Pub Date : 1991-12-02DOI: 10.1109/PNPM.1991.238776
Zhi-Wu Xu, O. Vel
The authors present a graph model based on Petri nets that can be used as a software development tool for parallel computational programs written in the Occam language. In parallel computing the cooperation aspect of concurrency is emphasized, rather than the competitive aspect of multiple processes found in operating system applications. In developing and debugging a parallel computational program, users often want to ensure that their program will terminate (that is, it stops in finite time) and be determinate (that is, the same input data always produce the same result). Using the Petri net graph model, termination and determinacy can be mathematically defined, and algorithms for detecting these properties developed. In fact, the graph model defines an operational semantics for a non-trivial subset of Occam, and can be used as a pedagogical aid as well as a tool for developing and synthesizing Occam programs in parallel computing applications.<>
{"title":"Petri net modelling of Occam programs for detecting indeterminacy, non-termination and deadlock anomalies","authors":"Zhi-Wu Xu, O. Vel","doi":"10.1109/PNPM.1991.238776","DOIUrl":"https://doi.org/10.1109/PNPM.1991.238776","url":null,"abstract":"The authors present a graph model based on Petri nets that can be used as a software development tool for parallel computational programs written in the Occam language. In parallel computing the cooperation aspect of concurrency is emphasized, rather than the competitive aspect of multiple processes found in operating system applications. In developing and debugging a parallel computational program, users often want to ensure that their program will terminate (that is, it stops in finite time) and be determinate (that is, the same input data always produce the same result). Using the Petri net graph model, termination and determinacy can be mathematically defined, and algorithms for detecting these properties developed. In fact, the graph model defines an operational semantics for a non-trivial subset of Occam, and can be used as a pedagogical aid as well as a tool for developing and synthesizing Occam programs in parallel computing applications.<<ETX>>","PeriodicalId":137470,"journal":{"name":"Proceedings of the Fourth International Workshop on Petri Nets and Performance Models PNPM91","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1991-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130018997","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}
Pub Date : 1991-12-02DOI: 10.1109/PNPM.1991.238800
G. Florin, C. Fraize, S. Natkin
Probabilistic validation is a new approach to deal with large state transitions systems. The user's need is to prove that, for a given period of operations, that a given assertion on the reached states is true with a sufficient level of probability. The system to be validated is modeled by a stochastic Petri net. The analysis relies on a partial exploration of the reachability set and tries to reach as quickly as possible critical states (states in which the assertion is not verified). An exact linear program solution allows to 'travel' through the graph. The main goal of the paper is to present the principles of this searching algorithm.<>
{"title":"Searching best paths to worst states","authors":"G. Florin, C. Fraize, S. Natkin","doi":"10.1109/PNPM.1991.238800","DOIUrl":"https://doi.org/10.1109/PNPM.1991.238800","url":null,"abstract":"Probabilistic validation is a new approach to deal with large state transitions systems. The user's need is to prove that, for a given period of operations, that a given assertion on the reached states is true with a sufficient level of probability. The system to be validated is modeled by a stochastic Petri net. The analysis relies on a partial exploration of the reachability set and tries to reach as quickly as possible critical states (states in which the assertion is not verified). An exact linear program solution allows to 'travel' through the graph. The main goal of the paper is to present the principles of this searching algorithm.<<ETX>>","PeriodicalId":137470,"journal":{"name":"Proceedings of the Fourth International Workshop on Petri Nets and Performance Models PNPM91","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1991-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122499712","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}
Pub Date : 1991-12-02DOI: 10.1109/PNPM.1991.238784
G. Juanole, Y. Atamna
The ability of the stochastic timed Petri net model for dealing with a great variety of firing time distributions is presented. The distributions can be: continuous (exponential or uniform); discrete (including the particular case of a deterministic distribution with a zero firing time (immediate transition) or a non zero firing time); mixed. This ability is based on a method of tractable computation whatever the distribution (in particular the difficult cases of the discrete and mixed distributions), for obtaining a randomized state graph (which represents the dynamic behaviour of the system being modelled). Applications to queueing systems are considered: the queue M/G/1; the queue M/G/1/K. A general method for analysing queueing systems, which is based on an interpretation of the randomized state graph, is presented.<>
