Exact and approximate analysis of sojourn times in finite discriminatory processor sharing queues

Exact analysis of discriminatory processor sharing (DPS) systems has proven to be extremely hard. We describe how the sojourn time distribution can be obtained in closed-form for exponential service requirement distributions when there is admission control. The computational complexity suffers from the usual state-space explosion when the number of customer classes becomes large, or if the admission control allows for many concurrent customers. Through numerical experiments, we show that a time-scale decomposition approach provides an approximation that requires much less computational effort, while giving accurate results even when the classes do not have different time scales and are distinguished through the relative service shares only.