{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,22]],"date-time":"2025-12-22T18:38:21Z","timestamp":1766428701868},"reference-count":31,"publisher":"Elsevier BV","issue":"1-4","license":[{"start":{"date-parts":[[2000,2,1]],"date-time":"2000-02-01T00:00:00Z","timestamp":949363200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Performance Evaluation"],"published-print":{"date-parts":[[2000,2]]},"DOI":"10.1016\/s0166-5316(99)00063-2","type":"journal-article","created":{"date-parts":[[2002,7,25]],"date-time":"2002-07-25T23:20:22Z","timestamp":1027639222000},"page":"165-188","source":"Crossref","is-referenced-by-count":17,"title":["Markov regenerative stochastic Petri nets with general execution policies: supplementary variable analysis and a prototype tool"],"prefix":"10.1016","volume":"39","author":[{"given":"Reinhard","family":"German","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/S0166-5316(99)00063-2_BIB1","doi-asserted-by":"crossref","first-page":"832","DOI":"10.1109\/32.29483","article-title":"The effect of execution policies on the semantics of stochastic Petri nets","volume":"15","author":"Ajmone Marsan","year":"1989","journal-title":"IEEE Trans. Software Engrg."},{"key":"10.1016\/S0166-5316(99)00063-2_BIB2","unstructured":"M. Ajmone Marsan, G. Balbo, G. Conte, S. Donatelli, G. Franceschinis, Modelling with Generalized Stochastic Petri Nets, Wiley, New York, 1995."},{"key":"10.1016\/S0166-5316(99)00063-2_BIB3","doi-asserted-by":"crossref","unstructured":"M. Ajmone Marsan, G. Chiola, On Petri nets with deterministic and exponentially distributed firing times, Advances in Petri Nets 1986, Lecture Notes in Computer Science, vol. 266, Springer, Berlin, 1987, pp. 132\u2013145.","DOI":"10.1007\/3-540-18086-9_23"},{"key":"10.1016\/S0166-5316(99)00063-2_BIB4","doi-asserted-by":"crossref","unstructured":"A. Bobbio, V.G. Kulkarni, A. Puliafito, M. Telek, K. Trivedi, Preemptive repeat identical transitions in Markov regenerative stochastic Petri nets, Proceedings of the Sixth International Conference on Petri Nets and Performance Models, Durham, NC, 1995, pp. 113\u2013122.","DOI":"10.1109\/PNPM.1995.524321"},{"key":"10.1016\/S0166-5316(99)00063-2_BIB5","unstructured":"A. Bobbio, A. Puliafito, M. Scarpa, M. Telek, WebSPN: a web-accessible Petri net tool, Proceedings of the 18th International Conference on Application and Theory of Petri Nets, Springer, Berlin, 1997."},{"key":"10.1016\/S0166-5316(99)00063-2_BIB6","doi-asserted-by":"crossref","unstructured":"A. Bobbio, M. Telek, Markov regenerative SPN with non-overlapping activity cycles, Proceedings of the International Performance and Dependability Symposium, Erlangen, Germany, 1995, pp. 124\u2013133.","DOI":"10.1109\/IPDS.1995.395811"},{"key":"10.1016\/S0166-5316(99)00063-2_BIB7","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/0166-5316(95)00008-L","article-title":"GreatSPN 1.7: graphical editor and analyzer for timed and stochastic Petri nets","volume":"24","author":"Chiola","year":"1995","journal-title":"Performance Evaluation"},{"key":"10.1016\/S0166-5316(99)00063-2_BIB8","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1016\/0166-5316(94)90021-3","article-title":"Markov regenerative stochastic Petri nets","volume":"20","author":"Choi","year":"1994","journal-title":"Performance Evaluation"},{"key":"10.1016\/S0166-5316(99)00063-2_BIB9","doi-asserted-by":"crossref","first-page":"506","DOI":"10.1109\/32.297939","article-title":"A characterization of the stochastic process underlying a stochastic Petri net","volume":"20","author":"Ciardo","year":"1994","journal-title":"IEEE Trans. Software Engrg."