{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T20:40:25Z","timestamp":1743021625775,"version":"3.40.3"},"publisher-location":"Cham","reference-count":26,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319390857"},{"type":"electronic","value":"9783319390864"}],"license":[{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016]]},"DOI":"10.1007\/978-3-319-39086-4_17","type":"book-chapter","created":{"date-parts":[[2016,6,8]],"date-time":"2016-06-08T09:09:16Z","timestamp":1465376956000},"page":"281-300","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Efficient Decomposition Algorithm for Stationary Analysis of Complex Stochastic Petri Net Models"],"prefix":"10.1007","author":[{"given":"Krist\u00f3f","family":"Marussy","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Attila","family":"Klenik","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vince","family":"Moln\u00e1r","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andr\u00e1s","family":"V\u00f6r\u00f6s","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Istv\u00e1n","family":"Majzik","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mikl\u00f3s","family":"Telek","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,6,9]]},"reference":[{"key":"17_CR1","series-title":"Lecture Notes in Computer Science","first-page":"1","volume-title":"Advances in Petri Nets 1989, Covers the 9th European Workshop on Applications and Theory in Petri Nets, held in Venice, Italy in June 1988, Selected Paper","author":"M Ajmone\u00a0Marsan","year":"1988","unstructured":"Ajmone\u00a0Marsan, M.: Stochastic Petri nets: an elementary introduction. In: Rozenberg, G. (ed.) Advances in Petri Nets 1989, Covers the 9th European Workshop on Applications and Theory in Petri Nets, held in Venice, Italy in June 1988, Selected Paper. LNCS, vol. 424, pp. 1\u201329. Springer, Heidelberg (1988)"},{"key":"17_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1007\/3-540-48320-9_12","volume-title":"CONCUR, 1999 Concurrency Theory","author":"C Baier","year":"1999","unstructured":"Baier, C., Katoen, J.P., Hermanns, H.: Approximative symbolic model checking of continuous-time Markov chains. In: Baeten, J.C.M., Mauw, S. (eds.) CONCUR, 1999 Concurrency Theory. LNCS, vol. 1664, pp. 146\u2013161. Springer, Heidelberg (1999)"},{"key":"17_CR3","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971538","volume-title":"Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods","author":"R Barrett","year":"1994","unstructured":"Barrett, R., Berry, M.W., Chan, T.F., Demmel, J., Donato, J., Dongarra, J., Eijkhout, V., Pozo, R., Romine, C., Van der Vorst, H.: Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, vol. 43. SIAM, Philadelphia (1994)"},{"key":"17_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"356","DOI":"10.1007\/3-540-68061-6_32","volume-title":"Computer Performance Evaluation","author":"F Bause","year":"1998","unstructured":"Bause, F., Buchholz, P., Kemper, P.: A toolbox for functional and quantitative analysis of DEDS. In: Puigjaner, R., Savino, N.N., Serra, B. (eds.) TOOLS 1998. LNCS, vol. 1469, p. 356. Springer, Heidelberg (1998)"},{"issue":"7","key":"17_CR5","doi-asserted-by":"publisher","first-page":"838","DOI":"10.1016\/j.future.2006.02.006","volume":"22","author":"A Benoit","year":"2006","unstructured":"Benoit, A., Plateau, B., Stewart, W.J.: Memory-efficient Kronecker algorithms with applications to the modelling of parallel systems. Future Gener. Comp. Syst. 22(7), 838\u2013847 (2006)","journal-title":"Future Gener. Comp. Syst."},{"key":"17_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"499","DOI":"10.1007\/3-540-60692-0_70","volume-title":"Foundations of Software Technology and Theoretical Computer Science","author":"A Bianco","year":"1995","unstructured":"Bianco, A., de Alfaro, L.: Model checking of probabilistic and nondeterministic systems. In: Thiagarajan, P.S. (ed.) FSTTCS 1995. LNCS, vol. 1026, pp. 499\u2013513. Springer, Heidelberg (1995)"},{"issue":"2","key":"17_CR7","doi-asserted-by":"publisher","first-page":"166","DOI":"10.1109\/32.761443","volume":"25","author":"P Buchholz","year":"1999","unstructured":"Buchholz, P.: Hierarchical structuring of superposed GSPNs. IEEE Trans. Softw. Eng. 25(2), 166\u2013181 (1999)","journal-title":"IEEE Trans. Softw. Eng."