Pub Date : 2003-09-02DOI: 10.1109/PNPM.2003.1231550
G. Bucci, L. Sassoli, E. Vicario
In the development of reactive systems, correctness and performance requirements are often intertwined. An integral approach to both the aspects of the problem requires models and analysis techniques which jointly capture probabilistic and minimum/maximum characterization of time delays. A discrete time extension of Time Petri Nets is introduced, which extends minimum/maximum timing constraints with a discrete probability density. As a characterizing trait, the model is interpreted according to a semantics of true concurrency, representing dynamic behavior in terms of the probability that a set of transitions fires at the current tick of the clock. Behavioral and probabilistic rules in the semantics of the model are soundly captured into an enumerative technique which represents the state space of the model as a transition system labeled with delays and probabilities. This enables both Markovian analysis techniques and inspection algorithms supporting verification of sequencing and minimum/maximum durational properties.
{"title":"A discrete time model for performance evaluation and correctness verification of real time systems","authors":"G. Bucci, L. Sassoli, E. Vicario","doi":"10.1109/PNPM.2003.1231550","DOIUrl":"https://doi.org/10.1109/PNPM.2003.1231550","url":null,"abstract":"In the development of reactive systems, correctness and performance requirements are often intertwined. An integral approach to both the aspects of the problem requires models and analysis techniques which jointly capture probabilistic and minimum/maximum characterization of time delays. A discrete time extension of Time Petri Nets is introduced, which extends minimum/maximum timing constraints with a discrete probability density. As a characterizing trait, the model is interpreted according to a semantics of true concurrency, representing dynamic behavior in terms of the probability that a set of transitions fires at the current tick of the clock. Behavioral and probabilistic rules in the semantics of the model are soundly captured into an enumerative technique which represents the state space of the model as a transition system labeled with delays and probabilities. This enables both Markovian analysis techniques and inspection algorithms supporting verification of sequencing and minimum/maximum durational properties.","PeriodicalId":134699,"journal":{"name":"10th International Workshop on Petri Nets and Performance Models, 2003. Proceedings.","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126752556","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 : 2003-09-02DOI: 10.1109/PNPM.2003.1231544
Simona Bernardi, S. Donatelli
{"title":"Building Petri net scenarios for dependable automation systems","authors":"Simona Bernardi, S. Donatelli","doi":"10.1109/PNPM.2003.1231544","DOIUrl":"https://doi.org/10.1109/PNPM.2003.1231544","url":null,"abstract":"","PeriodicalId":134699,"journal":{"name":"10th International Workshop on Petri Nets and Performance Models, 2003. Proceedings.","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129509163","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 : 2003-09-02DOI: 10.1109/PNPM.2003.1231538
A. Miner
In this paper, we consider random variables expressed in terms of the time required for the state of a stochastic Petri net to pass from a set of starting markings to a set of stopping markings. These random variables have continuous phase-type distributions when the all transitions have exponentially-distributed firing delays. We demonstrate how to numerically compute the distribution of the random variable using both explicit techniques and an implicit approach based on multi-way decision diagrams and matrix diagrams. We present an efficient matrix-vector multiplication algorithm for matrix diagrams that is necessary for numerical solution. We demonstrate the efficiency of our approaches using several models. The lower storage requirements of the implicit approach effectively increases the size of models that can be analyzed by about an order of magnitude.
