{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T23:50:01Z","timestamp":1649202601248},"reference-count":30,"publisher":"Elsevier BV","issue":"1-4","license":[{"start":{"date-parts":[[2001,4,1]],"date-time":"2001-04-01T00:00:00Z","timestamp":986083200000},"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":[[2001,4]]},"DOI":"10.1016\/s0166-5316(00)00057-2","type":"journal-article","created":{"date-parts":[[2002,7,25]],"date-time":"2002-07-25T16:01:38Z","timestamp":1027612898000},"page":"187-209","source":"Crossref","is-referenced-by-count":3,"title":["Hybrid analysis of SGSPNs with time-dependent transition rates"],"prefix":"10.1016","volume":"44","author":[{"given":"Peter","family":"Buchholz","sequence":"first","affiliation":[]}],"member":"78","reference":[{"issue":"2","key":"10.1016\/S0166-5316(00)00057-2_BIB1","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1145\/190.191","article-title":"A class of generalized stochastic Petri nets for performance evaluation of multiprocessor systems","volume":"2","author":"Ajmone-Marsan","year":"1984","journal-title":"ACM Trans. Comput. Syst."},{"key":"10.1016\/S0166-5316(00)00057-2_BIB2","doi-asserted-by":"crossref","unstructured":"M. Ajmone-Marsan, G. Chiola, On Petri nets with deterministic and exponential firing times, in: G. Rozenberg (Ed.), Advances in Petri Nets, 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(00)00057-2_BIB3","doi-asserted-by":"crossref","unstructured":"F. Bause, P. Buchholz, P. Kemper, A toolbox for functional and quantitative analysis of DEDS, in: R. Pujanger, N.N. Savino, B. Serra (Eds.), Quantitative Evaluation of Computing and Communication Systems, Lecture Notes in Computer Science, Vol. 1469, Springer, Berlin, 1998, pp. 356\u2013359.","DOI":"10.1007\/3-540-68061-6_32"},{"key":"10.1016\/S0166-5316(00)00057-2_BIB4","doi-asserted-by":"crossref","unstructured":"P. Buchholz, A notion of equivalence for stochastic Petri nets, in: G. De Michelis, M. Diaz (Eds.), Application and Theory of Petri Nets, Lecture Notes in Computer Science, Vol. 935, Springer, Berlin, 1995, pp. 161\u2013180.","DOI":"10.1007\/3-540-60029-9_39"},{"key":"10.1016\/S0166-5316(00)00057-2_BIB5","unstructured":"P. Buchholz, Iterative decomposition and aggregation of labelled GSPNs, in: J. Desel, M. Silva (Eds.), Application and Theory of Petri Nets, Lecture Notes in Computer Science, Vol. 1420, Springer, Berlin, 1998, pp. 226\u2013245."},{"issue":"2","key":"10.1016\/S0166-5316(00)00057-2_BIB6","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1145\/280265.280274","article-title":"A new approach combining simulation and randomization for the analysis of large continuous time Markov chains","volume":"8","author":"Buchholz","year":"1998","journal-title":"ACM Trans. Modeling Comput. Simulation"},{"issue":"2","key":"10.1016\/S0166-5316(00)00057-2_BIB7","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1109\/32.761443","article-title":"Hierarchical structuring of superposed GSPNs","volume":"25","author":"Buchholz","year":"1999","journal-title":"IEEE Trans. Software Eng."},{"key":"10.1016\/S0166-5316(00)00057-2_BIB8","doi-asserted-by":"crossref","unstructured":"P. Buchholz, G. Ciardo, S. Donatelli, P. Kemper, Complexity of Kronecker operations and sparse matrices with applications to the solution of Markov models. INFORMS J. Comput. 12 (3) (2000) 203\u2013222.","DOI":"10.1287\/ijoc.12.3.203.12634"},{"key":"10.1016\/S0166-5316(00)00057-2_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 Eng."},{"key":"10.1016\/S0166-5316(00)00057-2_BIB10","doi-asserted-by":"crossref","unstructured":"G. Ciardo, A.S. Miner, A data structure for the efficient Kronecker solution of GSPNs, in: P. Buchholz, M. Silva (Eds.), Proceedings of the Eighth International Workshop on Petri Nets and Performance Models, IEEE CS Press, 1999, pp. 22\u201331.","DOI":"10.1109\/PNPM.1999.796529"},{"key":"10.1016\/S0166-5316(00)00057-2_BIB11","doi-asserted-by":"crossref","unstructured":"P.J. Courtois, Decomposability Queueing and Computer System Applications, Academic Press, New York, 1977.","DOI":"10.1016\/B978-0-12-193750-8.50011-8"},{"key":"10.1016\/S0166-5316(00)00057-2_BIB12","doi-asserted-by":"crossref","unstructured":"S. Donatelli, Superposed generalized stochastic Petri nets: definition and efficient solution, in: R. Valette (Ed.), Application and Theory of Petri Nets, Lecture Notes in Computer Science, Vol. 815, Springer, Berlin, 1994, pp. 258\u2013277.","DOI":"10.1007\/3-540-58152-9_15"},{"key":"10.1016\/S0166-5316(00)00057-2_BIB13","doi-asserted-by":"crossref","unstructured":"J. Bechta Dugan, K.S. Trivedi, R.M. Geist, V.F. Nicola, Extended stochastic Petri nets: applications and analysis, in: E. Gelenbe (Ed.), Performance, Vol. 84, North-Holland, Amsterdam, 1984.","DOI":"10.21236\/ADA148439"},{"key":"10.1016\/S0166-5316(00)00057-2_BIB14","doi-asserted-by":"crossref","unstructured":"J. Dunkel, H. Stahl, On the transient analysis of stiff Markoff chains, in: L. Simoncini (Ed.), Dependable Computing for Critical Applications, Springer, Berlin, 1993.","DOI":"10.1007\/978-3-7091-4009-3_6"},{"issue":"2","key":"10.1016\/S0166-5316(00)00057-2_BIB15","doi-asserted-by":"crossref","first-page":"926","DOI":"10.1287\/opre.32.2.343","article-title":"The randomization technique as a modeling tool and solution procedure for transient Markov processes","volume":"32","author":"Gross","year":"1984","journal-title":"Oper. Res."