{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,11]],"date-time":"2026-04-11T02:26:48Z","timestamp":1775874408145,"version":"3.50.1"},"publisher-location":"Berlin, Heidelberg","reference-count":51,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540724827","type":"print"},{"value":"9783540725220","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"DOI":"10.1007\/978-3-540-72522-0_3","type":"book-chapter","created":{"date-parts":[[2007,6,5]],"date-time":"2007-06-05T19:02:12Z","timestamp":1181070132000},"page":"83-131","source":"Crossref","is-referenced-by-count":54,"title":["Introduction to Generalized Stochastic Petri Nets"],"prefix":"10.1007","author":[{"given":"Gianfranco","family":"Balbo","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"3_CR1","doi-asserted-by":"crossref","unstructured":"Agerwala, T.: Putting Petri nets to work. IEEE Computer, 85\u201394 (December 1979)","DOI":"10.1109\/MC.1979.1658580"},{"issue":"7","key":"3_CR2","doi-asserted-by":"publisher","first-page":"832","DOI":"10.1109\/32.29483","volume":"15","author":"M. Ajmone Marsan","year":"1989","unstructured":"Ajmone Marsan, M., Balbo, G., Bobbio, A., Chiola, G., Conte, G., Cumani, A.: The effect of execution policies on the semantics and analysis of stochastic Petri nets. IEEE Transactions on Software Engineering\u00a015(7), 832\u2013846 (1989)","journal-title":"IEEE Transactions on Software Engineering"},{"key":"3_CR3","first-page":"44","volume-title":"Proc. Intern. Workshop on Petri Nets and Performance Models","author":"M. Ajmone Marsan","year":"1987","unstructured":"Ajmone Marsan, M., Balbo, G., Chiola, G., Conte, G.: Generalized stochastic Petri nets revisited: Random switches and priorities. In. In: Proc. Intern. Workshop on Petri Nets and Performance Models, Madison, WI, USA, August 1987, pp. 44\u201353. IEEE Computer Society Press, Los Alamitos (1987)"},{"key":"3_CR4","doi-asserted-by":"crossref","unstructured":"Ajmone Marsan, M., Balbo, G., Conte, G.: A class of generalized stochastic Petri nets for the performance analysis of multiprocessor systems. ACM Transactions on Computer Systems\u00a01 (1984)","DOI":"10.1145\/190.191"},{"key":"3_CR5","volume-title":"Performance Models of Multiprocessor Systems","author":"M. Ajmone Marsan","year":"1986","unstructured":"Ajmone Marsan, M., Balbo, G., Conte, G.: Performance Models of Multiprocessor Systems. MIT Press, Cambridge (1986)"},{"key":"3_CR6","volume-title":"Modelling with Generalized Stochastic Petri Nets","author":"M. Ajmone Marsan","year":"1995","unstructured":"Ajmone Marsan, M., Balbo, G., Conte, G., Donatelli, S., Franceschinis, G.: Modelling with Generalized Stochastic Petri Nets. J. Wiley, Chichester (1995)"},{"key":"3_CR7","volume-title":"Proc. Intern. Workshop on Timed Petri Nets","year":"1985","unstructured":"Ajmone Marsan, M., Balbo, G., Trivedi, K.S. (eds.): Proc. Intern. Workshop on Timed Petri Nets, Torino, Italy, July 1985. IEEE-CS Press, Los Alamitos (1985)"},{"key":"3_CR8","unstructured":"Ajmone Marsan, M., Chiola, G.: On Petri nets with deterministic and exponential transition firing times. In: Proc. 7 th European Workshop on Application and Theory of Petri Nets, Oxford, England, June 1986, pp. 151\u2013165 (1986)"},{"issue":"1","key":"3_CR9","first-page":"125","volume":"14","author":"H. Alaiwan","year":"1982","unstructured":"Alaiwan, H., Memmi, G.: Algorithmes de recherche des solutions entieres positives d\u2019un systeme d\u2019equations lineaires homogeneus en nombres entieres. Revue Technique Thomson-CSF\u00a014(1), 125\u2013135 (1982)","journal-title":"Revue Technique