Performance evaluation of polling systems by means of the power-series algorithm

Polling systems are widely used to model communication networks with several classes of messages, a single transmission channel and a collision-free access protocol. However, they can only be analysed exactly for some special service disciplines. The power-series algorithm provides a means for the numerical analysis of polling systems with a moderate number of stations, for a wide variety of access protocols. This paper contains a general description of the power-series algorithm, with emphasis on the application to a general class of polling systems with Poisson arrival streams, with Coxian service and switching time distributions, with infinite buffers, with a fixed periodic visit order, and with a Bernoulli schedule for each visit to a station. The applicability and the complexity of the algorithm are discussed for several more service disciplines for polling systems.