Abstract

Workflow graphs extend classical flow charts with concurrent fork and join nodes. They constitute the core of business processing languages such as BPMN or UML Activity Diagrams. The activities of a workflow graph are executed by humans or machines, generically called resources. If concurrent activities cannot be executed in parallel by lack of resources, the time needed to execute the workflow increases. We study the problem of computing the minimal number of resources necessary to fully exploit the concurrency of a given workflow, and execute it as fast as possible (i.e., as fast as with unlimited resources).

Highlights

  • IntroductionA workflow graph is a classical control-flow graph (or flow chart) extended with concurrent fork and join

  • A workflow graph is a classical control-flow graph extended with concurrent fork and join

  • It is easy to see that NG is free-choice and sound, and in [15] we show the result of applying the reduction to a small graph and prove that G has an independent set of size at least k iff the concurrency threshold of (NG, MI ) is at least 2|E| + k

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Summary

Introduction

A workflow graph is a classical control-flow graph (or flow chart) extended with concurrent fork and join. The resource threshold of a deterministic workflow with k activities is a number between 1 and k Determining this number can be seen as a scheduling problem. If a workflow with concurrency threshold k is executed with k resources, we can always start the task of a place immediately after a token arrives, and this schedule already achieves the fastest runtime achievable with unlimited resources. We design an algorithm to compute bounds on the concurrency threshold using a combination of linear optimization and state-space exploration. We evaluate it on a benchmark suite of 642 sound freechoice workflow nets from an industrial source (IBM) [9].

Preliminaries
Resource Threshold
Resource Threshold Is NP-complete for Acyclic Marked Graphs
Acyclic Free-Choice Workflow Nets May Have no Optimal Online Schedulers
Concurrency Threshold
Concurrency Threshold of Marked Graphs
Concurrency Threshold of Free-Choice Nets
Approximating the Concurrency Threshold
Concurrency Threshold: A Practical Approach
Conclusion
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