In the past, Petri net modeling was dominated by the evolution of the model in response to the needs of the applications and problems associated with analyzing the model. The result has been a diverse and confused set of models and notations which hinders new research. New applications are appearing that use the Petri net as the model of choice. By adopting some standards in notation and nomenclature the communication between research groups is enhanced. In addition, by completely dropping redundant models or models with minor variations, the community will be able to obtain a more focused view for further research.<>
{"title":"Petri net modeling-the past, the present, and the future","authors":"Michael K. Molloy","doi":"10.1109/PNPM.1989.68534","DOIUrl":"https://doi.org/10.1109/PNPM.1989.68534","url":null,"abstract":"In the past, Petri net modeling was dominated by the evolution of the model in response to the needs of the applications and problems associated with analyzing the model. The result has been a diverse and confused set of models and notations which hinders new research. New applications are appearing that use the Petri net as the model of choice. By adopting some standards in notation and nomenclature the communication between research groups is enhanced. In addition, by completely dropping redundant models or models with minor variations, the community will be able to obtain a more focused view for further research.<<ETX>>","PeriodicalId":366060,"journal":{"name":"Proceedings of the Third International Workshop on Petri Nets and Performance Models, PNPM89","volume":"1481 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":"132761507","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 VAXcluster is a closely coupled multicomputer system that consists of two or more VAX computers, one or more hierarchical storage controllers (HSCs), two or more disks, and a tar coupler. The Markov model of VAX cluster system availability suffers from state-space explosion as the number of VAX computers in the cluster increases. This has necessitated the use of approximate Markov models. The authors develop exact availability models of VAXcluster systems by means of stochastic Petri nets.<>
{"title":"Stochastic Petri net modeling of VAXcluster system availability","authors":"O. Ibe, A. Sathaye, R. C. Howe, Kishor S. Trivedi","doi":"10.1109/PNPM.1989.68545","DOIUrl":"https://doi.org/10.1109/PNPM.1989.68545","url":null,"abstract":"A VAXcluster is a closely coupled multicomputer system that consists of two or more VAX computers, one or more hierarchical storage controllers (HSCs), two or more disks, and a tar coupler. The Markov model of VAX cluster system availability suffers from state-space explosion as the number of VAX computers in the cluster increases. This has necessitated the use of approximate Markov models. The authors develop exact availability models of VAXcluster systems by means of stochastic Petri nets.<<ETX>>","PeriodicalId":366060,"journal":{"name":"Proceedings of the Third International Workshop on Petri Nets and Performance Models, PNPM89","volume":"18 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":"114309542","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 generalized stochastic Petri net (GSPN) performability model of a parallel and distributed computation is developed. The performance-related activities such as computations and communications are orders of magnitude faster than the component failure and repair activities. Based on the notion of time-scale decomposition, a hierarchy of two levels is defined. At the lower level the performance submodel describes the activities in the application program, while at the higher level the component failure and repair submodel for the underlying architecture defines the current configuration of processors and communication links available for the computation. These two submodels define the reward model needed for performability analysis. Two parallel FFT (fast Fourier transform) algorithms on a hypercube architecture are presented to illustrate the above modeling technique. A general and extended reliability model of the hypercube is also developed. Various performability measures are presented to demonstrate the importance of performability evaluation for mission-critical parallel applications.<>
{"title":"Performability analysis of parallel and distributed algorithms","authors":"H. Ammar, S. Islam, S. Deng","doi":"10.1109/PNPM.1989.68557","DOIUrl":"https://doi.org/10.1109/PNPM.1989.68557","url":null,"abstract":"A generalized stochastic Petri net (GSPN) performability model of a parallel and distributed computation is developed. The performance-related activities such as computations and communications are orders of magnitude faster than the component failure and repair activities. Based on the notion of time-scale decomposition, a hierarchy of two levels is defined. At the lower level the performance submodel describes the activities in the application program, while at the higher level the component failure and repair submodel for the underlying architecture defines the current configuration of processors and communication links available for the computation. These two submodels define the reward model needed for performability analysis. Two parallel FFT (fast Fourier transform) algorithms on a hypercube architecture are presented to illustrate the above modeling technique. A general and extended reliability model of the hypercube is also developed. Various performability measures are presented to demonstrate the importance of performability evaluation for mission-critical parallel applications.<<ETX>>","PeriodicalId":366060,"journal":{"name":"Proceedings of the Third International Workshop on Petri Nets and Performance Models, PNPM89","volume":"31 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":"131050419","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 type of Petri nets called generalized stochastic high-level Petri nets (GSHLPNs), combining the quantities of GSPNs and SHLPNs, is presented. The automated construction of compound continuous-time Markov chains (CTMCs) from GSHLPNs is also considered. A formalism for the description of compound markings allowing a symbolic firing of the net to obtain a compound CTMC with correct state group is derived. The construction of the compound CTMC requires an algorithm to test the equivalence of compound markings. I tis shown that, in the general case and for bounded number of rotation groups, the problem is polynomially equivalent to graph isomorphism, a problem whose classification in the NP world is currently open.<>
