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A Markovian Concurrency Measure 1

The notion of concurrency plays a central role in parallel processing, and has been studied rather extensively over the last decade mostly from algebraic and/or semantic point of view. This explains why the published literature on concurrency measures is scanty. J. Françon [10] has shown how to count explicitely the number of correct (i.e. without deadlock) behaviours of parallel systems under the mutual exclusion policy. His measure is in fact the inverse of the radius of convergence of some generating function and no implementation based on this approach has been realized until now. J. Beauquier, B. Bérard and L. Thimonier [3] consider also all behaviours of the concurrent systems and their measure, based on Arnold-Nivat's model, is the average waiting time of the processes. It has been shown [12] that the computation of this measure is often time and space consuming. B. Charron-Bost [5] introduces a coefficient which reflects the interaction between the different processors during the execution of a parallel computation. It is an interesting investigation of the problem we consider here.