Nondeterministic Probabilistic Petri Net — A New Method to Study Qualitative and Quantitative Behaviors of System
Yang Liu1,2,3 (刘阳), Huai-Kou Miao1 (缪淮扣), Senior Member, CCF, Hong-Wei Zeng1 (曾红卫), Yan Ma2 (马艳), and Pan Liu1 (刘攀)
1. School of Computer Engineering and Science, Shanghai University, Shanghai 200072, China;
2. School of Information Science and Technology, Taishan University, Taian 271021, China;
3. State Key Laboratory of Novel Software Technology, Nanjing University, Nanjing 210093, China
Abstract There are many variants of Petri net at present, and some of them can be used to model system with both function and performance specification, such as stochastic Petri net, generalized stochastic Petri net and probabilistic Petri net. In this paper, we utilize extended Petri net to address the issue of modeling and verifying system with probability and nondeterminism besides function aspects. Using probabilistic Petri net as reference, we propose a new mixed model NPPN (Nondeterministic Probabilistic Petri Net) system, which can model and verify systems with qualitative and quantitative behaviours. Then we develop a kind of process algebra for NPPN system to interpret its algebraic semantics, and an actionbased PCTL (Probabilistic Computation Tree Logic) to interpret its logical semantics. Afterwards we present the rules for compositional operation of NPPN system based on NPPN system process algebra, and the model checking algorithm based on the action-based PCTL. In order to put the NPPN system into practice, we develop a friendly and visual tool for modeling, analyzing, simulating, and verifying NPPN system using action-based PCTL. The usefulness and effectiveness of the NPPN system are illustrated by modeling and model checking an elaborate model of travel arrangements workflow.
This work was supported by the National Natural Science Foundation of China under Grant Nos. 60970007, 61073050 and 61170044, the National Basic Research 973 Program of China under Grant No. 2007CB310800, the Shanghai Leading Academic Discipline Project of China under Grant No. J50103, and the Natural Science Foundation of Shandong Province of China under Grant No. ZR2012FQ013.
Cite this article:
Yang Liu, Huai-Kou Miao, Hong-Wei Zeng, Yan Ma, and Pan Liu.Nondeterministic Probabilistic Petri Net — A New Method to Study Qualitative and Quantitative Behaviors of System[J] Journal of Computer Science and Technology, 2013,V28(1): 203-216
 Girault C, Valk R. Petri Nets for System Engineering: AGuide to Modeling, Verification, and Application. Springer-Verlag, 2003. Lin C. Stochastic Petri Net and System Performance Evaluation(2nd Edition). Tsinghua University Press, 2005, pp.1-2.(in Chinese) Noe J D, Nutt G J. Macro e-nets representation of parallelsystems. IEEE Transactions on Computers, 1973, C-22(8):718-727. Merlin P M, Farber D J. Recoverability of communicationprotocols: Implications of a theoretical study. IEEE Transactionson Communications, 1976, 24(9): 1036-1043. Molloy M K. On the integration of delay and throughput measuresin distributed processing models [Ph.D. Thesis]. Universityof California, Los Angeles, USA, 1981. Natkin S. Les reseaux de PETRI stochastiques et leur application`a l’′evaluation des syst`emes informatiques [Ph.D. Thesis].CNAM, Paris, France, 1980. (In French) Symons F JW. Introduction to numerical Petri nets, a generalgraphical model of concurrent processing systems. AustralianTelecommunications Research, 1980, 14(1): 28-33. Marsan M A, Conte G, Balbo G. A class of generalizedstochastic Petri nets for the performance evaluation of multiprocessorsystems. ACM Transactions on Computer Systems,1984, 2(2): 93-122. Petri C A. Introduction to