{"title":"On phased delay stochastic Petri nets: definition and an application","authors":"Rob Jones, G. Ciardo","doi":"10.1109/PNPM.2001.953366","DOIUrl":null,"url":null,"abstract":"We present a novel stochastic Petri net formalism where both discrete and continuous phase-type firing delays can appear simultaneously in the same model. By capturing non-Markovian behavior in discrete or continuous time, as appropriate, the formalism affords higher modeling fidelity. Alone, discrete or continuous phase-type Petri nets have simple underlying Markov chains, but mixing the two complicates matters. We show that, in a mixed model where discrete-time transitions are synchronized, the underlying process is semi-regenerative and we can employ Markov renewal theory to formulate stationary or time-dependent solutions. Also noteworthy are the computational trade-offs between the so-called embedded and subordinate Markov chains, which we employ to improve the overall solution efficiency. We present a preliminary stationary solution method that shows promise in terms of time and space efficiency and demonstrate it on an aeronautical data link system application.","PeriodicalId":364695,"journal":{"name":"Proceedings 9th International Workshop on Petri Nets and Performance Models","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2001-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"13","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings 9th International Workshop on Petri Nets and Performance Models","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/PNPM.2001.953366","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 13
Abstract
We present a novel stochastic Petri net formalism where both discrete and continuous phase-type firing delays can appear simultaneously in the same model. By capturing non-Markovian behavior in discrete or continuous time, as appropriate, the formalism affords higher modeling fidelity. Alone, discrete or continuous phase-type Petri nets have simple underlying Markov chains, but mixing the two complicates matters. We show that, in a mixed model where discrete-time transitions are synchronized, the underlying process is semi-regenerative and we can employ Markov renewal theory to formulate stationary or time-dependent solutions. Also noteworthy are the computational trade-offs between the so-called embedded and subordinate Markov chains, which we employ to improve the overall solution efficiency. We present a preliminary stationary solution method that shows promise in terms of time and space efficiency and demonstrate it on an aeronautical data link system application.