The problem of computing both upper and lower bounds for the steady-state performance of timed and stochastic Petri nets is studied. In particular, linear programming problems defined on the incidence matrix of underlying Petri net are used to compute bounds for the throughput of transitions for live and bounded nets with a unique possibility of steady-state behavior. These classes of nets are defined and their characteristics are studied. The bounds proposed here depend on the initial marking and the mean values of the delays but not on the probability distributions (thus including both the deterministic and the stochastic cases); moreover they can be also computed for non-ergodic models. Connections between results and techniques typical of qualitative and quantitative analysis of Petri models are stressed.<>
{"title":"Properties and steady-state performance bounds for Petri nets with unique repetitive firing count vector","authors":"J. Campos, G. Chiola, M. Suárez","doi":"10.1109/PNPM.1989.68554","DOIUrl":"https://doi.org/10.1109/PNPM.1989.68554","url":null,"abstract":"The problem of computing both upper and lower bounds for the steady-state performance of timed and stochastic Petri nets is studied. In particular, linear programming problems defined on the incidence matrix of underlying Petri net are used to compute bounds for the throughput of transitions for live and bounded nets with a unique possibility of steady-state behavior. These classes of nets are defined and their characteristics are studied. The bounds proposed here depend on the initial marking and the mean values of the delays but not on the probability distributions (thus including both the deterministic and the stochastic cases); moreover they can be also computed for non-ergodic models. Connections between results and techniques typical of qualitative and quantitative analysis of Petri models are stressed.<<ETX>>","PeriodicalId":366060,"journal":{"name":"Proceedings of the Third International Workshop on Petri Nets and Performance Models, PNPM89","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124562064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Methods are presented for computing tight bounds for steady-state token probabilities of a class of generalized stochastic net (GSPN) models. Such bounds also give a better estimate of the error produced when decompositions and aggregations are used to compute the various performance measures. First a method is described to compute the best lower and upper bounds for conditional token probabilities of a class of GSPN when only the subsequent is considered. The authors show that such bounds can be improved if additional information about other subnets is available. They extend the technique and outline an algorithm to compute the bounds for error due to aggregation and decomposition at the GSPN level. An example is presented to illustrate the technique and algorithm.<>
{"title":"On bounds for token probabilities in a class of generalized stochastic Petri nets","authors":"H. Ammar, S. Islam","doi":"10.1109/PNPM.1989.68555","DOIUrl":"https://doi.org/10.1109/PNPM.1989.68555","url":null,"abstract":"Methods are presented for computing tight bounds for steady-state token probabilities of a class of generalized stochastic net (GSPN) models. Such bounds also give a better estimate of the error produced when decompositions and aggregations are used to compute the various performance measures. First a method is described to compute the best lower and upper bounds for conditional token probabilities of a class of GSPN when only the subsequent is considered. The authors show that such bounds can be improved if additional information about other subnets is available. They extend the technique and outline an algorithm to compute the bounds for error due to aggregation and decomposition at the GSPN level. An example is presented to illustrate the technique and algorithm.<<ETX>>","PeriodicalId":366060,"journal":{"name":"Proceedings of the Third International Workshop on Petri Nets and Performance Models, PNPM89","volume":"1247 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120940066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A synthesis technique that relieves the complexity problems that can be encountered in verification of concurrent systems by avoiding verification is presented. With this technique, Petri nets are used for modeling concurrent systems. A temporal matrix is used to record relationship (concurrent, exclusive, serial, etc.) among processes and to detect rule violations as new generations are generated. A set of synthesis rules was developed for incrementally generating new processes without incurring logical incorrectness. The authors develop an algorithm to detect rule violations and to update the T-matrix. The complexity of the algorithm is polynomial and O(N/sup 3/), where N is the total number of pseudo-processes when the final system design is completed.<>