{"title":"Computing response time distributions using stochastic Petri nets and matrix diagrams","authors":"A. Miner","doi":"10.1109/PNPM.2003.1231538","DOIUrl":"https://doi.org/10.1109/PNPM.2003.1231538","url":null,"abstract":"In this paper, we consider random variables expressed in terms of the time required for the state of a stochastic Petri net to pass from a set of starting markings to a set of stopping markings. These random variables have continuous phase-type distributions when the all transitions have exponentially-distributed firing delays. We demonstrate how to numerically compute the distribution of the random variable using both explicit techniques and an implicit approach based on multi-way decision diagrams and matrix diagrams. We present an efficient matrix-vector multiplication algorithm for matrix diagrams that is necessary for numerical solution. We demonstrate the efficiency of our approaches using several models. The lower storage requirements of the implicit approach effectively increases the size of models that can be analyzed by about an order of magnitude.","PeriodicalId":134699,"journal":{"name":"10th International Workshop on Petri Nets and Performance Models, 2003. Proceedings.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129305140","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 : 2003-09-02DOI: 10.1109/PNPM.2003.1231541
A. Heindl, E. Biersack
We compare discrete-state stochastic Petri nets (SPNs) and fluid stochastic Petri nets (FSPNs) with a mixed discrete-continuous state space in their application to openloop video broadcasting systems. For both classes, we present models of the Video-on-Demand client-server system, which generally capture all relevant system aspects in a concise and graphical way. Differences in model design as well as solution techniques for various variants of these models are discussed. By simulation, we obtain measures related to blocked video playout, which allow us to evaluate customer satisfaction against bandwidth requirements. While the FSPN model has advantages in model specification and evaluation efficiency, all presented models excel in their flexibility – both in defining various performance measures and in their extensibility to include, for instance, full VCR functionality and arbitrary user behavior.
{"title":"Discrete-state and fluid stochastic petri net models for open-loop video-on-demand systems:a comparative case study","authors":"A. Heindl, E. Biersack","doi":"10.1109/PNPM.2003.1231541","DOIUrl":"https://doi.org/10.1109/PNPM.2003.1231541","url":null,"abstract":"We compare discrete-state stochastic Petri nets (SPNs) and fluid stochastic Petri nets (FSPNs) with a mixed discrete-continuous state space in their application to openloop video broadcasting systems. For both classes, we present models of the Video-on-Demand client-server system, which generally capture all relevant system aspects in a concise and graphical way. Differences in model design as well as solution techniques for various variants of these models are discussed. By simulation, we obtain measures related to blocked video playout, which allow us to evaluate customer satisfaction against bandwidth requirements. While the FSPN model has advantages in model specification and evaluation efficiency, all presented models excel in their flexibility – both in defining various performance measures and in their extensibility to include, for instance, full VCR functionality and arbitrary user behavior.","PeriodicalId":134699,"journal":{"name":"10th International Workshop on Petri Nets and Performance Models, 2003. Proceedings.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126159033","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 : 2003-09-02DOI: 10.1109/PNPM.2003.1231543
J. Bradley, N. Dingle, P. Harrison, W. Knottenbelt
Semi-Markov Stochastic Petri Nets (SM-SPNs) are a highlevel formalism for defining semi-Markov processes. We present an extended Continuous Stochastic Logic (eCSL) which provides an expressive way to articulate performance queries at the SM-SPN model level. eCSL supports queries involving steady-state, transient and passage time measures. We demonstrate this by formulating and answering eCSL queries on an SM-SPN model of a distributed voting system with up to states.
{"title":"Performance queries on semi-Markov stochastic Petri nets with an extended continuous stochastic logic","authors":"J. Bradley, N. Dingle, P. Harrison, W. Knottenbelt","doi":"10.1109/PNPM.2003.1231543","DOIUrl":"https://doi.org/10.1109/PNPM.2003.1231543","url":null,"abstract":"Semi-Markov Stochastic Petri Nets (SM-SPNs) are a highlevel formalism for defining semi-Markov processes. We present an extended Continuous Stochastic Logic (eCSL) which provides an expressive way to articulate performance queries at the SM-SPN model level. eCSL supports queries involving steady-state, transient and passage time measures. We demonstrate this by formulating and answering eCSL queries on an SM-SPN model of a distributed voting system with up to states.","PeriodicalId":134699,"journal":{"name":"10th International Workshop on Petri Nets and Performance Models, 2003. Proceedings.","volume":"83 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129071721","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 : 2003-09-02DOI: 10.1109/PNPM.2003.1231547
G. Balbo, S. C. Bruell, M. Sereno
In this paper we show that multi-class BCMP queueing networks can be represented by means of Product Form Solution Stochastic Petri Nets (PF-SPNs). Since the first time PF-SPNs were proposed, one of their main drawbacks concerned the fact that there was no clear relation between PFSPNs and PF-QNs, in particular the well-known multi-class BCMP-QNs. It is important to note that the existence of the product form solution is not a property of the formalism, but of the underlying Markovian process. Hence, the fact that PF-SPNs (and also PF-GSPNs) cannot directly represent BCMP-QNs is one of the weaknesses of the SPN productform results. The results presented in this paper overcome this weakness. In particular, we show that starting from a detailed GSPN representation of each of the BCMP station types, it is possible to derive equivalent compact PF-SPN representations for each station type.