{"title":"Dealing with arbitrary time distributions with the stochastic timed Petri net model-application to queueing systems","authors":"G. Juanole, Y. Atamna","doi":"10.1109/PNPM.1991.238784","DOIUrl":"https://doi.org/10.1109/PNPM.1991.238784","url":null,"abstract":"The ability of the stochastic timed Petri net model for dealing with a great variety of firing time distributions is presented. The distributions can be: continuous (exponential or uniform); discrete (including the particular case of a deterministic distribution with a zero firing time (immediate transition) or a non zero firing time); mixed. This ability is based on a method of tractable computation whatever the distribution (in particular the difficult cases of the discrete and mixed distributions), for obtaining a randomized state graph (which represents the dynamic behaviour of the system being modelled). Applications to queueing systems are considered: the queue M/G/1; the queue M/G/1/K. A general method for analysing queueing systems, which is based on an interpretation of the randomized state graph, is presented.<<ETX>>","PeriodicalId":137470,"journal":{"name":"Proceedings of the Fourth International Workshop on Petri Nets and Performance Models PNPM91","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1991-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122724358","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}
Pub Date : 1991-12-02DOI: 10.1109/PNPM.1991.238803
C. Lindemann
Introduces an algorithm for calculating steady-state solutions of DSPN models. The described method employs the randomization technique enhanced by a stable calculation of Poisson probabilities. A complete re-design and re-implementation of the appropriate components implemented in the version 1.4 of the software package GreatSPN has lead to significant savings in both computation time and memory space. These benefits are illustrated by DSPN models taken from the literature. The author considers DSPN models for an E/sub r//D/1/K queueing system and a fault-tolerant clocking system. These examples show that the model solutions are calculated with significantly less computational effort and a better error control by the algorithm described than by the method implemented in the version 1.4 of the software package GreatSPN.<>
{"title":"An improved numerical algorithm for calculating steady-state solutions of deterministic and stochastic Petri net models","authors":"C. Lindemann","doi":"10.1109/PNPM.1991.238803","DOIUrl":"https://doi.org/10.1109/PNPM.1991.238803","url":null,"abstract":"Introduces an algorithm for calculating steady-state solutions of DSPN models. The described method employs the randomization technique enhanced by a stable calculation of Poisson probabilities. A complete re-design and re-implementation of the appropriate components implemented in the version 1.4 of the software package GreatSPN has lead to significant savings in both computation time and memory space. These benefits are illustrated by DSPN models taken from the literature. The author considers DSPN models for an E/sub r//D/1/K queueing system and a fault-tolerant clocking system. These examples show that the model solutions are calculated with significantly less computational effort and a better error control by the algorithm described than by the method implemented in the version 1.4 of the software package GreatSPN.<<ETX>>","PeriodicalId":137470,"journal":{"name":"Proceedings of the Fourth International Workshop on Petri Nets and Performance Models PNPM91","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1991-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133990648","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}
Pub Date : 1991-12-02DOI: 10.1109/PNPM.1991.238779
J. Magott, Kamil Skudlarski
Stochastic safe marked graphs with exponentially distributed firing time of timed transitions are investigated. An approximate method for estimating the mean cycle time is proposed. The method gives a value that tends to be greater than the exact one. It is of polynomial computational complexity. The estimate is much better than the best PERT network upper bound for networks with exponentially distributed durations of activities. The method is compared with the best upper bound for mean cycle time of stochastic marked graphs. The reasons of error of the above two methods are different. Therefore, one of the methods completes the other, and for given stochastic safe marked graphs one can choose the better one from the two estimates. The approximate method can be used for estimating the mean time of stochastic safe marked graphs with NBUE distributed firing times.<>
{"title":"Estimating the mean cycle time for stochastic safe marked graphs","authors":"J. Magott, Kamil Skudlarski","doi":"10.1109/PNPM.1991.238779","DOIUrl":"https://doi.org/10.1109/PNPM.1991.238779","url":null,"abstract":"Stochastic safe marked graphs with exponentially distributed firing time of timed transitions are investigated. An approximate method for estimating the mean cycle time is proposed. The method gives a value that tends to be greater than the exact one. It is of polynomial computational complexity. The estimate is much better than the best PERT network upper bound for networks with exponentially distributed durations of activities. The method is compared with the best upper bound for mean cycle time of stochastic marked graphs. The reasons of error of the above two methods are different. Therefore, one of the methods completes the other, and for given stochastic safe marked graphs one can choose the better one from the two estimates. The approximate method can be used for estimating the mean time of stochastic safe marked graphs with NBUE distributed firing times.<<ETX>>","PeriodicalId":137470,"journal":{"name":"Proceedings of the Fourth International Workshop on Petri Nets and Performance Models PNPM91","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1991-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114463046","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}