{"title":"The algorithm of a synthesis technique for concurrent systems","authors":"Y. Yaw, Fuin-Law, Wei-De Ju","doi":"10.1109/PNPM.1989.68560","DOIUrl":"https://doi.org/10.1109/PNPM.1989.68560","url":null,"abstract":"A synthesis technique that relieves the complexity problems that can be encountered in verification of concurrent systems by avoiding verification is presented. With this technique, Petri nets are used for modeling concurrent systems. A temporal matrix is used to record relationship (concurrent, exclusive, serial, etc.) among processes and to detect rule violations as new generations are generated. A set of synthesis rules was developed for incrementally generating new processes without incurring logical incorrectness. The authors develop an algorithm to detect rule violations and to update the T-matrix. The complexity of the algorithm is polynomial and O(N/sup 3/), where N is the total number of pseudo-processes when the final system design is completed.<<ETX>>","PeriodicalId":366060,"journal":{"name":"Proceedings of the Third International Workshop on Petri Nets and Performance Models, PNPM89","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116945523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The modeling power of the extended-time Petri net is shown. Among its salient features are that there is a firing interval associated with each transition, the probability density function is distributed over the firing interval, and any kind of probability density function can be considered. This model allows a qualitative analysis (considering time constraints) and a quantitative analysis. Particular consideration is given to the modeling of a one-way data transfer protocol (such as the one used in the class 0 transport protocol). This protocol, the Petri net model of which has an unbounded reachability tree, cannot be analyzed with any of the different types of stochastic Petri nets because these models are based on an underlying PN model, the reachability tree of which must be bounded.<>
{"title":"On the pertinence of the extended time Petri net model for analyzing communication activities","authors":"G. Juanole, J. L. Roux","doi":"10.1109/PNPM.1989.68556","DOIUrl":"https://doi.org/10.1109/PNPM.1989.68556","url":null,"abstract":"The modeling power of the extended-time Petri net is shown. Among its salient features are that there is a firing interval associated with each transition, the probability density function is distributed over the firing interval, and any kind of probability density function can be considered. This model allows a qualitative analysis (considering time constraints) and a quantitative analysis. Particular consideration is given to the modeling of a one-way data transfer protocol (such as the one used in the class 0 transport protocol). This protocol, the Petri net model of which has an unbounded reachability tree, cannot be analyzed with any of the different types of stochastic Petri nets because these models are based on an underlying PN model, the reachability tree of which must be bounded.<<ETX>>","PeriodicalId":366060,"journal":{"name":"Proceedings of the Third International Workshop on Petri Nets and Performance Models, PNPM89","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129490183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A new solution is presented for the steady-state probability computing of closed synchronized queuing networks. A closed synchronized queuing network is a particular Markov stochastic Petri net (bounded and monovaluated Petri net with a strongly connected reachability graph and constant firing rates independent of markings). The authors show that the steady-state probability distribution can be expressed using matrix products. The results generalize the Gordon-Newell theorem. The solution is similar to the Gordon-Newell product form solution using a matrix and vectors instead of scalars. A prototype solver developed from the preceding result is presented.<>
{"title":"Matrix product form solution for closed synchronized queuing networks","authors":"G. Florin, S. Natkin","doi":"10.1109/PNPM.1989.68537","DOIUrl":"https://doi.org/10.1109/PNPM.1989.68537","url":null,"abstract":"A new solution is presented for the steady-state probability computing of closed synchronized queuing networks. A closed synchronized queuing network is a particular Markov stochastic Petri net (bounded and monovaluated Petri net with a strongly connected reachability graph and constant firing rates independent of markings). The authors show that the steady-state probability distribution can be expressed using matrix products. The results generalize the Gordon-Newell theorem. The solution is similar to the Gordon-Newell product form solution using a matrix and vectors instead of scalars. A prototype solver developed from the preceding result is presented.<<ETX>>","PeriodicalId":366060,"journal":{"name":"Proceedings of the Third International Workshop on Petri Nets and Performance Models, PNPM89","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131567171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A combining of GSPNs (generalized stochastic Petri nets) and PERT networks is used in order to reduce the computational complexity of performance evaluation of concurrent processes modeled by GSPNs. The authors propose the following methodology. First, for PERT networks, an algorithm with good accuracy and computational complexity criteria should be formulated. Second, for safe GSPNs with acyclic behavior, a modification of the algorithm should be created. Third, another algorithm for safe GSPNs with cyclic behavior should be constructed.<>