Thomson-CSF"},{"key":"3_CR10","unstructured":"Alaiwan, H., Toudic, J.M.: Research des semiflots, des verrous et des trappes dans le reseaux de Petri. Technique et Science Informatiques\u00a04(1) (1985)"},{"key":"3_CR11","first-page":"307","volume-title":"Performance Models for Discrete Event Systems with Synchronisations: Formalisms and Analysis Techniques","author":"G. Balbo","year":"1998","unstructured":"Balbo, G.: Exponential stochastic petri nets. In: Balbo, G., Silva, M. (eds.) Performance Models for Discrete Event Systems with Synchronisations: Formalisms and Analysis Techniques, pp. 307\u2013344. KRONOS, Zaragoza (1998)"},{"key":"3_CR12","first-page":"345","volume-title":"Performance Models for Discrete Event Systems with Synchronisations: Formalisms and Analysis Techniques","author":"G. Balbo","year":"1998","unstructured":"Balbo, G.: Non-exponential stochastic petri nets. In: Balbo, G., Silva, M. (eds.) Performance Models for Discrete Event Systems with Synchronisations: Formalisms and Analysis Techniques, pp. 345\u2013385. KRONOS, Zaragoza (1998)"},{"key":"3_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1007\/3-540-44667-2_3","volume-title":"Lectures on Formal Methods and Performance Analysis","author":"G. Balbo","year":"2001","unstructured":"Balbo, G.: Introduction to stochastic petri nets. In: Brinksma, E., Hermanns, H., Katoen, J.-P. (eds.) Lectures on Formal Methods and Performance Analysis. LNCS, vol.\u00a02090, pp. 84\u2013155. Springer, Heidelberg (2001)"},{"key":"3_CR14","volume-title":"Performance Models for Discrete Event Systems with Synchronizations: Formalisms and Analysis Techniques","year":"1998","unstructured":"Balbo, G., Silva, M. (eds.): Performance Models for Discrete Event Systems with Synchronizations: Formalisms and Analysis Techniques. KRONOS, Zaragoza (1998)"},{"key":"3_CR15","volume-title":"Proc. 3 rd Intern. Workshop on Petri Nets and Performance Models","author":"A. Blakemore","year":"1989","unstructured":"Blakemore, A.: The cost of eliminating vanishing markings from generalized stochastic Petri nets. In: Proc. 3 rd Intern. Workshop on Petri Nets and Performance Models, Kyoto, Japan, December 1989, IEEE Computer Society Press, Los Alamitos (1989)"},{"key":"3_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1007\/3-540-58152-9_8","volume-title":"Application and Theory of Petri Nets 1994","author":"P. Buchholz","year":"1994","unstructured":"Buchholz, P.: Hierarchical high level Petri nets for complex system analysis. In: Valette, R. (ed.) ICATPN 1994. LNCS, vol.\u00a0815, pp. 119\u2013138. Springer, Heidelberg (1994)"},{"key":"3_CR17","first-page":"187","volume-title":"Proc. 3 rd Intern. Workshop on Petri Nets and Performance Models","author":"P. Chen","year":"1989","unstructured":"Chen, P., Bruell, S.C., Balbo, G.: Alternative methods for incorporating non-exponential distributions into stochastic Petri nets. In: Proc. 3 rd Intern. Workshop on Petri Nets and Performance Models, Kyoto, Japan, December 1989, pp. 187\u2013197. IEEE Computer Society Press, Los Alamitos (1989)"},{"issue":"2","key":"3_CR18","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1109\/32.214828","volume":"19","author":"G. Chiola","year":"1993","unstructured":"Chiola, G., Ajmone Marsan, M., Balbo, G., Conte, G.: Generalized stochastic Petri nets: A definition at the net level and its implications. IEEE Transactions on Software Engineering\u00a019(2), 89\u2013107 (1993)","journal-title":"IEEE Transactions on Software Engineering"},{"key":"3_CR19","doi-asserted-by":"crossref","unstructured":"Chiola, G., Dutheillet, C., Franceschinis, G., Haddad, S.: Stochastic