{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,4]],"date-time":"2025-03-04T06:00:00Z","timestamp":1741068000232,"version":"3.38.0"},"reference-count":16,"publisher":"SAGE Publications","issue":"8","license":[{"start":{"date-parts":[[2009,8,1]],"date-time":"2009-08-01T00:00:00Z","timestamp":1249084800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIMULATION"],"published-print":{"date-parts":[[2009,8]]},"abstract":"<jats:p> Generalized stochastic Petri nets (GSPNs) are widely used in the performance analysis of computer and communications systems. Response time densities and quantiles are often key outputs of such analysis. These can be extracted from a GSPN\u2019s underlying semi-Markov process using a method based on numerical Laplace transform inversion. This method typically requires the solution of thousands of systems of complex linear equations, each of rank n, where n is the number of states in the model. For large models substantial processing power is needed and the computation must therefore be distributed. In this paper we describe the implementation of a response time analysis module for the Platform Independent Petri net Editor (PIPE2) which interfaces with Hadoop, an open-source implementation of Google\u2019s MapReduce distributed programming environment, to provide distributed calculation of response time densities in GSPN models. The software is validated with results calculated analytically as well as simulated results for larger models. Excellent scalability is shown. <\/jats:p>","DOI":"10.1177\/0037549709340785","type":"journal-article","created":{"date-parts":[[2009,8,13]],"date-time":"2009-08-13T16:24:53Z","timestamp":1250180693000},"page":"497-509","source":"Crossref","is-referenced-by-count":8,"title":["Distributed Response Time Analysis of GSPN Models with MapReduce"],"prefix":"10.1177","volume":"85","author":[{"given":"Oliver J.","family":"Haggarty","sequence":"first","affiliation":[{"name":"Department of Computing Imperial College London 180 Queen's Gate, London SW7 2BZ, UK,"}]},{"given":"William J.","family":"Knottenbelt","sequence":"additional","affiliation":[{"name":"Department of Computing Imperial College London 180 Queen's Gate, London SW7 2BZ, UK,"}]},{"given":"Jeremy T.","family":"Bradley","sequence":"additional","affiliation":[{"name":"Department of Computing Imperial College London 180 Queen's Gate, London SW7 2BZ, UK,"}]}],"member":"179","published-online":{"date-parts":[[2009,8,13]]},"reference":[{"volume-title":"PIPE v2.5: a Petri net tool for performance modelling","year":"2007","author":"Bonet, P.","key":"atypb1"},{"volume-title":"Proceedings of the 3rd ACM Workshop on Software and Performance (WOSP 2002)","author":"Dingle, N.J.","key":"atypb2"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-322-86501-4"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2003.12.018"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1007\/BF01158520"},{"volume-title":"Proceedings of ACM SIGMETRICS","author":"Knottenbelt, W.J.","key":"atypb6"},{"key":"atypb7","unstructured":"Muppala, J.K. and K.S. Trivedi. 1992. Numerical transient analysis of finite Markovian queueing systems. In U.N. Bhat and I.V. Basawa, Eds, Queueing and Related Models, pp. 262-284."},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1287\/opre.32.4.926"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpdc.2004.03.017"},{"volume-title":"Proceedings of the 1st International Conference on the Quantitative Evaluation of Systems (QEST 2004)","author":"Bradley, J.T.","key":"atypb10"},{"volume-title":"Parallel Computation of Response Time Densities and Quantiles in Large Markov and Semi-Markov Models. PhD thesis","year":"2004","author":"Dingle, N.J.","key":"atypb11"},{"volume-title":"Proceedings of the OSDI\u201904: Sixth Symposium on Operating System Design and Implementation","author":"Dean, J.","key":"atypb12"},{"volume-title":"Proceedings of the 4th IEEE International Conference on eScience","author":"Ekanayake, J.","key":"atypb13"},{"volume-title":"Petri Nets Group Project Final Report. Technical report","year":"2007","author":"Kimber, T.","key":"atypb14"},{"volume-title":"Generalised Markovian Analysis of Timed Transition Systems. Master\u2019s thesis","year":"1996","author":"Knottenbelt, W.J.","key":"atypb15"},{"volume-title":"Proceeding of the 4th International Workshop on Petri nets and Performance Models (PNPM\u201991)","author":"Woodside, C.M.","key":"atypb16"}],"container-title":["SIMULATION"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0037549709340785","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0037549709340785","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,3]],"date-time":"2025-03-03T22:35:31Z","timestamp":1741041331000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/0037549709340785"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,8]]},"references-count":16,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2009,8]]}},"alternative-id":["10.1177\/0037549709340785"],"URL":"https:\/\/doi.org\/10.1177\/0037549709340785","relation":{},"ISSN":["0037-5497","1741-3133"],"issn-type":[{"type":"print","value":"0037-5497"},{"type":"electronic","value":"1741-3133"}],"subject":[],"published":{"date-parts":[[2009,8]]}}}