Pub Date : 1991-12-02DOI: 10.1109/PNPM.1991.238778
S. Rajsbaum
Stochastic marked graphs (SMGs) are marked graphs in which transmission delays of tokens, and firing durations are random variables. A technique is presented to study the performance of SMGs. The main performance measure is the rate of computation, i.e., the average number of firings of a vertex, per time unit. The effect of the topology and the probability of the random variables on the rate is investigated. For deterministic random variables, the rate is maximized, while for exponential random variables the rate is minimized (among a natural class of distributions). For random variables with exponential distribution several bounds on the rate are provided. The bounds depend on the degrees of the vertices and on the average number of tokens in a cycle, but not on the number of vertices itself. In particular, it is shown that the rate is at least the optimal (deterministic) rate, divided by a logarithmic factor of the vertex degrees. Thus, for some graphs the rate does not diminish below a bound, regardless of the number of vertices.<>
{"title":"Stochastic marked graphs","authors":"S. Rajsbaum","doi":"10.1109/PNPM.1991.238778","DOIUrl":"https://doi.org/10.1109/PNPM.1991.238778","url":null,"abstract":"Stochastic marked graphs (SMGs) are marked graphs in which transmission delays of tokens, and firing durations are random variables. A technique is presented to study the performance of SMGs. The main performance measure is the rate of computation, i.e., the average number of firings of a vertex, per time unit. The effect of the topology and the probability of the random variables on the rate is investigated. For deterministic random variables, the rate is maximized, while for exponential random variables the rate is minimized (among a natural class of distributions). For random variables with exponential distribution several bounds on the rate are provided. The bounds depend on the degrees of the vertices and on the average number of tokens in a cycle, but not on the number of vertices itself. In particular, it is shown that the rate is at least the optimal (deterministic) rate, divided by a logarithmic factor of the vertex degrees. Thus, for some graphs the rate does not diminish below a bound, regardless of the number of vertices.<<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":"121777355","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.1991.238773
G. Chiola, G. Franceschinis
Well-formed coloured Petri nets (WN) have been recently defined as a new formalism that allows the automatic identification of model symmetries by means of the construction of the symbolic reachability graph (SRG). The authors define a sufficient structural condition for the simplification of the colour structure of the net that can exploit symmetries not detectable with the SRG. The simplified WNs may have reduced SRG and in any case are easier to analyze by means of the SRG technique.<>
{"title":"A structural colour simplification in well-formed coloured nets","authors":"G. Chiola, G. Franceschinis","doi":"10.1109/PNPM.1991.238773","DOIUrl":"https://doi.org/10.1109/PNPM.1991.238773","url":null,"abstract":"Well-formed coloured Petri nets (WN) have been recently defined as a new formalism that allows the automatic identification of model symmetries by means of the construction of the symbolic reachability graph (SRG). The authors define a sufficient structural condition for the simplification of the colour structure of the net that can exploit symmetries not detectable with the SRG. The simplified WNs may have reduced SRG and in any case are easier to analyze by means of the SRG technique.<<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":"126260235","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.1991.238781
C. Woodside, Yao Li
Performance analysis of Petri net models is limited by state explosion in the underlying Markovian model. To overcome this problem, an iterative approximate technique is obtained, using a number of auxiliary models, each of much lower state complexity. It is demonstrated on a substantial model which represents a parallel implementation of two layers of protocols for data communications. The model represents ten separate software tasks and their interactions via rendezvous, and is based on a testbed implementation in the laboratory. Submodels can be constructed in various ways, and this is illustrated with four different decompositions. Their state space complexity, solution time and solution accuracy are evaluated.<>
{"title":"Performance Petri net analysis of communications protocol software by delay-equivalent aggregation","authors":"C. Woodside, Yao Li","doi":"10.1109/PNPM.1991.238781","DOIUrl":"https://doi.org/10.1109/PNPM.1991.238781","url":null,"abstract":"Performance analysis of Petri net models is limited by state explosion in the underlying Markovian model. To overcome this problem, an iterative approximate technique is obtained, using a number of auxiliary models, each of much lower state complexity. It is demonstrated on a substantial model which represents a parallel implementation of two layers of protocols for data communications. The model represents ten separate software tasks and their interactions via rendezvous, and is based on a testbed implementation in the laboratory. Submodels can be constructed in various ways, and this is illustrated with four different decompositions. Their state space complexity, solution time and solution accuracy are evaluated.<<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":"128309426","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.1991.238792
S. Caselli, G. Conte