{"title":"Automated construction of compound Markov chains from generalized stochastic high-level Petri nets","authors":"J.A. Carasco","doi":"10.1109/PNPM.1989.68543","DOIUrl":"https://doi.org/10.1109/PNPM.1989.68543","url":null,"abstract":"A new type of Petri nets called generalized stochastic high-level Petri nets (GSHLPNs), combining the quantities of GSPNs and SHLPNs, is presented. The automated construction of compound continuous-time Markov chains (CTMCs) from GSHLPNs is also considered. A formalism for the description of compound markings allowing a symbolic firing of the net to obtain a compound CTMC with correct state group is derived. The construction of the compound CTMC requires an algorithm to test the equivalence of compound markings. I tis shown that, in the general case and for bounded number of rotation groups, the problem is polynomially equivalent to graph isomorphism, a problem whose classification in the NP world is currently open.<<ETX>>","PeriodicalId":366060,"journal":{"name":"Proceedings of the Third International Workshop on Petri Nets and Performance Models, PNPM89","volume":"224 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":"114746457","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 generalized stochastic Petri net can be analyzed by studying the reachability graph of feasible markings. An examination is made of the problem of eliminating vanishing states during the solution of a generalized stochastic Petri net. The asymptotic complexity of a matrix-based algorithm is shown to grow quadratically with the number of tangible states. A simpler graph-based algorithm that executes much more rapidly on typical models is examined. Some alternatives to elimination are discussed.<>
{"title":"The cost of eliminating vanishing markings from generalized stochastic Petri nets","authors":"A. Blakemore","doi":"10.1109/PNPM.1989.68542","DOIUrl":"https://doi.org/10.1109/PNPM.1989.68542","url":null,"abstract":"A generalized stochastic Petri net can be analyzed by studying the reachability graph of feasible markings. An examination is made of the problem of eliminating vanishing states during the solution of a generalized stochastic Petri net. The asymptotic complexity of a matrix-based algorithm is shown to grow quadratically with the number of tangible states. A simpler graph-based algorithm that executes much more rapidly on typical models is examined. Some alternatives to elimination are discussed.<<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":"129387741","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 computational complexity of reachability problems for Petri nets is analyzed and a new class of Petri nets is introduced. A net of the class is composed of subnets of state machines. Sufficient conditions on initial and target markings are obtained under which the reachability problem for the class is solvable in deterministic polynomial time. Also presented is an algorithm that examines in deterministic polynomial time whether a Petri net is in the class.<>
{"title":"A class of Petri nets and a reachability problem solvable in deterministic polynomial time","authors":"Keiko Nakamura, Kiyohiko Nakamura, A. Ichikawa","doi":"10.1109/PNPM.1989.68559","DOIUrl":"https://doi.org/10.1109/PNPM.1989.68559","url":null,"abstract":"The computational complexity of reachability problems for Petri nets is analyzed and a new class of Petri nets is introduced. A net of the class is composed of subnets of state machines. Sufficient conditions on initial and target markings are obtained under which the reachability problem for the class is solvable in deterministic polynomial time. Also presented is an algorithm that examines in deterministic polynomial time whether a Petri net is in the class.<<ETX>>","PeriodicalId":366060,"journal":{"name":"Proceedings of the Third International Workshop on Petri Nets and Performance Models, PNPM89","volume":"14 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":"123038236","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}
Exact results are presented for the average customer waiting and sojourn times in systems comprising a number of finite-capacity queues cyclically attended by several servers. The system behavior is described using generalized stochastic Petri nets (GSPN), and the performance indices are obtained numerically by means of GreatSPN, a software tool for the analysis of GSPN. The average waiting and sojourn times of customers in Markovian multiserver multiunique systems are computed exactly for the first time; they were previously estimated by other authors using approximate models.<>
{"title":"GSPN models of multiserver multiqueue systems","authors":"M. Marsan, S. Donatelli, F. Neri","doi":"10.1109/PNPM.1989.68536","DOIUrl":"https://doi.org/10.1109/PNPM.1989.68536","url":null,"abstract":"Exact results are presented for the average customer waiting and sojourn times in systems comprising a number of finite-capacity queues cyclically attended by several servers. The system behavior is described using generalized stochastic Petri nets (GSPN), and the performance indices are obtained numerically by means of GreatSPN, a software tool for the analysis of GSPN. The average waiting and sojourn times of customers in Markovian multiserver multiunique systems are computed exactly for the first time; they were previously estimated by other authors using approximate models.<<ETX>>","PeriodicalId":366060,"journal":{"name":"Proceedings of the Third International Workshop on Petri Nets and Performance Models, PNPM89","volume":"195 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":"133205777","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}