{"title":"Combining generalized stochastic Petri nets and PERT networks for the performance evaluation of concurrent processes","authors":"J. Magott, Kamil Skudlarski","doi":"10.1109/PNPM.1989.68558","DOIUrl":"https://doi.org/10.1109/PNPM.1989.68558","url":null,"abstract":"A combining of GSPNs (generalized stochastic Petri nets) and PERT networks is used in order to reduce the computational complexity of performance evaluation of concurrent processes modeled by GSPNs. The authors propose the following methodology. First, for PERT networks, an algorithm with good accuracy and computational complexity criteria should be formulated. Second, for safe GSPNs with acyclic behavior, a modification of the algorithm should be created. Third, another algorithm for safe GSPNs with cyclic behavior should be constructed.<<ETX>>","PeriodicalId":366060,"journal":{"name":"Proceedings of the Third International Workshop on Petri Nets and Performance Models, PNPM89","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114197576","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A novel approach to the application of an interval-labeled net model in logic simulation with timing among concurrent processes is introduced. By means of the model, logic circuit properties involving timing information can be specified and simulated in a multiprocessor-based environment using the token-passing algorithm. A logic simulator with timing information with a structure based on this approach is proposed.<>
{"title":"Logic simulation with interval-labelled net model","authors":"P. P. K. Chiu, P. Cheung","doi":"10.1109/PNPM.1989.68547","DOIUrl":"https://doi.org/10.1109/PNPM.1989.68547","url":null,"abstract":"A novel approach to the application of an interval-labeled net model in logic simulation with timing among concurrent processes is introduced. By means of the model, logic circuit properties involving timing information can be specified and simulated in a multiprocessor-based environment using the token-passing algorithm. A logic simulator with timing information with a structure based on this approach is proposed.<<ETX>>","PeriodicalId":366060,"journal":{"name":"Proceedings of the Third International Workshop on Petri Nets and Performance Models, PNPM89","volume":"97 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117203978","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Colored Petri nets (CPN) are useful for the development of very compact and easy to understand models of systems with interacting concurrent components. A CPN model can be used for a qualitative analysis of the modeled system; when timing is also added, a quantitative analysis can be done. Unfortunately, the analysis can be prevented by excessive size of the reachability graph (RG) of the net, which can grow exponentially as a function of the number of places and the cardinality of color domains. A method that automatically exploits the symmetries intrinsic in the model reducing the RG size is presented: it can be applied to a subclass of CPNs called regular nets (RN). Some nontrivial examples are presented to demonstrate that the automatically achieved reductions are comparable to those devised for these systems by thoroughly studying their behavior.<>
{"title":"Colored GSPN models and automatic symmetry detection","authors":"G. Chiola, G. Franceschinis","doi":"10.1109/PNPM.1989.68539","DOIUrl":"https://doi.org/10.1109/PNPM.1989.68539","url":null,"abstract":"Colored Petri nets (CPN) are useful for the development of very compact and easy to understand models of systems with interacting concurrent components. A CPN model can be used for a qualitative analysis of the modeled system; when timing is also added, a quantitative analysis can be done. Unfortunately, the analysis can be prevented by excessive size of the reachability graph (RG) of the net, which can grow exponentially as a function of the number of places and the cardinality of color domains. A method that automatically exploits the symmetries intrinsic in the model reducing the RG size is presented: it can be applied to a subclass of CPNs called regular nets (RN). Some nontrivial examples are presented to demonstrate that the automatically achieved reductions are comparable to those devised for these systems by thoroughly studying their behavior.<<ETX>>","PeriodicalId":366060,"journal":{"name":"Proceedings of the Third International Workshop on Petri Nets and Performance Models, PNPM89","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125556615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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