},{"key":"10.1016\/S0166-5316(00)00057-2_BIB16","unstructured":"R.A. Howard, Dynamic Probabilistic Systems: Semi-Markov and Decision Processes, Vol II, Wiley, New York, 1971."},{"key":"10.1016\/S0166-5316(00)00057-2_BIB17","first-page":"87","article-title":"Markoff chains as an aid in the study of Markoff processes","volume":"36","author":"Jensen","year":"1953","journal-title":"Skand. Aktuarietidskr."},{"issue":"9","key":"10.1016\/S0166-5316(00)00057-2_BIB18","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1109\/32.541433","article-title":"Numerical analysis of superposed GSPNs","volume":"22","author":"Kemper","year":"1996","journal-title":"IEEE Trans. Software Eng."},{"issue":"2","key":"10.1016\/S0166-5316(00)00057-2_BIB19","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1109\/32.761444","article-title":"Transient analysis of superposed GSPNs","volume":"25","author":"Kemper","year":"1999","journal-title":"IEEE Trans. Software Eng."},{"key":"10.1016\/S0166-5316(00)00057-2_BIB20","unstructured":"A.M. Law, W.D. Kelton, Simulation Modeling and Analysis, Wiley, New York, 1991."},{"issue":"3","key":"10.1016\/S0166-5316(00)00057-2_BIB21","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1002\/nav.3800260304","article-title":"Simulation of nonhomogeneous Poisson processes by thinning","volume":"26","author":"Lewis","year":"1979","journal-title":"Naval Res. Logistics Quart."},{"key":"10.1016\/S0166-5316(00)00057-2_BIB22","unstructured":"D. Litzba, M. Sczittnick, F.J. Stewing, Yet another simulation output analysis algorithm: the autoregressive, online-update evaluation technique of the modelling tool, HIT, in: Proceedings of the Third European Simulation Congress, 1989."},{"issue":"4","key":"10.1016\/S0166-5316(00)00057-2_BIB23","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1145\/226275.226278","article-title":"A comparative study of parallel algorithms for simulating continuous time Markov chains","volume":"5","author":"Nicol","year":"1995","journal-title":"ACM Trans. Modeling Comput. Simulation"},{"key":"10.1016\/S0166-5316(00)00057-2_BIB24","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1145\/317786.317819","article-title":"On the stochastic structure of parallelism and synchronisation models for distributed algorithms","volume":"13","author":"Plateau","year":"1985","journal-title":"Perform. Eval. Rev."},{"issue":"1","key":"10.1016\/S0166-5316(00)00057-2_BIB25","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1109\/49.64901","article-title":"Reduced base model construction for stochastic activity networks","volume":"9","author":"Sanders","year":"1991","journal-title":"IEEE J. Selected Areas Commun."},{"key":"10.1016\/S0166-5316(00)00057-2_BIB26","doi-asserted-by":"crossref","unstructured":"W.H. Sanders, J.F. Meyer, A unified approach for specifying measures of performance, dependability and performability, in: A. Avizienis, J. Laprie (Eds.), Dependable Computing for Critical Applications: Dependable Computing and Fault-Tolerant Systems, Vol. 4, Springer, Berlin, 1991.","DOI":"10.1007\/978-3-7091-9123-1_10"},{"issue":"4","key":"10.1016\/S0166-5316(00)00057-2_BIB27","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1287\/opre.34.4.573","article-title":"Uniformization and hybrid simulation\/analytic models of renewal processes","volume":"34","author":"Shantikumar","year":"1986","journal-title":"Oper. Res."},{"key":"10.1016\/S0166-5316(00)00057-2_BIB28","unstructured":"R.B. Sidje, W.J. Stewart, A survey of methods for computing large sparse matrix exponentials arising in Markov chains, submitted for publication."},{"key":"10.1016\/S0166-5316(00)00057-2_BIB29","unstructured":"W.J. Stewart, Introduction to the Numerical Solution of Markov Chains, Princeton University Press, Princeton, NJ, 1994."},{"key":"10.1016\/S0166-5316(00)00057-2_BIB30","doi-asserted-by":"crossref","unstructured":"K.S. Trivedi, G. Ciardo, M. Mahorta, R.A. Sahner, Dependability and performability analysis, in: L. Donatelli, R. Nelson (Eds.), Performance Evaluation of Computer and Communication Systems Joint Tutorial Papers of Performance\u201993 and Sigmetrics\u201993, Lecture Notes in Computer Science, Vol. 729, Springer, Berlin, 1993, pp. 587\u2013612.","DOI":"10.1007\/BFb0013869"}],"container-title":["Performance Evaluation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0166531600000572?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0166531600000572?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2020,1,15]],"date-time":"2020-01-15T17:26:50Z","timestamp":1579109210000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0166531600000572"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,4]]},"references-count":30,"journal-issue":{"issue":"1-4","published-print":{"date-parts":[[2001,4]]}},"alternative-id":["S0166531600000572"],"URL":"https:\/\/doi.org\/10.1016\/s0166-5316(00)00057-2","relation":{},"ISSN":["0166-5316"],"issn-type":[{"value":"0166-5316","type":"print"}],"subject":[],"published":{"date-parts":[[2001,4]]}}}