Describes a GSPN-based approach to performance evaluation of parallel MIMD architectures with mesh interconnection schemes. The analysis considers regular computational structures in which data exchange and inter-process synchronization require communication only among processors that are physically connected. The effectiveness of the modeling technique for this class of architectures is shown through examples considering both the effect of the interaction policies among processes and the benefit of multitrasking on the global efficiency of the architecture.<>
{"title":"GSPN models of concurrent architectures with mesh topology","authors":"S. Caselli, G. Conte","doi":"10.1109/PNPM.1991.238792","DOIUrl":"https://doi.org/10.1109/PNPM.1991.238792","url":null,"abstract":"Describes a GSPN-based approach to performance evaluation of parallel MIMD architectures with mesh interconnection schemes. The analysis considers regular computational structures in which data exchange and inter-process synchronization require communication only among processors that are physically connected. The effectiveness of the modeling technique for this class of architectures is shown through examples considering both the effect of the interaction policies among processes and the benefit of multitrasking on the global efficiency of the architecture.<<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":"131100194","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.1991.238786
M. Marsan, S. Donatelli, F. Neri, U. Rubino
The GSPN modeling technique can be used in may different ways. It allows the simple development of detailed, easy-to-understand models of complex systems, that typically are very costly to solve due to their exceedingly large state spaces. However, GSPNs can also be used to develop compact, abstract models with much smaller state spaces at the expense of a greater modeling effort. The authors use an example to show how a compact GSPN model can be developed by progressively abstracting the description of the system behaviour, starting with a very simple and detailed model. The chosen example is a multiserver random polling system.<>
{"title":"On the construction of abstract GSPNs: an exercise in modeling","authors":"M. Marsan, S. Donatelli, F. Neri, U. Rubino","doi":"10.1109/PNPM.1991.238786","DOIUrl":"https://doi.org/10.1109/PNPM.1991.238786","url":null,"abstract":"The GSPN modeling technique can be used in may different ways. It allows the simple development of detailed, easy-to-understand models of complex systems, that typically are very costly to solve due to their exceedingly large state spaces. However, GSPNs can also be used to develop compact, abstract models with much smaller state spaces at the expense of a greater modeling effort. The authors use an example to show how a compact GSPN model can be developed by progressively abstracting the description of the system behaviour, starting with a very simple and detailed model. The chosen example is a multiserver random polling 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":"126412034","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.1991.238798
O. Botti, F. Cindio
Starting from the Petri net model of Occam which uses 1-safe PT nets, the paper develops, on the top of it, a timed net model, using Generalized Stochastic Petri Nets (GSPN), to allow a performance analysis of Occam programs. As an example, the authors carry out the comparison of different placements of an Occam program over a given set of distributed processors.<>
{"title":"From basic to timed net models of Occam: an application to program placement","authors":"O. Botti, F. Cindio","doi":"10.1109/PNPM.1991.238798","DOIUrl":"https://doi.org/10.1109/PNPM.1991.238798","url":null,"abstract":"Starting from the Petri net model of Occam which uses 1-safe PT nets, the paper develops, on the top of it, a timed net model, using Generalized Stochastic Petri Nets (GSPN), to allow a performance analysis of Occam programs. As an example, the authors carry out the comparison of different placements of an Occam program over a given set of distributed processors.<<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":"131854783","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.1991.238790
B. Haverkort
Addresses the problem of calculating performability measures from performability models of fault-tolerant computer systems. Since these systems tend to be large and complex, the corresponding performability models will in general also be large and complex. To alleviate the largeness problem to some extent the author uses generalized stochastic Petri nets to describe the models. Still however, many models cannot be solved with the current numerical techniques, although they are conveniently and often compactly described. In the paper the author discusses two heuristic state space truncation techniques that allow us to obtain very good approximations while only assessing a few percent of the overall state space. He gives examples of the usage, but also theoretical evidence in the correctness of the employed truncation techniques. He furthermore shows that GSPNs are very suitable for implementing (describing) the proposed truncation techniques.<>
{"title":"Approximate performability analysis using generalized stochastic Petri nets","authors":"B. Haverkort","doi":"10.1109/PNPM.1991.238790","DOIUrl":"https://doi.org/10.1109/PNPM.1991.238790","url":null,"abstract":"Addresses the problem of calculating performability measures from performability models of fault-tolerant computer systems. Since these systems tend to be large and complex, the corresponding performability models will in general also be large and complex. To alleviate the largeness problem to some extent the author uses generalized stochastic Petri nets to describe the models. Still however, many models cannot be solved with the current numerical techniques, although they are conveniently and often compactly described. In the paper the author discusses two heuristic state space truncation techniques that allow us to obtain very good approximations while only assessing a few percent of the overall state space. He gives examples of the usage, but also theoretical evidence in the correctness of the employed truncation techniques. He furthermore shows that GSPNs are very suitable for implementing (describing) the proposed truncation techniques.<<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":"121059786","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.1991.238801