},{"key":"10.1016\/S0166-5316(99)00063-2_BIB10","doi-asserted-by":"crossref","unstructured":"D.R. Cox, The analysis of non-Markov stochastic processes by the inclusion of supplementary variables, Proc. Camb. Phil. Soc. (Math. Phys. Sci.) 51 (1955) 433-441.","DOI":"10.1017\/S0305004100030437"},{"key":"10.1016\/S0166-5316(99)00063-2_BIB11","unstructured":"A. Cumani, ESP\u2014a package for the evaluation of stochastic Petri nets with phase-type distributed transition times, Proceedings of the International Workshop Timed Petri Nets, Torino, Italy, 1985, pp. 278\u2013184."},{"key":"10.1016\/S0166-5316(99)00063-2_BIB12","doi-asserted-by":"crossref","unstructured":"R. German, New results for the analysis of deterministic and stochastic Petri nets, Proceedings of the IEEE International Performance and Dependability Symposium, Erlangen, Germany, 1995, pp. 114\u2013123.","DOI":"10.1109\/IPDS.1995.395812"},{"key":"10.1016\/S0166-5316(99)00063-2_BIB13","unstructured":"R. German, Avoiding fill-in in the analysis of Markov-regenerative stochastic Petri nets, Proceedings of the Fouth International Workshop on Performability Modeling of Computer and Communication Systems, Williamsburg, VA, 1998, pp. 62\u201366."},{"key":"10.1016\/S0166-5316(99)00063-2_BIB14","doi-asserted-by":"crossref","unstructured":"R. German, Markov regenerative stochastic Petri nets with general execution policies: supplementary variable analysis and a prototype tool, in: R. Puigjaner, N.N. Savino, B. Serra (Eds.), Computer Performance Evaluation, Modelling Techniques and Tools, 10th International Conference on Tools\u201998, Palma de Mallorca, Spain, Lecture Notes in Computer Science, vol. 1469, Springer, Berlin, 1998.","DOI":"10.1007\/3-540-68061-6_21"},{"key":"10.1016\/S0166-5316(99)00063-2_BIB15","unstructured":"R. German, Cascaded deterministic and stochastic Petri nets, Proceedings of the Third International Meeting on the Numerical Solution of Markov Chains, Zaragoza, Spain, 1999, pp. 111\u2013130."},{"key":"10.1016\/S0166-5316(99)00063-2_BIB16","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/0166-5316(95)00010-U","article-title":"TimeNET: a Toolkit for evaluating non-Markovian stochastic Petri nets","volume":"24","author":"German","year":"1995","journal-title":"Performance Evaluation"},{"key":"10.1016\/S0166-5316(99)00063-2_BIB17","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1016\/0166-5316(94)90020-5","article-title":"Analysis of stochastic Petri nets by the method of supplementary variables","volume":"20","author":"German","year":"1994","journal-title":"Performance Evaluation"},{"key":"10.1016\/S0166-5316(99)00063-2_BIB18","unstructured":"R. German, A.P. van Moorsel, M.A. Qureshi, W.H. Sanders, Solution of stochastic Petri nets with general distributions, rate and impulse rewards, Application and Theory of Petri Nets 1996, Proceedings of the 17th International Conference Osaka, Japan, Lecture Notes in Computer Science, vol. 1091, Springer, Berlin, 1996, pp. 172\u2013191."},{"key":"10.1016\/S0166-5316(99)00063-2_BIB19","doi-asserted-by":"crossref","unstructured":"R. German, M. Telek, Formal Relation of Markov renewal theory and supplementary variables in the analysis of stochastic Petri nets, Proceedings of the Eighth International Conference on Petri Nets and Performance Models, Zaragoza, Spain, 1999, pp. 64\u201373.","DOI":"10.1109\/PNPM.1999.796537"},{"key":"10.1016\/S0166-5316(99)00063-2_BIB20","first-page":"144","article-title":"The GI\/PH\/1 queue: a method to find the transition matrix","volume":"20","author":"Grassmann","year":"1982","journal-title":"INFOR"},{"key":"10.1016\/S0166-5316(99)00063-2_BIB21","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1214\/aoms\/1177705991","article-title":"On time dependent queuing processes","volume":"31","author":"Keilson","year":"1960","journal-title":"Ann. Math. Statist."