Calculation of the performance region of an easy-to-optimize alternative for Generalized Processor Sharing

Service differentiation is a basic requirement in every modern queueing system with multiple classes of customers. In this paper, we look at Hierarchical Generalized Processor Sharing (H-GPS), which is a discrete-time hierarchically-structured implementation of the well-known idealized Generalized Processor Sharing (GPS) scheduling discipline. We prove that, for three classes, H-GPS can be configured to obtain any performance possible by other scheduling mechanisms, such as priority queueing or GPS. The hierarchical nature of a H-GPS system, however, has the major advantage that optimization is easier and more intuitive. To this end, we also present an algorithm to calculate the configuration parameters for H-GPS given a certain performance objective.