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We initiate the study of probabilistic parallel programs with dynamic processcreation and synchronisation. To this end, we introduce probabilisticsplit-join systems (pSJSs), a model for parallel programs, generalising bothprobabilistic pushdown systems (a model for sequential probabilistic proceduralprograms which is equivalent to recursive Markov chains) and stochasticbranching processes (a classical mathematical model with applications invarious areas such as biology, physics, and language processing). Our pSJSmodel allows for a possibly recursive spawning of parallel processes; thespawned processes can synchronise and return values. We study the basicperformance measures of pSJSs, especially the distribution and expectation ofspace, work and time. Our results extend and improve previously known resultson the subsumed models. We also show how to do performance analysis inpractice, and present two case studies illustrating the modelling power ofpSJSs.

On Probabilistic Parallel Programs with Process Creation and Synchronisation