Dealing with arbitrary time distributions with the stochastic timed Petri net model-application to queueing systems

The ability of the stochastic timed Petri net model for dealing with a great variety of firing time distributions is presented. The distributions can be: continuous (exponential or uniform); discrete (including the particular case of a deterministic distribution with a zero firing time (immediate transition) or a non zero firing time); mixed. This ability is based on a method of tractable computation whatever the distribution (in particular the difficult cases of the discrete and mixed distributions), for obtaining a randomized state graph (which represents the dynamic behaviour of the system being modelled). Applications to queueing systems are considered: the queue M/G/1; the queue M/G/1/K. A general method for analysing queueing systems, which is based on an interpretation of the randomized state graph, is presented