general net theory. In LectureNotes in Computer Science 84, Brauer W (ed.), Springer-Verlag, 1980, pp.1-19. Balbo G. Introduction to generalized stochastic Petri net. InProc. the 7th Int. Conf. Formal Methods for PerformanceEvaluation, May 2007, pp.83-131. Baier C, Katoen J P. Principles of Model Checking. MITPress, 2008. Albanese M, Chellappa R, Moscato V, Picariello A, SubrahmanianV S, Turaga P, Udrea O. A constrained probabilisticPetri net framework for human activity detection in video.IEEE Transactions on Multimedia, 2008, 10(8): 1429-1443. Kudlek M. Probability in Petri nets. Fundamenta Informaticae— Concurrency Specification and Programming, 2005,67(1/3): 121-130. Benveniste A, Fabre E, Haar S. Markov nets: Probabilisticmodels for distributed and concurrent systems. IEEE Transactionson Automatic Control, 2003, 48(11): 1936-1950. Segala R. Modeling and verification of randomized distributedreal-time systems [Ph.D. Thesis]. Massachusetts Institute ofTechnology, Cambridge, USA, 1995. Yuan C Y. Principle and Application of Petri Net. Beijing:Publishing House of Electronics Industry, 2005, pp.66-78. (inChinese) Han T T. Diagnosis, synthesis and analysis of probabilisticmodels [Ph.D. Thesis]. RWTH Aachen University, Germany,2009. Ash R B, Dol′eans-Dade C A. Probability and Measure Theory(2nd edition). Academic Press, 2000, pp.3-10. Milner R. Communication and Concurrency. Prentice-Hall,1989, pp.10-36. Hoare C A R. Communicating Sequential Processes. Prentice-Hall, 1985, pp.81-100. Heljanko K, Junttila T, Latvala T. Incremental and completebounded model checking for full PLTL. In Proc. the 17th InternationalConference on Computer Aided Verification, July2005, pp.98-111. Hansson H, Jonsson B. A logic for reasoning about time andreliability. Formal Aspects of Computing, 1994, 6(5): 512-535. Bianco A, de Alfaro L. Model checking of probabilistic andnondeterministic systems. In Proc. the 15th Conference onFoundations of Software Technology and Theoretical ComputerScience, December 1995, pp.499-513. Emerson E A, Mok A K, Sistla A P, Srinivasan J. Quantitativetemporal reasoning. Real Time Systems, 1992, 4(4):331-352. Baier C, Katoen J P, Hermanns H. Approximate symbolicmodel checking of continuous-time Markov chains. In Proc.the 10th International Conference on Concurrency Theory,August 1999, pp.146-162. Kindler E, Vesper T. ESTL: A temporal logic for events andstates. In Proc. the 19th International Conference of Applicationand Theory of Petri Nets, June 1998, pp.365-384. Feng L, Kwiatkowska M, Parker D. Compositional verificationof probabilistic systems using learning. In Proc. the 7thInternational Conference on Quantitative Evaluation of Systems,September 2010, pp.133-142. Bonet P, Llado C M, Puijaner R, Knottenbelt W J. PIPEv2.5: A Petri net tool for performance modelling. In Proc.the 23rd Latin American Conference on Informatics, October2007. Yuan C Y, ZhaoW, Zhang S K, Huang Y. A three-layer modelfor business processes: Process logic, case semantics and workflowmanagement. Journal of Computer Science and Technology,2007, 22(3): 410-425. Varacca D. Probability, nondeterminism and concurrency:Two denotational models for probabilistic computation[Ph.D. Thesis]. University of Aarhus, Aarhus, Denmark,2003. Varacca D, Völzer H, Winskel G. Probabilistic event structuresand domains. Theoretical Computer Science — ConcurrencyTheory, 2006, 358(2): 173-199, Hermanns H. Interactive markov chains: The quest for quantifiedquality. In Lecture Notes in Computer Science 2428,2002, pp.57-87. Neuhäusser M R. Model checking nondeterministic and randomlytimed systems [Ph.D. Thesis]. RWTH Aachen University,Germany, 2010.
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