. It is shown that our previously proposed algorithm gives the unique bandwidth allocation and it is equivalent to the well-known Newton-Rapson method. In numerical study, the performance of finding the unique bandwidth allocation based on other known root finding methods is compared with that of our previous algorithm. We also investigate the impact of the length of the unit time on the accuracy of the performance measures.