Polynomial Analysis Algorithms for Free Choice Probabilistic Workflow Nets

TL;DR

This paper introduces polynomial-time algorithms for analyzing expected rewards in Probabilistic Workflow Nets by leveraging reductions that preserve expected reward, avoiding exponential complexity of Markov decision process construction.

Contribution

It extends workflow net analysis to probabilistic models, providing reduction rules that enable polynomial-time computation of expected rewards.

Findings

Expected reward is independent of scheduler due to Markov decision process semantics.

Reduction rules preserve expected reward and enable polynomial-time algorithms.

Implementation shows practical efficiency on benchmark models.

Abstract

We study Probabilistic Workflow Nets (PWNs), a model extending van der Aalst's workflow nets with probabilities. We give a semantics for PWNs in terms of Markov Decision Processes and introduce a reward model. Using a result by Varacca and Nielsen, we show that the expected reward of a complete execution of the PWN is independent of the scheduler. Extending previous work on reduction of non-probabilistic workflow nets, we present reduction rules that preserve the expected reward. The rules lead to a polynomial-time algorithm in the size of the PWN (not of the Markov decision process) for the computation of the expected reward. In contrast, since the Markov decision process of PWN can be exponentially larger than the PWN itself, all algorithms based on constructing the Markov decision process require exponential time. We report on a sample implementation and its performance on a collection of benchmarks.