In: Billington, J.; Diaz, M.; Rozenberg, G.: Lecture Notes in Computer Science, Vol. 1605: Application of Petri Nets to Communication Networks, pages 176-209. Springer-Verlag, 1999.
Abstract: The paper shows that stochastic Petri nets (SPNs) can be used for the evaluation of polling mechanisms. Polling mechanisms (or systems) appear in many forms in computer-communication systems: the well-known token-ring and token-bus network access schemes such as present in IEEE P802.4/5 and in FDDI, and the scheduling mechanisms in switching fabrics, e.g.; for ATM systems, operate along the lines of polling systems. Polling systems have been studied for many years now, and many analytical techniques have been developed to analyze them. It seems, however, that a number of system aspects cannot be covered adequately by such analytical approaches. Most notably are time-dependent polling variants where the amount of service a station receives per visit is time-limited, load-dependent polling strategies where the ordering of station visits is dependent on the loading of the stations, as well as non-Poisson arrival processes. Therefore, SPN-based models are proposed that can cope with these system aspects. The two major problems that appear when taking the SPN approach are the size of the underlying CTMC and the use of non-exponential timing. The latter problem is not really addressed in this paper; rather it is circumvented by employing the well-known method of stages, thus even worsening the state space size problem. The first problem is coped with by presenting two decompositional approaches and by presenting a subclass of SPNs that allows for an efficient matrix-geometric solution, thus avoiding the explicit generation of the overall state space.
Keywords: communication systems, performance evaluation, polling mechanisms, stochastic Petri nets.