},{"issue":"3","key":"17_CR8","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1287\/ijoc.12.3.203.12634","volume":"12","author":"P Buchholz","year":"2000","unstructured":"Buchholz, P., Ciardo, G., Donatelli, S., Kemper, P.: Complexity of memory-efficient Kronecker operations with applications to the solution of Markov models. INFORMS J. Comput. 12(3), 203\u2013222 (2000)","journal-title":"INFORMS J. Comput."},{"issue":"2","key":"17_CR9","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1145\/288197.288202","volume":"26","author":"P Buchholz","year":"1998","unstructured":"Buchholz, P., Kemper, P.: On generating a hierarchy for GSPN analysis. SIGMETRICS Perform. Eval. Rev. 26(2), 5\u201314 (1998)","journal-title":"SIGMETRICS Perform. Eval. Rev."},{"key":"17_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"256","DOI":"10.1007\/978-3-540-24611-4_8","volume-title":"Validation of Stochastic Systems: A Guide to Current Research","author":"P Buchholz","year":"2004","unstructured":"Buchholz, P., Kemper, P.: Kronecker based matrix representations for large Markov models. In: Baier, C., Haverkort, B.R., Hermanns, H., Katoen, J.-P., Siegle, M. (eds.) Validation of Stochastic Systems: A Guide to Current Research. LNCS, vol. 2925, pp. 256\u2013295. Springer, Heidelberg (2004)"},{"key":"17_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1007\/978-3-540-45232-4_6","volume-title":"Computer Performance Evaluation. Modelling Techniques and Tools","author":"G Ciardo","year":"2003","unstructured":"Ciardo, G., Jones, R.L., Miner, A.S., Siminiceanu, R.: Logical and stochastic modeling with SMART. In: Kemper, P., Sanders, W.H. (eds.) TOOLS 2003. LNCS, vol. 2794, pp. 78\u201397. Springer, Heidelberg (2003)"},{"key":"17_CR12","unstructured":"Ciardo, G., Miner, A.S.: A data structure for the efficient Kronecker solution of GSPNs. In: The 8th International Workshop on Petri Nets and Performance Models, 1999, pp. 22\u201331. IEEE (1999)"},{"key":"17_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1007\/978-3-642-29072-5_3","volume-title":"Transactions on Petri Nets and Other Models of Concurrency V","author":"G Ciardo","year":"2012","unstructured":"Ciardo, G., Zhao, Y., Jin, X.: Ten years of saturation: a Petri net perspective. In: Jensen, K., Donatelli, S., Kleijn, J. (eds.) Transactions on Petri Nets and Other Models of Concurrency V. LNCS, vol. 6900, pp. 51\u201395. Springer, Heidelberg (2012)"},{"key":"17_CR14","doi-asserted-by":"crossref","unstructured":"Czekster, R.M., Rose, C., Fernandes, P.H.L., de Lima, A.M., Webber, T.: Kronecker descriptor partitioning for parallel algorithms. In: McGraw, R.M., Imsand, E.S., Chinni, M.J. (eds.) Proceedings of the 2010 Spring Simulation Multiconference, SpringSim 2010, Orlando, Florida, USA, 11\u201315, April 2010, p. 242. SCS\/ACM (2010)","DOI":"10.1145\/1878537.1878789"},{"key":"17_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"258","DOI":"10.1007\/3-540-58152-9_15","volume-title":"Application and Theory of Petri Nets 1994","author":"S Donatelli","year":"1994","unstructured":"Donatelli, S.: Superposed generalized stochastic Petri nets: Definition and efficient solution. In: Valette, R. (ed.) Application and Theory of Petri Nets 1994. LNCS, vol. 815, pp. 258\u2013277. Springer, Heidelberg (1994)"},{"key":"17_CR16","unstructured":"Fernandes, P., Presotto, R., Sales, A., Webber, T.: An alternative algorithm to multiply a vector by a Kronecker represented descriptor. In: 21st UK Performance Engineering Workshop, pp. 57\u201367 (2005)"},{"key":"17_CR17","unstructured":"Ghosh, R.: Scalable stochastic models for cloud services. Ph.D. thesis, Duke University (2012)"},{"issue":"9","key":"17_CR18","doi-asserted-by":"publisher","first-page":"615","DOI":"10.1109\/32.541433","volume":"22","author":"P Kemper","year":"1996","unstructured":"Kemper, P.: Numerical analysis of superposed GSPNs. IEEE Trans. Softw. Eng. 22(9), 615\u2013628 (1996)","journal-title":"IEEE Trans. Softw. Eng."