Pub Date : 1991-12-02DOI: 10.1109/PNPM.1991.238780
G. Ciardo, Kishor S. Trivedi
The authors present a decomposition approach for the solution of large stochastic Petri nets (SPNs). The overall model consists of a set of submodels whose interactions are described by an import graph. Each node of the graph corresponds to a parametrized SPN submodel and an arc from submodel A to submodel B corresponds to a parameter value that B must receive from A. The quantities exchanged between submodels are based on only three primitives. The import graph is normally cyclic, so the solution method is based on fixed point iteration. The authors apply their technique to the analysis of a flexible manufacturing system.<>
{"title":"A decomposition approach for stochastic Petri net models","authors":"G. Ciardo, Kishor S. Trivedi","doi":"10.1109/PNPM.1991.238780","DOIUrl":"https://doi.org/10.1109/PNPM.1991.238780","url":null,"abstract":"The authors present a decomposition approach for the solution of large stochastic Petri nets (SPNs). The overall model consists of a set of submodels whose interactions are described by an import graph. Each node of the graph corresponds to a parametrized SPN submodel and an arc from submodel A to submodel B corresponds to a parameter value that B must receive from A. The quantities exchanged between submodels are based on only three primitives. The import graph is normally cyclic, so the solution method is based on fixed point iteration. The authors apply their technique to the analysis of a flexible manufacturing system.<<ETX>>","PeriodicalId":137470,"journal":{"name":"Proceedings of the Fourth International Workshop on Petri Nets and Performance Models PNPM91","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1991-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132555502","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}
Pub Date : 1991-12-02DOI: 10.1109/PNPM.1991.238799
K. Onaga, Manuel Silva, Toshimasa Watanabe
Introduces a Petri net based perspective to periodic schedules. These are classified, according to the time interpretation in multiple-server semantics and/or transitions firing periodicity constraints, into strict and general periodic schedules. Using a net transformation rule, the computation of the general schedule class can be done through techniques for the strict subclass. A necessary and sufficient condition for the feasibility of a strict periodic schedule is given. Estimating the truncation error at initial firing time epoch tau /sub 1/ allows to get linear systems of inequalities as necessary conditions for a schedule to be feasible. An linear programming (LP) based heuristic approach is proposed to deal with the computation of 'optimum' (i.e. minimal time) strict periodic schedules under the single-server semantics.<>
{"title":"On periodic schedules for deterministically timed Petri net systems","authors":"K. Onaga, Manuel Silva, Toshimasa Watanabe","doi":"10.1109/PNPM.1991.238799","DOIUrl":"https://doi.org/10.1109/PNPM.1991.238799","url":null,"abstract":"Introduces a Petri net based perspective to periodic schedules. These are classified, according to the time interpretation in multiple-server semantics and/or transitions firing periodicity constraints, into strict and general periodic schedules. Using a net transformation rule, the computation of the general schedule class can be done through techniques for the strict subclass. A necessary and sufficient condition for the feasibility of a strict periodic schedule is given. Estimating the truncation error at initial firing time epoch tau /sub 1/ allows to get linear systems of inequalities as necessary conditions for a schedule to be feasible. An linear programming (LP) based heuristic approach is proposed to deal with the computation of 'optimum' (i.e. minimal time) strict periodic schedules under the single-server semantics.<<ETX>>","PeriodicalId":137470,"journal":{"name":"Proceedings of the Fourth International Workshop on Petri Nets and Performance Models PNPM91","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1991-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115624357","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}
Pub Date : 1991-12-02DOI: 10.1109/PNPM.1991.238788
J. Campos, Beatriz Sánchez, M. Suárez
Addresses the computation of lower bounds for the steady-state throughput of stochastic Petri nets with immediate and exponentially distributed service times of transitions. The authors try to deeply bridge stochastic Petri net theory to untimed Petri net and queueing networks theories. Previous results for general service time distributions are improved for the case of Markovian nets by considering some pessimistic transformation rules operating locally on the net structure, its initial marking, and stochastic interpretation. Special interest have the obtained results for the case of live and bounded free choice nets and live marked graphs systems.<>
