An Example of Modelling and Evaluation of a Con- Current Program Using Coloured Stochastic Petri Nets: Lamport's Fast Mutual Exclusion Algorithm. 4 Conclusions

So called \recursive equations" have been introduced by Baccelli et al. as a convenient way of characterizing the behavior of stochastic Petri net models in terms of transition ring instances and of creation and destruction times for tokens in places [1, 2]. Such equations have been used to prove model properties as well as to speed up simulation by parallel processing techniques in the case of Marked Graph structures with FIFO token ow [3]. We extend the technique to the case of high-level net models in which con icts among transitions and ring disciplines di erent from FIFO are allowed. We propose the new name of \Occurrence Equations" to characterize the technique more precisely. Di erent execution policies that have been considered in the literature are discussed, showing the consequences they induce on the net occurrence equations. Some possible uses of the equations for the development of compositional modeling techniques as well as for model simulation are also outlined.