{"title":"On the relations between BCMP queueing networks and product form solution stochastic petri nets","authors":"G. Balbo, S. C. Bruell, M. Sereno","doi":"10.1109/PNPM.2003.1231547","DOIUrl":"https://doi.org/10.1109/PNPM.2003.1231547","url":null,"abstract":"In this paper we show that multi-class BCMP queueing networks can be represented by means of Product Form Solution Stochastic Petri Nets (PF-SPNs). Since the first time PF-SPNs were proposed, one of their main drawbacks concerned the fact that there was no clear relation between PFSPNs and PF-QNs, in particular the well-known multi-class BCMP-QNs. It is important to note that the existence of the product form solution is not a property of the formalism, but of the underlying Markovian process. Hence, the fact that PF-SPNs (and also PF-GSPNs) cannot directly represent BCMP-QNs is one of the weaknesses of the SPN productform results. The results presented in this paper overcome this weakness. In particular, we show that starting from a detailed GSPN representation of each of the BCMP station types, it is possible to derive equivalent compact PF-SPN representations for each station type.","PeriodicalId":134699,"journal":{"name":"10th International Workshop on Petri Nets and Performance Models, 2003. Proceedings.","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131664610","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 : 2003-09-02DOI: 10.1109/PNPM.2003.1231549
D. Lime, O. Roux
In this paper, we propose a method for building the state class graph of a bounded time Petri net (TPN) as a timed automaton (TA). We consider bounded TPN, whose underlying net is not necessarily bounded. We prove that the obtained TA is timed-bisimilar to the initial TPN. The number of clocks of the automaton is much lower than with other methods available. It allows us to check real-time properties on bounded TPN with efficient TA model-checkers. We have implemented the method, and give some experimental results in this paper, illustrating the efficiency of the algorithm in terms of clock number.
{"title":"State class timed automaton of a time Petri net","authors":"D. Lime, O. Roux","doi":"10.1109/PNPM.2003.1231549","DOIUrl":"https://doi.org/10.1109/PNPM.2003.1231549","url":null,"abstract":"In this paper, we propose a method for building the state class graph of a bounded time Petri net (TPN) as a timed automaton (TA). We consider bounded TPN, whose underlying net is not necessarily bounded. We prove that the obtained TA is timed-bisimilar to the initial TPN. The number of clocks of the automaton is much lower than with other methods available. It allows us to check real-time properties on bounded TPN with efficient TA model-checkers. We have implemented the method, and give some experimental results in this paper, illustrating the efficiency of the algorithm in terms of clock number.","PeriodicalId":134699,"journal":{"name":"10th International Workshop on Petri Nets and Performance Models, 2003. Proceedings.","volume":"230 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114599194","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 : 2003-09-02DOI: 10.1109/PNPM.2003.1231548
S. Haar
The heaps of pieces modelling approach (see Gaubert/Mairesse, PNPM'99) admits a (max,+)-linear model for the time consumption, under earliest firing and a given trace, of safe T-timed nets. The present paper shows that this type of model can be extended, using an appropriate partial order semantics under cluster view, to include stochastic choice and timing; we give the algorithmic construction of that semantics and obtain a semi-Markov property in multi-dimensional real time.