Several model classes for system evaluation exist and are capable of representing the kind of complex behavior exhibited by contemporary distributed computer architectures and computer-communication networks. However, a number of problems associated with the evaluation of large-scale systems arise because of the size and complexity of the stochastic process derived from the underlying net model, which serves as a 'base model' for subsequent solution of the measures in question. If this base model is constructed by standard means, e.g. it is identified with the marking behavior of the net, traditional methods of solution quickly become intractable for large systems, limiting their application to systems of only moderate complexity. This problem is addressed in the stochastic activity networks (SANs) by developing base model construction methods that account for symmetries in SAN structure and are tailored to the variable in question (e.g. response time, time to failure, etc.). It is found that such a technique can yield dramatic reductions in state-space size while preserving stochastic properties required for practical means of solution. This technique permits direct construction of a reduced base model, thus avoiding size limitations associated with more traditional approaches to model amplification.<>
{"title":"Reduced base model construction methods for stochastic activity networks","authors":"W. Sanders, J. F. Meyer","doi":"10.1109/PNPM.1989.68541","DOIUrl":"https://doi.org/10.1109/PNPM.1989.68541","url":null,"abstract":"Several model classes for system evaluation exist and are capable of representing the kind of complex behavior exhibited by contemporary distributed computer architectures and computer-communication networks. However, a number of problems associated with the evaluation of large-scale systems arise because of the size and complexity of the stochastic process derived from the underlying net model, which serves as a 'base model' for subsequent solution of the measures in question. If this base model is constructed by standard means, e.g. it is identified with the marking behavior of the net, traditional methods of solution quickly become intractable for large systems, limiting their application to systems of only moderate complexity. This problem is addressed in the stochastic activity networks (SANs) by developing base model construction methods that account for symmetries in SAN structure and are tailored to the variable in question (e.g. response time, time to failure, etc.). It is found that such a technique can yield dramatic reductions in state-space size while preserving stochastic properties required for practical means of solution. This technique permits direct construction of a reduced base model, thus avoiding size limitations associated with more traditional approaches to model amplification.<<ETX>>","PeriodicalId":366060,"journal":{"name":"Proceedings of the Third International Workshop on Petri Nets and Performance Models, PNPM89","volume":"207 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":"134111061","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}
Development of computational tools and techniques dealing with large-scale Petri nets will provide a firm foundation of Petri net theory. A discussion is presented of the computational complexity aspect of the legal firing sequence problem (LFS) and some related problems of Petri nets, each having applications to practical problems. Their NP-completeness and polynomial-time solvability are presented.<>
{"title":"Legal firing sequence and related problems of Petri nets","authors":"Toshimasa Watanabe, Y. Mizobata, K. Onaga","doi":"10.1109/PNPM.1989.68561","DOIUrl":"https://doi.org/10.1109/PNPM.1989.68561","url":null,"abstract":"Development of computational tools and techniques dealing with large-scale Petri nets will provide a firm foundation of Petri net theory. A discussion is presented of the computational complexity aspect of the legal firing sequence problem (LFS) and some related problems of Petri nets, each having applications to practical problems. Their NP-completeness and polynomial-time solvability are presented.<<ETX>>","PeriodicalId":366060,"journal":{"name":"Proceedings of the Third International Workshop on Petri Nets and Performance Models, PNPM89","volume":"26 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":"114298514","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}
Unbounded timed Petri nets are place-unbounded free-choice place/transition nets with exponentially distributed firing times associated with transitions of a net. In such nets the finite state space is generated by a finite set of linear equations. The regularity of this linear description can be used for a 'projection' (or 'folding') of the infinite state space into an equivalent finite representation that can be described by a finite set of nonlinear equilibrium equations. The solution of these equations determines the stationary probabilities of the states. Many performance measures can be obtained directly from this stationary solution. Such unbounded nets can eliminate the state explosion problem of some models by using unbounded but simple approximations to bounded but complex models.<>
{"title":"Performance evaluation using unbounded timed Petri nets","authors":"W. M. Zuberek","doi":"10.1109/PNPM.1989.68551","DOIUrl":"https://doi.org/10.1109/PNPM.1989.68551","url":null,"abstract":"Unbounded timed Petri nets are place-unbounded free-choice place/transition nets with exponentially distributed firing times associated with transitions of a net. In such nets the finite state space is generated by a finite set of linear equations. The regularity of this linear description can be used for a 'projection' (or 'folding') of the infinite state space into an equivalent finite representation that can be described by a finite set of nonlinear equilibrium equations. The solution of these equations determines the stationary probabilities of the states. Many performance measures can be obtained directly from this stationary solution. Such unbounded nets can eliminate the state explosion problem of some models by using unbounded but simple approximations to bounded but complex models.<<ETX>>","PeriodicalId":366060,"journal":{"name":"Proceedings of the Third International Workshop on Petri Nets and Performance Models, PNPM89","volume":"191 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":"121736710","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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