A series expansion approach for finite-capacity processor sharing queues

This paper investigates a finite capacity queueing system in a Markovian setting with power control and various flavours of processor sharing policies like generalised and discriminatory processor sharing. Allowing for multiple customer classes, the Markovian description of the system at hand obviously suffers from the state space explosion problem. By some numerical examples, we show that numerical Taylor series expansion techniques provide the required numerical accuracy at a limited computational cost. More precisely, the computational complexity of calculating the first N terms in the series expansion of the steady-state probability vector is O(KMN), with M the size of the state space of the Markov chain and K the number of classes.