{"title":"Distributed semi-Markov processes in stochastic T-timed Petri nets","authors":"S. Haar","doi":"10.1109/PNPM.2003.1231548","DOIUrl":"https://doi.org/10.1109/PNPM.2003.1231548","url":null,"abstract":"The heaps of pieces modelling approach (see Gaubert/Mairesse, PNPM'99) admits a (max,+)-linear model for the time consumption, under earliest firing and a given trace, of safe T-timed nets. The present paper shows that this type of model can be extended, using an appropriate partial order semantics under cluster view, to include stochastic choice and timing; we give the algorithmic construction of that semantics and obtain a semi-Markov property in multi-dimensional real time.","PeriodicalId":134699,"journal":{"name":"10th International Workshop on Petri Nets and Performance Models, 2003. Proceedings.","volume":"131 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131801320","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 : 2003-09-02DOI: 10.1109/PNPM.2003.1231540
R. German, M. Gribaudo, G. Horváth, M. Telek
In this paper, we analyze the stationary behaviour of FSPNs with single fluid place and mutually dependent continuous and discrete part. The proposed analysis technique is restricted to the cases when the fluid rate does not change sign in a given marking. We provide the set of ordinary differential equations and boundary conditions that determines the stationary behaviour and we discuss potential numerical methods that evaluate the stationary distribution based on this description. The numerical analysis of FSPN models of telecommunication systems demonstrate the applicability of the introduced analysis methods.
{"title":"Stationary analysis of FSPNs with mutually dependent discrete and continuous parts","authors":"R. German, M. Gribaudo, G. Horváth, M. Telek","doi":"10.1109/PNPM.2003.1231540","DOIUrl":"https://doi.org/10.1109/PNPM.2003.1231540","url":null,"abstract":"In this paper, we analyze the stationary behaviour of FSPNs with single fluid place and mutually dependent continuous and discrete part. The proposed analysis technique is restricted to the cases when the fluid rate does not change sign in a given marking. We provide the set of ordinary differential equations and boundary conditions that determines the stationary behaviour and we discuss potential numerical methods that evaluate the stationary distribution based on this description. The numerical analysis of FSPN models of telecommunication systems demonstrate the applicability of the introduced analysis methods.","PeriodicalId":134699,"journal":{"name":"10th International Workshop on Petri Nets and Performance Models, 2003. Proceedings.","volume":"34 47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132828324","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 : 2003-09-02DOI: 10.1109/PNPM.2003.1231546
M. Sereno
We consider a particular class of Stochastic Petri Nets exhibiting a Product Form Solution over sub-nets. For this type of product form models we provide a normalisation constant algorithm for computing the performance indices of such SPNs. The considered Product Form Solution criterion is based on a factorisation of the equilibrium distribution of the model in terms of distributions of the Continuous Time Markov Chains of the basic sub-models and hence, although all the derivations presented in this paper concern Stochastic Petri Net models, they can easily be adapted to other performance formalisms where the identification of classes of models exhibiting a Product Form Solution over sub-models is possible.
{"title":"Computational algorithms for product-form of competing Markov chains","authors":"M. Sereno","doi":"10.1109/PNPM.2003.1231546","DOIUrl":"https://doi.org/10.1109/PNPM.2003.1231546","url":null,"abstract":"We consider a particular class of Stochastic Petri Nets exhibiting a Product Form Solution over sub-nets. For this type of product form models we provide a normalisation constant algorithm for computing the performance indices of such SPNs. The considered Product Form Solution criterion is based on a factorisation of the equilibrium distribution of the model in terms of distributions of the Continuous Time Markov Chains of the basic sub-models and hence, although all the derivations presented in this paper concern Stochastic Petri Net models, they can easily be adapted to other performance formalisms where the identification of classes of models exhibiting a Product Form Solution over sub-models is possible.","PeriodicalId":134699,"journal":{"name":"10th International Workshop on Petri Nets and Performance Models, 2003. Proceedings.","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129716056","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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