Well-Formed coloured nets for symmetric modelling applications. IEEE Transactions on Computers\u00a042(11) (1993)","DOI":"10.1109\/12.247838"},{"key":"3_CR20","volume-title":"Proc. 3 rd Intern. Workshop on Petri Nets and Performance Models","author":"G. Chiola","year":"1989","unstructured":"Chiola, G., Franceschinis, G.: Colored GSPN models and automatic symmetry detection. In: Proc. 3 rd Intern. Workshop on Petri Nets and Performance Models, Kyoto, Japan, December 1989, IEEE Computer Society Press, Los Alamitos (1989)"},{"key":"3_CR21","doi-asserted-by":"crossref","unstructured":"Chiola, G., Franceschinis, G., Gaeta, R., Ribaudo, M.: GreatSPN1.7: GRaphical Editor and Analyzer for Timed and Stochastic Petri Nets. Performance Evaluation (Special Issues on Performance Modelling Tools)\u00a024 (1995)","DOI":"10.1016\/0166-5316(95)00008-L"},{"key":"3_CR22","series-title":"Lecture Notes in Computer Science","volume-title":"Application and Theory of Petri Nets 1993","author":"H. Choi","year":"1993","unstructured":"Choi, H., Kulkarni, G., Trivedi, K.S.: Transient analysis of deterministic and stochastic petri nets. In: Ajmone Marsan, M. (ed.) ICATPN 1993. LNCS, vol.\u00a0691, Springer, Heidelberg (1993)"},{"key":"3_CR23","unstructured":"Choi, H., Kulkarni, V.S., Trivedi, K.S.: Markov regenerative stochastic Petri nets. In: Proc. of Performance 93, Rome, Italy (September 1993)"},{"key":"3_CR24","unstructured":"Ciardo, G.: Analysis of large Petri net models. PhD thesis, Department of Computer Science, Duke University, Durham, NC, USA (1989)"},{"key":"3_CR25","doi-asserted-by":"publisher","first-page":"170","DOI":"10.1109\/PNPM.1993.393453","volume-title":"Proc. 5 th Intern. Workshop on Petri Nets and Performance Models","author":"G. Ciardo","year":"1993","unstructured":"Ciardo, G., German, R., Lindemann, C.: A characterization of the stochastic process underlying a stochastic Petri net. In: Proc. 5 th Intern. Workshop on Petri Nets and Performance Models, Toulouse, France, Oct. 1993, pp. 170\u2013179. IEEE Computer Society Press, Los Alamitos (1993)"},{"key":"3_CR26","doi-asserted-by":"publisher","first-page":"160","DOI":"10.1109\/PNPM.1993.393454","volume-title":"Proc. 5 th Intern. Workshop on Petri Nets and Performance Models","author":"G. Ciardo","year":"1993","unstructured":"Ciardo, G., Lindemann, C.: Analysis of deterministic and stochastic Petri nets. In: Proc. 5 th Intern. Workshop on Petri Nets and Performance Models, Toulouse, France, Oct. 1993, pp. 160\u2013169. IEEE Computer Society Press, Los Alamitos (1993)"},{"issue":"4","key":"3_CR27","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1016\/0166-5316(91)90003-L","volume":"12","author":"G. Ciardo","year":"1991","unstructured":"Ciardo, G., Muppala, J., Trivedi, K.S.: On the solution of GSPN reward models. Performance Evaluation\u00a012(4), 237\u2013253 (1991)","journal-title":"Performance Evaluation"},{"key":"3_CR28","doi-asserted-by":"publisher","first-page":"583","DOI":"10.1016\/0026-2714(82)90033-6","volume":"22","author":"A. Cumani","year":"1982","unstructured":"Cumani, A.: On the canonical representation of homogeneousMarkov processes modelling failure time distributions. Microelectron Reliability\u00a022, 583\u2013602 (1982)","journal-title":"Microelectron Reliability"},{"key":"3_CR29","doi-asserted-by":"crossref","unstructured":"Dugan, J.B., Trivedi, K.S., Geist, R.M., Nicola, V.F.: Extended stochastic Petri nets: Applications and analysis. In: Proc. PERFORMANCE \u201984, Paris, France (December 1984)","DOI":"10.21236\/ADA148439"},{"key":"3_CR30","volume-title":"Proc. 3 rd Intern. Workshop on Petri