Greg Findlow
Vautherin's results relating the behaviour of classes of coloured (high-level) Petri nets to ordinary Petri nets (skeletons for the classes) are examined, and their usefulness and ease of application are investigated. The feasibility of using skeletons for the purpose of 'first estimate' verifications of nets (in particular, for the early detection of deadlocks, i.e. reachable dead markings) is considered. It is found that because the relationship established by Vautherin between the dead markings of a coloured net and those of the corresponding skeleton does not differentiate between reachable and unreachable markings, deadlock-freeness of a coloured net and deadlock-freeness of its skeletons are essentially independent properties.<>
{"title":"Can skeletons really be used to detect deadlocks of nets?","authors":"Greg Findlow","doi":"10.1109/PNPM.1991.238801","DOIUrl":"https://doi.org/10.1109/PNPM.1991.238801","url":null,"abstract":"Vautherin's results relating the behaviour of classes of coloured (high-level) Petri nets to ordinary Petri nets (skeletons for the classes) are examined, and their usefulness and ease of application are investigated. The feasibility of using skeletons for the purpose of 'first estimate' verifications of nets (in particular, for the early detection of deadlocks, i.e. reachable dead markings) is considered. It is found that because the relationship established by Vautherin between the dead markings of a coloured net and those of the corresponding skeleton does not differentiate between reachable and unreachable markings, deadlock-freeness of a coloured net and deadlock-freeness of its skeletons are essentially independent properties.<<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":"130098977","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.1991.238802
H. Ammar, S. Deng
Addresses the problem of developing parallel simulation techniques to analyze complex Stochastic Petri Net (SPN) models. The approach of parallel simulation is to divide a general SPN spatially into several connected subnets. The various subnetworks are simulated in parallel by several logical processes (LPs) which synchronize. The rich and complex structure of Petri Nets necessitates the development of an algorithm which can handle general forms of network partitions. In the paper, an algorithm based on the Time Warp strategy for optimistic parallel simulation is presented. Time scale decomposition is also used with spatial decomposition to induce parallelism and reduce synchronization overhead. An example of performability analysis using both spatial and time-scale decomposition is presented.<>
{"title":"Time warp simulation of stochastic Petri nets","authors":"H. Ammar, S. Deng","doi":"10.1109/PNPM.1991.238802","DOIUrl":"https://doi.org/10.1109/PNPM.1991.238802","url":null,"abstract":"Addresses the problem of developing parallel simulation techniques to analyze complex Stochastic Petri Net (SPN) models. The approach of parallel simulation is to divide a general SPN spatially into several connected subnets. The various subnetworks are simulated in parallel by several logical processes (LPs) which synchronize. The rich and complex structure of Petri Nets necessitates the development of an algorithm which can handle general forms of network partitions. In the paper, an algorithm based on the Time Warp strategy for optimistic parallel simulation is presented. Time scale decomposition is also used with spatial decomposition to induce parallelism and reduce synchronization overhead. An example of performability analysis using both spatial and time-scale decomposition 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":"127578100","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.1991.238782
S. Donatelli
B. Plateau (1985) introduced an efficient way for solving stochastic processes that are derived from the composition of stochastic automata by making extensive use of the Kronecker (tensor) algebra for matrices. The author applies that efficient solution to a class of stochastic Petri nets (SPN) that has been called superposed stochastic automata (SSA). The solution has been implemented both with sequential and parallel programs. SSA are a rather restricted subclass of SPN, but the extension to the general case doesn't appear to pose any theoretical problem.<>
B. Plateau(1985)通过广泛使用矩阵的Kronecker(张量)代数，引入了一种求解随机过程的有效方法，这些随机过程是由随机自动机组成的。作者将该有效解应用于一类随机Petri网(SPN)，即叠加随机自动机(SSA)。该方案已在顺序和并行程序中实现。SSA是SPN的一个相当有限的子类，但将其推广到一般情况下似乎没有任何理论问题
{"title":"Superposed stochastic automata: a class of stochastic Petri nets amenable to parallel solution","authors":"S. Donatelli","doi":"10.1109/PNPM.1991.238782","DOIUrl":"https://doi.org/10.1109/PNPM.1991.238782","url":null,"abstract":"B. Plateau (1985) introduced an efficient way for solving stochastic processes that are derived from the composition of stochastic automata by making extensive use of the Kronecker (tensor) algebra for matrices. The author applies that efficient solution to a class of stochastic Petri nets (SPN) that has been called superposed stochastic automata (SSA). The solution has been implemented both with sequential and parallel programs. SSA are a rather restricted subclass of SPN, but the extension to the general case doesn't appear to pose any theoretical problem.<<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":"132924971","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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