{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T08:49:01Z","timestamp":1758271741986},"reference-count":20,"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)00061-9","type":"journal-article","created":{"date-parts":[[2002,7,25]],"date-time":"2002-07-25T19:20:22Z","timestamp":1027624822000},"page":"127-148","source":"Crossref","is-referenced-by-count":22,"title":["A probabilistic dynamic technique for the distributed generation of very large state spaces"],"prefix":"10.1016","volume":"39","author":[{"given":"W.J.","family":"Knottenbelt","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P.G.","family":"Harrison","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.A.","family":"Mestern","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P.S.","family":"Kritzinger","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/S0166-5316(99)00061-9_BIB1","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1145\/190.191","article-title":"A class of generalised stochastic Petri nets for the performance evaluation of multiprocessor systems","volume":"2","author":"Ajmone-Marsan","year":"1984","journal-title":"ACM Trans. Comput. Systems"},{"key":"10.1016\/S0166-5316(99)00061-9_BIB2","doi-asserted-by":"crossref","unstructured":"S.C. Allmaier, G. Horton, Parallel shared-memory state-space exploration in stochastic modeling, Lecture Notes in Computer Science,vol. 1253, Springer, Berlin, 1997, pp. 207\u2013218.","DOI":"10.1007\/3-540-63138-0_19"},{"key":"10.1016\/S0166-5316(99)00061-9_BIB3","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1145\/321879.321887","article-title":"Open, closed and mixed networks of queues with different classes of customers","volume":"22","author":"Basket","year":"1975","journal-title":"J. ACM"},{"key":"10.1016\/S0166-5316(99)00061-9_BIB4","doi-asserted-by":"crossref","unstructured":"F. Bause, Queueing Petri nets: a formalism for the combined qualitative and quantitative analysis of systems, in: Proceedings of the Fifth International Workshop on Petri nets and Performance Models, IEEE, October 1993.","DOI":"10.1109\/PNPM.1993.393439"},{"key":"10.1016\/S0166-5316(99)00061-9_BIB5","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/0166-5316(93)E0040-C","article-title":"Hierarchical Markovian models: symmetries and aggregation","volume":"22","author":"Buchholz","year":"1995","journal-title":"Performance Evaluation"},{"key":"10.1016\/S0166-5316(99)00061-9_BIB6","doi-asserted-by":"crossref","unstructured":"C. Caselli, G. Conte, P. Marenzoni, Parallel state exploration for GSPN models, in: Proceedings of the 16th International Conference on the Application and Theory and Petri Nets, Lecture Notes in Computer Science, vol. 935, Springer, Berlin, June 1995.","DOI":"10.1007\/3-540-60029-9_40"},{"issue":"1","key":"10.1016\/S0166-5316(99)00061-9_BIB7","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1287\/ijoc.10.1.82","article-title":"Distributed state space generation of discrete-state stochastic models","volume":"10","author":"Ciardo","year":"1998","journal-title":"INFORMS J. Comput."},{"issue":"4","key":"10.1016\/S0166-5316(99)00061-9_BIB8","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/0166-5316(91)90003-L","article-title":"On the solution of GSPN reward models","volume":"12","author":"Ciardo","year":"1991","journal-title":"Performance Evaluation"},{"issue":"1","key":"10.1016\/S0166-5316(99)00061-9_BIB9","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/0166-5316(93)90026-Q","article-title":"A decomposition approach for stochastic reward net models","volume":"18","author":"Ciardo","year":"1993","journal-title":"Performance Evaluation"},{"key":"10.1016\/S0166-5316(99)00061-9_BIB10","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1016\/0020-0190(83)90092-3","article-title":"Derivation of a termination detection algorithm for distributed computations","volume":"16","author":"Dijkstra","year":"1983","journal-title":"Inform. Process. Lett."