Nets and Performance Models","author":"C. Dutheillet","year":"1989","unstructured":"Dutheillet, C., Haddad, S.: Aggregation and disaggregation of states in colored stochastic Petri nets: Application to a multiprocessor architecture. In: Proc. 3 rd Intern. Workshop on Petri Nets and Performance Models, Kyoto, Japan, December 1989, IEEE Computer Society Press, Los Alamitos (1989)"},{"key":"3_CR31","unstructured":"Florin, G., Natkin, S.: Les reseaux de Petri stochastiques. Technique et Science Informatiques\u00a04(1) (1985)"},{"key":"3_CR32","first-page":"29","volume-title":"Proc. 3 rd Intern. Workshop on Petri Nets and Performance Models","author":"G. Florin","year":"1989","unstructured":"Florin, G., Natkin, S.: Matrix product form solution for closed synchronized queueing networks. In: Proc. 3 rd Intern. Workshop on Petri Nets and Performance Models, Kyoto, Japan, December 1989, pp. 29\u201339. IEEE Computer Society Press, Los Alamitos (1989)"},{"key":"3_CR33","unstructured":"German, R., Lindemann, C.: Analysis of stochastic Petri nets by the method of supplementary variables. In: Proc. of Performance 93, Rome, Italy (September 1993)"},{"key":"3_CR34","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1007\/978-3-540-47919-2_7","volume-title":"Advances in Petri Nets 1986. Proceedings of an Advanced Course, Bad Honnef, 8.-19. September 1986","author":"K. Lautenbach","year":"1987","unstructured":"Lautenbach, K.: Linear algebraic technique for place\/transition nets. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) APN 1986. LNCS, vol.\u00a0254, pp. 142\u2013167. Springer, Heidelberg (1987)"},{"key":"3_CR35","volume-title":"Proc. Intern. Workshop on Petri Nets and Performance Models","author":"C. Lin","year":"1987","unstructured":"Lin, C., Marinescu, D.C.: On stochastic high level Petri nets. In: Proc. Intern. Workshop on Petri Nets and Performance Models, Madison, WI, USA, August 1987, IEEE Computer Society Press, Los Alamitos (1987)"},{"key":"3_CR36","volume-title":"Proc. 5 th Intern. Workshop on Petri Nets and Performance Models","author":"V. Mainkar","year":"1993","unstructured":"Mainkar, V., Choi, H., Trivedi, K.: Sensitivity analysis of Markov regenerative stochastic Petri nets. In: Proc. 5 th Intern. Workshop on Petri Nets and Performance Models, Toulouse, France, Oct. 1993, IEEE Computer Society Press, Los Alamitos (1993)"},{"key":"3_CR37","series-title":"Informatik-Fachberichte","volume-title":"Proc. 2 nd European Workshop on Application and Theory of Petri Nets","author":"J. Martinez","year":"1981","unstructured":"Martinez, J., Silva, M.: A simple and fast algorithm to obtain all invariants of a generalized Petri net. In: Proc. 2 nd European Workshop on Application and Theory of Petri Nets, Bad Honnef, West Germany, September 1981. Informatik-Fachberichte, vol.\u00a052, Springer, Heidelberg (1981)"},{"issue":"9","key":"3_CR38","doi-asserted-by":"publisher","first-page":"1036","DOI":"10.1109\/TCOM.1976.1093424","volume":"24","author":"P.M. Merlin","year":"1976","unstructured":"Merlin, P.M., Farber, D.J.: Recoverability of communication protocols: Implications of a theoretical study. IEEE Transactions on Communications\u00a024(9), 1036\u20131043 (1976)","journal-title":"IEEE Transactions on Communications"},{"key":"3_CR39","unstructured":"Meyer, J.F., Movaghar, A., Sanders, W.H.: Stochastic activity networks: Structure, behavior, and application. In: Proc. Intern. Workshop on Timed Petri Nets, Torino,Italy, July 1985, pp. 106\u2013115 (1985)"},{"key":"3_CR40","unstructured":"Molloy, M.K.: On the Integration of Delay and Throughput Measures in Distributed