},{"key":"10.1016\/S0166-5316(99)00063-2_BIB22","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/0166-5316(93)E0035-4","article-title":"DSPNexpress: a software package for the efficient solution of deterministic and stochastic Petri nets","volume":"22","author":"Lindemann","year":"1995","journal-title":"Performance Evaluation"},{"key":"10.1016\/S0166-5316(99)00063-2_BIB23","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1007\/BF01439851","article-title":"Modeling discrete event systems with state-dependent deterministic service times","volume":"3","author":"Lindemann","year":"1993","journal-title":"Discrete Event Dynamic Systems: Theory and Applications"},{"key":"10.1016\/S0166-5316(99)00063-2_BIB24","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1016\/S0166-5316(96)90046-2","article-title":"Numerical analysis of deterministic and stochastic Petri nets with concurrent deterministic transitions","volume":"23","author":"Lindemann","year":"1996","journal-title":"Performance Evaluation"},{"key":"10.1016\/S0166-5316(99)00063-2_BIB25","doi-asserted-by":"crossref","unstructured":"L.M. Malhis, W.H. Sanders, An efficient two-stage iterative method for the steady-state analysis of Markov regenerative stochastic Petri net models, Performance Evaluation 27\/28 (1996) 583\u2013601.","DOI":"10.1016\/S0166-5316(96)90047-4"},{"key":"10.1016\/S0166-5316(99)00063-2_BIB26","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/0166-5316(95)00012-M","article-title":"The UltraSAN modeling environment","volume":"24","author":"Sanders","year":"1995","journal-title":"Performance Evaluation"},{"key":"10.1016\/S0166-5316(99)00063-2_BIB27","doi-asserted-by":"crossref","unstructured":"M. Telek, A. Bobbio, Markov regenerative stochastic Petri nets with age type general transitions, Application and Theory of Petri Nets, Proceedings of the 16th International Conference, Lecture Notes in Computer Science, vol. 935, Springer, Berlin, 1995, pp. 471\u2013489.","DOI":"10.1007\/3-540-60029-9_55"},{"key":"10.1016\/S0166-5316(99)00063-2_BIB28","doi-asserted-by":"crossref","unstructured":"M. Telek, A. Bobbio, L. Jereb, A. Puliafito, K.S. Trivedi, Steady state analysis of Markov regenerative SPN with age memory policy, Quantitative Evaluation of Computing and Communication Systems, Lecture Notes in Computer Science, vol. 977, Springer, Berlin, 1995, pp. 165\u2013179.","DOI":"10.1007\/BFb0024314"},{"key":"10.1016\/S0166-5316(99)00063-2_BIB29","doi-asserted-by":"crossref","unstructured":"M. Telek, A. Bobbio, A. Puliafito, Steady state solution of MRSPNs with mixed preemption policies, Proceedings of the IEEE International Performance and Dependability Symposium, Urbana-Champaign, IL, 1996, pp 106\u2013115.","DOI":"10.1109\/IPDS.1996.540212"},{"key":"10.1016\/S0166-5316(99)00063-2_BIB30","doi-asserted-by":"crossref","unstructured":"M. Telek, A. Horvath, Supplementary variable approach applied to the transient analysis of age-MRSPNs, Proceedings of the IEEE International Performance and Dependability Symposium, Durham, NC, pp. 44\u201351, 1998.","DOI":"10.1109\/IPDS.1998.707708"},{"key":"10.1016\/S0166-5316(99)00063-2_BIB31","unstructured":"S. Wolfram, The Mathematica Book, 3rd ed., Cambridge Unversity Press, Cambridge, 1996."}],"container-title":["Performance Evaluation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0166531699000632?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0166531699000632?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2020,1,29]],"date-time":"2020-01-29T05:09:44Z","timestamp":1580274584000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0166531699000632"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,2]]},"references-count":31,"journal-issue":{"issue":"1-4","published-print":{"date-parts":[[2000,2]]}},"alternative-id":["S0166531699000632"],"URL":"https:\/\/doi.org\/10.1016\/s0166-5316(99)00063-2","relation":{},"ISSN":["0166-5316"],"issn-type":[{"value":"0166-5316","type":"print"}],"subject":[],"published":{"date-parts":[[2000,2]]}}}