Pub Date : 2001-09-11DOI: 10.1109/PNPM.2001.953358
P. Buchholz, P. Kemper
Markov chain based analysis of GSPNs suffers from the state space explosion problem. In this paper we combine ideas from two different other approaches to analyze systems with very large state spaces. First, we represent the generator matrix as a sum of Kronecker products of small component matrices. Second, we use an extension of probabilistic decision graphs to represent probability vectors. The combination of these two concepts is the base for an iterative solution technique with the potential to handle extremely large Markov chains resulting from Superposed GSPNs or related model types.
{"title":"Compact representations of probability distributions in the analysis of Superposed GSPNs","authors":"P. Buchholz, P. Kemper","doi":"10.1109/PNPM.2001.953358","DOIUrl":"https://doi.org/10.1109/PNPM.2001.953358","url":null,"abstract":"Markov chain based analysis of GSPNs suffers from the state space explosion problem. In this paper we combine ideas from two different other approaches to analyze systems with very large state spaces. First, we represent the generator matrix as a sum of Kronecker products of small component matrices. Second, we use an extension of probabilistic decision graphs to represent probability vectors. The combination of these two concepts is the base for an iterative solution technique with the potential to handle extremely large Markov chains resulting from Superposed GSPNs or related model types.","PeriodicalId":364695,"journal":{"name":"Proceedings 9th International Workshop on Petri Nets and Performance Models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2001-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131457115","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 : 2001-09-11DOI: 10.1109/PNPM.2001.953359
J. Freiheit, A. Zimmermann
State-space explosion is one of the main problems in the area of the performance evaluation of Petri net models. This problem prevents the exact numerical analysis of complex real-life systems. To overcome the limitation of state spaces that are too large, many methods have been proposed in which the whole system is divided into small analysable parts. This paper presents one of these so-called decomposition methods. In contrast to known decomposition methods, the whole model is decomposed automatically in the presented approach. Afterwards, the submodels are aggregated. The paper presents a new iterative aggregation method called MIMO (multiple input, multiple output) graph-based aggregation. In a third step, an iterative analysis is used to compute performance measures using iterative response-time approximation. The method is explained by applying it to an example. It is integrated in the TimeNET modelling and analysis tool for stochastic Petri nets.
{"title":"A divide and conquer approach for the performance evaluation of large stochastic Petri nets","authors":"J. Freiheit, A. Zimmermann","doi":"10.1109/PNPM.2001.953359","DOIUrl":"https://doi.org/10.1109/PNPM.2001.953359","url":null,"abstract":"State-space explosion is one of the main problems in the area of the performance evaluation of Petri net models. This problem prevents the exact numerical analysis of complex real-life systems. To overcome the limitation of state spaces that are too large, many methods have been proposed in which the whole system is divided into small analysable parts. This paper presents one of these so-called decomposition methods. In contrast to known decomposition methods, the whole model is decomposed automatically in the presented approach. Afterwards, the submodels are aggregated. The paper presents a new iterative aggregation method called MIMO (multiple input, multiple output) graph-based aggregation. In a third step, an iterative analysis is used to compute performance measures using iterative response-time approximation. The method is explained by applying it to an example. It is integrated in the TimeNET modelling and analysis tool for stochastic Petri nets.","PeriodicalId":364695,"journal":{"name":"Proceedings 9th International Workshop on Petri Nets and Performance Models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2001-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116931384","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 : 2001-09-11DOI: 10.1109/PNPM.2001.953367
B. Tuffin, Louis-Marie Le Ny
We consider a monoclass threshold queue with hysteresis. Many applications of such a system can be found in the transport protocols of communication networks. Thresholds help to smooth the variations of delay and throughput, and hysteresis limits the number of (expensive) switches of the control mechanism. The queues are modeled and analysed by means of Stochastic Petri Nets (SPNs), a powerful paradigm to represent complex systems. The representation is shown to be very simple and can aid in the study and configuration of the queue to conform to design specifications. Moreover, Fluid Stochastic Petri Nets (FSPNs) are used as an approximation which might be helpful to analyse high speed networks. Numerical illustrations are given in order to validate the choice of threshold queues with hysteresis and their representation by SPNs and FSPNs.
{"title":"Modeling and analysis of threshold queues with hysteresis using stochastic Petri nets: the monoclass case","authors":"B. Tuffin, Louis-Marie Le Ny","doi":"10.1109/PNPM.2001.953367","DOIUrl":"https://doi.org/10.1109/PNPM.2001.953367","url":null,"abstract":"We consider a monoclass threshold queue with hysteresis. Many applications of such a system can be found in the transport protocols of communication networks. Thresholds help to smooth the variations of delay and throughput, and hysteresis limits the number of (expensive) switches of the control mechanism. The queues are modeled and analysed by means of Stochastic Petri Nets (SPNs), a powerful paradigm to represent complex systems. The representation is shown to be very simple and can aid in the study and configuration of the queue to conform to design specifications. Moreover, Fluid Stochastic Petri Nets (FSPNs) are used as an approximation which might be helpful to analyse high speed networks. Numerical illustrations are given in order to validate the choice of threshold queues with hysteresis and their representation by SPNs and FSPNs.","PeriodicalId":364695,"journal":{"name":"Proceedings 9th International Workshop on Petri Nets and Performance Models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2001-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126163348","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 : 2001-09-11DOI: 10.1109/PNPM.2001.953363
D. Deavours, W. Sanders
Mobius is an extensible framework and tool for performance and dependability modeling, and supports multiple modeling formalisms and solvers. As a framework, Mobius must be sufficiently general to capture the various formalism behaviors. Specifically, the Mobius execution policy must be flexible enough to accommodate the execution policies of all formalisms implemented in the framework. We know of no existing execution policy which is capable of doing this and meeting the many other goals of the framework. We present the Mobius execution policy that addresses these needs. In developing the policy, we have generalized the various preemption policies and made all aspects of the execution policy state-dependent, which has never before been considered. Because all aspects may be state-dependent, we also had to relax the assumption that work proceeds at a constant rate; this is also novel. Finally, we show that within the context of Mobius, the extra structure and overhead needed to implement a particular behavior can largely be avoided except when that behavior is present in a model.
{"title":"The Mobius execution policy","authors":"D. Deavours, W. Sanders","doi":"10.1109/PNPM.2001.953363","DOIUrl":"https://doi.org/10.1109/PNPM.2001.953363","url":null,"abstract":"Mobius is an extensible framework and tool for performance and dependability modeling, and supports multiple modeling formalisms and solvers. As a framework, Mobius must be sufficiently general to capture the various formalism behaviors. Specifically, the Mobius execution policy must be flexible enough to accommodate the execution policies of all formalisms implemented in the framework. We know of no existing execution policy which is capable of doing this and meeting the many other goals of the framework. We present the Mobius execution policy that addresses these needs. In developing the policy, we have generalized the various preemption policies and made all aspects of the execution policy state-dependent, which has never before been considered. Because all aspects may be state-dependent, we also had to relax the assumption that work proceeds at a constant rate; this is also novel. Finally, we show that within the context of Mobius, the extra structure and overhead needed to implement a particular behavior can largely be avoided except when that behavior is present in a model.","PeriodicalId":364695,"journal":{"name":"Proceedings 9th International Workshop on Petri Nets and Performance Models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2001-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127618608","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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