Processing Models. PhD thesis, UCLA, Los Angeles, CA (1981)"},{"key":"3_CR41","volume-title":"Proc. Intern. Workshop on Petri Nets and Performance Models","year":"1987","unstructured":"Molloy, M.K., Murata, T., Vernon, M.K. (eds.): Proc. Intern. Workshop on Petri Nets and Performance Models, Madison, Wisconsin, August 1987. IEEE-CS Press, Los Alamitos (1987)"},{"issue":"4","key":"3_CR42","doi-asserted-by":"publisher","first-page":"541","DOI":"10.1109\/5.24143","volume":"77","author":"T. Murata","year":"1989","unstructured":"Murata, T.: Petri nets: properties, analysis, and applications. Proceedings of the IEEE\u00a077(4), 541\u2013580 (1989)","journal-title":"Proceedings of the IEEE"},{"key":"3_CR43","unstructured":"Natkin, S.: Les Reseaux de Petri Stochastiques et leur Application a l\u2019Evaluation des Systemes Informatiques. These de Docteur Ingegneur, CNAM, Paris, France (1980)"},{"key":"3_CR44","volume-title":"Matrix Geometric Solutions in Stochastic Models","author":"M.F. Neuts","year":"1981","unstructured":"Neuts, M.F.: Matrix Geometric Solutions in Stochastic Models. Johns Hopkins University Press, Baltimore (1981)"},{"issue":"9","key":"3_CR45","doi-asserted-by":"publisher","first-page":"718","DOI":"10.1109\/TC.1973.5009150","volume":"31","author":"J.D. Noe","year":"1973","unstructured":"Noe, J.D., Nutt, G.J.: Macro e-nets representation of parallel systems. IEEE Transactions on Computers\u00a031(9), 718\u2013727 (1973)","journal-title":"IEEE Transactions on Computers"},{"key":"3_CR46","volume-title":"Petri Net Theory and the Modeling of Systems","author":"J.L. Peterson","year":"1981","unstructured":"Peterson, J.L.: Petri Net Theory and the Modeling of Systems. Prentice-Hall, Englewood Cliffs (1981)"},{"key":"3_CR47","unstructured":"Petri, C.A.: Communication with automata. Technical Report RADC-TR-65-377, Rome Air Dev. Center, New York, NY (1966)"},{"key":"3_CR48","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-69968-9","volume-title":"Petri Nets: an Introduction","author":"W. Reisig","year":"1985","unstructured":"Reisig, W.: Petri Nets: an Introduction. Springer, Heidelberg (1985)"},{"issue":"1","key":"3_CR49","first-page":"28","volume":"14","author":"F.J.W. Symons","year":"1980","unstructured":"Symons, F.J.W.: Introduction to numerical Petri nets, a general graphical model of concurrent processing systems. Australian Telecommunications Research\u00a014(1), 28\u201333 (1980)","journal-title":"Australian Telecommunications Research"},{"key":"3_CR50","series-title":"Lecture Notes in Computer Science","volume-title":"Application and Theory of Petri Nets 1995","author":"M. Telek","year":"1995","unstructured":"Telek, M., Bobbio, A.: Markov regenerative stochastic petri nets with age type general transitions. In: DeMichelis, G., D\u00edaz, M. (eds.) ICATPN 1995. LNCS, vol.\u00a0935, Springer, Heidelberg (1995)"},{"key":"3_CR51","volume-title":"Matrix Iterative Analysis","author":"R.S. Varga","year":"1962","unstructured":"Varga, R.S.: Matrix Iterative Analysis. Prentice-Hall, Englewood Cliffs (1962)"}],"container-title":["Lecture Notes in Computer Science","Formal Methods for Performance Evaluation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-72522-0_3.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,19]],"date-time":"2020-11-19T05:34:20Z","timestamp":1605764060000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-72522-0_3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"ISBN":["9783540724827","9783540725220"],"references-count":51,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-72522-0_3","relation":{},"subject":[]}}