Approximate performance models of polling systems using stochastic Petri nets

The performance of a polling system is modeled by stochastic Petri nets and its analysis is done by numerically solving the underlying Markov chain. One key problem in using stochastic Petri nets for real applications is that the size of underlying Markov chain tends to be large, and thus to be computationally intractable. In order to carry out the performance analysis of a large complex system in practice, the authors develop approximation methods at the Petri net level for the finite population, asymmetric polling systems and analyze the error due to the approximation. The mean cycle time and the mean response time of the system are approximated by the folding method and by the fixed-point iteration method. The effect of an increasing number of customers on the polling systems is studied using these approximations. The approximation methods are shown to save more than 95% of computation cost without a concomitant loss in accuracy. The methods perform very well at low offered loads