Polynomial analysis algorithms for free choice Probabilistic Workflow Nets

Esparza, Javier; Hoffmann, Philipp; Saha, Ratul

doi:10.1016/j.peva.2017.09.006

Cited by 11 publications

(17 citation statements)

References 6 publications

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“…For every scheduler, the semantics assigns to the TPWN an expected time to termination. Using results of [11], we prove that this expected time is actually independent of the scheduler, and so that the notion "expected time of a TPWN" is well defined.…”

Section: Introductionmentioning

confidence: 73%

“…The following result follows easily from the definitions (see also [11]): Lemma 1. [11] Let N be a 1-safe workflow net.…”

Section: Preliminariesmentioning

confidence: 96%

“…The following result follows easily from the definitions (see also [11]): Lemma 1. [11] Let N be a 1-safe workflow net. If N is confusion-free then for every reachable marking M the conflict sets C(M ) are a partition of the set of transitions enabled at M .…”

Section: Preliminariesmentioning

confidence: 96%

“…In a former paper we introduced Probabilistic Workflow Nets (PWN), a foundation for the extension of Petri nets with probabilities and rewards [11]. We presented a polynomial time algorithm for the computation of the expected cost of free-choice workflow nets, a subclass of PWN of particular interest for the workflow process community (see e.g.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper we introduce Timed PWNs (TPWNs), an extension of PWNs with time. Following [11], we define a semantics in terms of Markov Decision Processes (MDPs), where, loosely speaking, the nondeterminism of the MDP models absence of information about the order in which concurrent transitions are executed. For every scheduler, the semantics assigns to the TPWN an expected time to termination.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Computing the Expected Execution Time of Probabilistic Workflow Nets

Meyer

Esparza

Offtermatt

2019

Tools and Algorithms for the Construction and Analysis of Systems

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Free-Choice Workflow Petri nets, also known as Workflow Graphs, are a popular model in Business Process Modeling. In this paper we introduce Timed Probabilistic Workflow Nets (TPWNs), and give them a Markov Decision Process (MDP) semantics. Since the time needed to execute two parallel tasks is the maximum of the times, and not their sum, the expected time cannot be directly computed using the theory of MDPs with rewards. In our first contribution, we overcome this obstacle with the help of "earliest-first" schedulers, and give a single exponential-time algorithm for computing the expected time. In our second contribution, we show that computing the expected time is #P-hard, and so polynomial algorithms are very unlikely to exist. Further, #P-hardness holds even for workflows with a very simple structure in which all transitions times are 1 or 0, and all probabilities are 1 or 0.5. Our third and final contribution is an experimental investigation of the runtime of our algorithm on a set of industrial benchmarks. Despite the negative theoretical results, the results are very encouraging. In particular, the expected time of every workflow in a popular benchmark suite with 642 workflow nets can be computed in milliseconds.1 In [2], which examines many different notions of soundness, this is called easy soundness.

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Section: Introductionmentioning

confidence: 73%

“…The following result follows easily from the definitions (see also [11]): Lemma 1. [11] Let N be a 1-safe workflow net.…”

Section: Preliminariesmentioning

confidence: 96%