{"title":"Throughput lower bounds for Markovian Petri nets: transformation techniques","authors":"J. Campos, Beatriz Sánchez, M. Suárez","doi":"10.1109/PNPM.1991.238788","DOIUrl":"https://doi.org/10.1109/PNPM.1991.238788","url":null,"abstract":"Addresses the computation of lower bounds for the steady-state throughput of stochastic Petri nets with immediate and exponentially distributed service times of transitions. The authors try to deeply bridge stochastic Petri net theory to untimed Petri net and queueing networks theories. Previous results for general service time distributions are improved for the case of Markovian nets by considering some pessimistic transformation rules operating locally on the net structure, its initial marking, and stochastic interpretation. Special interest have the obtained results for the case of live and bounded free choice nets and live marked graphs systems.<<ETX>>","PeriodicalId":137470,"journal":{"name":"Proceedings of the Fourth International Workshop on Petri Nets and Performance Models PNPM91","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1991-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114733433","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}
Pub Date : 1991-12-02DOI: 10.1109/PNPM.1991.238783
G. Klas, Reinhard Matuschka
A new hierarchical evaluation procedure for generalized stochastic Petri nets (GSPN) is being presented. It is based on extensions of flow equivalent aggregation (FEA). At every level of hierarchy, subnets are approximated by substitute networks. As criterion for the similarity of the networks, the subnetwork time distribution (STD) is used which is the sojourn time distribution of a token X in a subnet conditioned on the token distribution at the epoch of arrival of X and the context into which the net is embedded for determining the STD. The computation of a substitute network's type and parameters is outlined. The performance of this technique called FEAD (FEA based on subnetwork time distribution) is discussed by means of examples.<>
提出了一种新的广义随机Petri网(GSPN)分级评价方法。它是基于流动等效聚集(FEA)的扩展。在每一层次结构中，子网都是由替代网络近似表示的。采用子网时间分布(STD)作为判定网络相似性的标准，即令牌X在子网中的停留时间分布，该时间分布取决于令牌X到达时间点的分布和网络所处的环境，并给出了替代网络类型和参数的计算方法。通过实例讨论了基于子网时间分布的FEAD (FEA based on subnetwork time distribution)技术的性能
{"title":"Subnetwork time distributions as a means for multilevel evaluation of generalized stochastic Petri nets","authors":"G. Klas, Reinhard Matuschka","doi":"10.1109/PNPM.1991.238783","DOIUrl":"https://doi.org/10.1109/PNPM.1991.238783","url":null,"abstract":"A new hierarchical evaluation procedure for generalized stochastic Petri nets (GSPN) is being presented. It is based on extensions of flow equivalent aggregation (FEA). At every level of hierarchy, subnets are approximated by substitute networks. As criterion for the similarity of the networks, the subnetwork time distribution (STD) is used which is the sojourn time distribution of a token X in a subnet conditioned on the token distribution at the epoch of arrival of X and the context into which the net is embedded for determining the STD. The computation of a substitute network's type and parameters is outlined. The performance of this technique called FEAD (FEA based on subnetwork time distribution) is discussed by means of examples.<<ETX>>","PeriodicalId":137470,"journal":{"name":"Proceedings of the Fourth International Workshop on Petri Nets and Performance Models PNPM91","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1991-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129548822","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}
Pub Date : 1991-12-02DOI: 10.1109/PNPM.1991.238775
Takashi Kobayashi, K. Kurihara
A new method is described for analyzing scheduling policy for interference avoidance. The traditional queuing theory assuming a first-come-first-served policy is not suitable for analyzing scheduling policy. Stochastic Petri net (SPN) is suitable for analyzing scheduling policy, because with it job arrival states, resource assignment states, and job flow due to these states can be modeled. However, if the scheduling logic is described in detail with SPN, a combinatorial explosion is soon encountered. Therefore, a new method is proposed to cut down the size of SPN model and to analyze the control policy of a magnetic tape library.<>
提出了一种新的抗干扰调度策略分析方法。传统的排队理论假设先到先得的策略不适合分析调度策略。随机Petri网(Stochastic Petri net, SPN)适用于调度策略分析，因为它可以对作业到达状态、资源分配状态以及由这些状态引起的作业流进行建模。然而，如果用SPN详细描述调度逻辑，很快就会遇到组合爆炸。为此，提出了一种减小SPN模型大小和分析磁带库控制策略的新方法。
{"title":"Performance model of interference avoidance policy using stochastic Petri nets","authors":"Takashi Kobayashi, K. Kurihara","doi":"10.1109/PNPM.1991.238775","DOIUrl":"https://doi.org/10.1109/PNPM.1991.238775","url":null,"abstract":"A new method is described for analyzing scheduling policy for interference avoidance. The traditional queuing theory assuming a first-come-first-served policy is not suitable for analyzing scheduling policy. Stochastic Petri net (SPN) is suitable for analyzing scheduling policy, because with it job arrival states, resource assignment states, and job flow due to these states can be modeled. However, if the scheduling logic is described in detail with SPN, a combinatorial explosion is soon encountered. Therefore, a new method is proposed to cut down the size of SPN model and to analyze the control policy of a magnetic tape library.<<ETX>>","PeriodicalId":137470,"journal":{"name":"Proceedings of the Fourth International Workshop on Petri Nets and Performance Models PNPM91","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1991-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134106759","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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