Maximal average loss rates for a single GPS server system with finite buffers

Considers a single server system with finite buffers that services |W| sessions. It is assumed that the multiplexing scheme is generalized processor sharing (GPS). The authors consider the problem of determining the session arrival functions that result in the maximal average packet loss rate for each session. They prove that the worst case average loss rate occurs when the arrival functions are nearly periodic and inputs are bursts at the beginning of each period. A second proof is given by casting this problem in the framework of a Markov decision process. The authors address a fundamental question: what aspects of systems result in worst case arrival processes being (nearly) periodic?