},{"issue":"4","key":"17_CR19","doi-asserted-by":"publisher","first-page":"589","DOI":"10.1016\/S1571-0661(05)80394-9","volume":"68","author":"M Kwiatkowska","year":"2002","unstructured":"Kwiatkowska, M., Mehmood, R., Norman, G., Parker, D.: A symbolic out-of-core solution method for Markov models. Electron. Notes Theoret. Comput. Sci. 68(4), 589\u2013604 (2002)","journal-title":"Electron. Notes Theoret. Comput. Sci."},{"issue":"2","key":"17_CR20","doi-asserted-by":"publisher","first-page":"128","DOI":"10.1007\/s10009-004-0140-2","volume":"6","author":"M Kwiatkowska","year":"2004","unstructured":"Kwiatkowska, M., Norman, G., Parker, D.: Probabilistic symbolic model checking with PRISM: a hybrid approach. Int. J. Softw. Tools Technol. Transfer 6(2), 128\u2013142 (2004)","journal-title":"Int. J. Softw. Tools Technol. Transfer"},{"key":"17_CR21","unstructured":"Miner, A.S.: Efficient solution of GSPNs using canonical matrix diagrams. In: 9th International Workshop on Petri Nets and Performance Models, 2001, pp. 101\u2013110. IEEE (2001)"},{"key":"17_CR22","unstructured":"Roux, P., Siminiceanu, R.: Model checking with edge-valued decision diagrams. In: Mu\u00f1oz, C.A. (ed.) Second NASA Formal Methods Symposium - NFM 2010, Washington D.C., USA, 13\u201315 April 2010. Proceedings. NASA Conference Proceedings, vol. NASA\/CP-2010-216215, pp. 222\u2013226 (2010)"},{"key":"17_CR23","doi-asserted-by":"publisher","DOI":"10.2307\/j.ctvcm4gtc","volume-title":"Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling","author":"WJ Stewart","year":"2009","unstructured":"Stewart, W.J.: Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling. Princeton University Press, Princeton (2009)"},{"issue":"2","key":"17_CR24","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1137\/0913035","volume":"13","author":"HA Van der Vorst","year":"1992","unstructured":"Van der Vorst, H.A.: Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM J. Scientific Stat. Comput. 13(2), 631\u2013644 (1992)","journal-title":"SIAM J. Scientific Stat. Comput."},{"issue":"5","key":"17_CR25","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1016\/j.peva.2011.02.005","volume":"68","author":"M Wan","year":"2011","unstructured":"Wan, M., Ciardo, G., Miner, A.S.: Approximate steady-state analysis of large Markov models based on the structure of their decision diagram encoding. Performance Eval. 68(5), 463\u2013486 (2011)","journal-title":"Performance Eval."},{"key":"17_CR26","doi-asserted-by":"crossref","unstructured":"Zhao, Y., Ciardo, G.: A two-phase Gauss-Seidel algorithm for the stationary solution of EVMDD-encoded CTMCs. In: Ninth International Conference on Quantitative Evaluation of Systems, QEST 2012, London, United Kingdom, 17\u201320 September 2012, pp. 74\u201383. IEEE Computer Society (2012)","DOI":"10.1109\/QEST.2012.34"}],"container-title":["Lecture Notes in Computer Science","Application and Theory of Petri Nets and Concurrency"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-39086-4_17","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,13]],"date-time":"2023-11-13T03:05:26Z","timestamp":1699844726000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-319-39086-4_17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016]]},"ISBN":["9783319390857","9783319390864"],"references-count":26,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-39086-4_17","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2016]]},"assertion":[{"value":"9 June 2016","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"PETRI NETS","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Applications and Theory of Petri Nets and Concurrency","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Torun","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Poland","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2016","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"19 June 2016","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"24 June 2016","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"37","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"apn2016","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}