On Probabilistic Parallel Programs with Process Creation and Synchronisation

TL;DR

This paper introduces probabilistic split-join systems (pSJSs), a novel model for analyzing parallel programs with dynamic process creation and synchronization, extending existing models and enabling detailed performance analysis.

Contribution

The paper presents pSJSs, a new probabilistic model for parallel programs with recursive spawning and synchronization, generalizing previous models and providing tools for performance evaluation.

Findings

Extended and improved analysis results for space, work, and time distributions.

Practical methods for performance analysis of probabilistic parallel programs.

Case studies demonstrating the modeling capabilities of pSJSs.

Abstract

We initiate the study of probabilistic parallel programs with dynamic process creation and synchronisation. To this end, we introduce probabilistic split-join systems (pSJSs), a model for parallel programs, generalising both probabilistic pushdown systems (a model for sequential probabilistic procedural programs which is equivalent to recursive Markov chains) and stochastic branching processes (a classical mathematical model with applications in various areas such as biology, physics, and language processing). Our pSJS model allows for a possibly recursive spawning of parallel processes; the spawned processes can synchronise and return values. We study the basic performance measures of pSJSs, especially the distribution and expectation of space, work and time. Our results extend and improve previously known results on the subsumed models. We also show how to do performance analysis in practice, and present two case studies illustrating the modelling power of pSJSs.