},{"key":"10.1016\/S0166-5316(99)00061-9_BIB11","doi-asserted-by":"crossref","unstructured":"A. Geist, A. Beguelin, J. Dongarra, W. Jiang, R. Manchek, V. Sunderam, PVM Parallel Virtual Machine: A User\u2019s Guide and Tutorial for Networked Parallel Computing, MIT Press, Cambridge, MA, 1994.","DOI":"10.7551\/mitpress\/5712.001.0001"},{"key":"10.1016\/S0166-5316(99)00061-9_BIB12","unstructured":"W. Gropp, E. Lusk, A. Skjellum, Using MPI: Portable Parallel Programming with the Message Passing Interface, MIT Press, Cambridge, MA, 1994."},{"key":"10.1016\/S0166-5316(99)00061-9_BIB13","unstructured":"G.J. Holzmann, Design and Validation of Computer Protocols, Prentice-Hall, Englewood Cliffs, NJ, 1991."},{"key":"10.1016\/S0166-5316(99)00061-9_BIB14","doi-asserted-by":"crossref","unstructured":"G.J. Holzmann, An analysis of bistate hashing, in: Proceedings of the IFIP\/PSTV95: Conference on Protocol Specification, Testing and Verification, Warsaw, Poland, Chapman & Hall, London, 1995.","DOI":"10.1007\/978-0-387-34892-6_19"},{"issue":"1","key":"10.1016\/S0166-5316(99)00061-9_BIB15","first-page":"24","article-title":"Hardware of AP3000 scalar parallel server","volume":"33","author":"Ishihata","year":"1997","journal-title":"Fujitsu Sci. Tech. J."},{"key":"10.1016\/S0166-5316(99)00061-9_BIB16","doi-asserted-by":"crossref","unstructured":"P. Kemper, Numerical analysis of superposed GSPNs, in: Proceedings of the Sixth International Workshop on Petri Nets and Performance Models, IEEE Computer Society Press, Silver Spring, MD, 1995, pp. 52\u201362.","DOI":"10.1109\/PNPM.1995.524315"},{"key":"10.1016\/S0166-5316(99)00061-9_BIB17","unstructured":"W.J. Knottenbelt, Generalised Markovian analysis of timed transition systems, Master\u2019s thesis, University of Cape Town, 1996."},{"key":"10.1016\/S0166-5316(99)00061-9_BIB18","unstructured":"W.J. Knottenbelt, P.G. Harrison, Distributed disk-based solution techniques for large Markov models, in: Proceedings of the Third International Meeting on the Numerical Solution of Markov Chains (NSMC\u201999), Zaragoza, Spain, 6\u201310 September 1999, pp. 58\u201375."},{"key":"10.1016\/S0166-5316(99)00061-9_BIB19","doi-asserted-by":"crossref","unstructured":"U. Stern, D.L. Dill, Improved probabilistic verification by hash compaction, in: IFIP WG 10.5 Advanced Research Working Conference on Correct Hardware Design and Verification Methods, 1995.","DOI":"10.1007\/3-540-60385-9_13"},{"key":"10.1016\/S0166-5316(99)00061-9_BIB20","doi-asserted-by":"crossref","unstructured":"P.Wolper, D. Leroy, Reliable hashing without collision detection, Lecture Notes in Computer Science, vol. 697, Springer, Berlin, 1993, pp. 59\u201370.","DOI":"10.1007\/3-540-56922-7_6"}],"container-title":["Performance Evaluation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0166531699000619?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0166531699000619?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2020,1,29]],"date-time":"2020-01-29T00:09:38Z","timestamp":1580256578000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0166531699000619"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,2]]},"references-count":20,"journal-issue":{"issue":"1-4","published-print":{"date-parts":[[2000,2]]}},"alternative-id":["S0166531699000619"],"URL":"https:\/\/doi.org\/10.1016\/s0166-5316(99)00061-9","relation":{},"ISSN":["0166-5316"],"issn-type":[{"value":"0166-5316","type":"print"}],"subject":[],"published":{"date-parts":[[2000,2]]}}}