动态工作流的Petri网建模技术和服务质量分析
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摘要
随着计算机技术、云计算和经济全球化的迅速发展,工作流技术被广泛应用到各种领域中。然而,所有的领域都存在某种程度和形式上变化因素,这意味着在业务过程执行过程中,组织或企业需要调整它们的活动以应对这些影响因素。为了使工作流能够适应日益激烈的竞争环境、动态多变的市场环境和个性化的用户需求,必须提高工作流的动态性、柔性和适应性。这些特性在给企业带来巨大经济效益的同时,也对工作流模型提出了巨大挑战,如经常会使过程实例在运行过程中偏离预定义的过程并失去控制。如何处理工作流实例运行过程中的跃迁,使变换后的过程既能实现原有目标,又能避免运行脱节等一系列问题,成为当前迫切需要解决的问题。
工作流的动态变化主要包括业务流程变动、实例迁移、工作流演进等,本文主要研究建模动态工作流的技术,以及实现工作流实例迁移的跃迁规则。
首先,本文针对具有资源约束的工作流、具有随机性的工作流分别提出了动态库所Petri网(DPPN)和变迁可编程Petri网(TPPN)。在此基础上,我们考虑具有由变量(或属性)描述的本地存储的库所,提出了可编程Petri网(PPN),详述了它的变迁发生规则,并给出了PPN与高级Petri网等价的构造性证明。然后,通过修改PPN得到了可编程工作流网(PWN)的定义,并深入分析了PWN的动态变化机制。
然后,我们将网重写系统结合PWN得出了基于PWN的重写网的定义和重写规则。PWN重写网的模型和规则能够实现各种变化模式的所有操作,并且能够改变控制流变化的支持特征。其中,支持特征能够从系统的角度对比现有的过程管理技术。有两种方式可以改变重写网的业务流程：(1)改变PWN的编程函数。(2)通过改变现有业务流程的结构来改进当前系统的性能或添加、删除和更新服务以适应环境和业务需求的变化。为处理运行实例的跃迁,提出了守恒状态等的定义,并证明了某些性质。
最后,针对包含动态服务组合的工作流的随机性,我们引入随机网络演算,用到达曲线和服务曲线,分析基于网络的服务组合中的时延和数据积压界限。由此可以得出随机服务保障下动态服务组合的QoS评价,并通过系统模拟与实例来分析两种情景下的性能。
Along with the rapid development of computer technology, cloud computing and economic globalization, workflow technology is currently being applied in quite diverse domains. However, the factors of change are present in some degree and form in process in almost all domains. It means that organizations or enterprises need to adjust their activities to deal with these factors in the execution of business processes. In order to adapt the increasingly fierce competition, dynamic changeable market environment and personalized user requirements, the dynamics, flexibility and adaptability of workflow systems must be improved. These characteristics not only bring to enterprises huge economic efficiency, but also provide a huge challenge to workflow models. For example, process instances are usually deviating from the pre-defined processes in runtime and loosing the control. How to handle the transition of the workflow instance in runtime, guarantee the transformed process which can not only realize the original target, but also avoid running detached and so on, become an urgent problem to be solved.
The dynamic changes of workflow mainly include process changes, instance migration and workflow evolution and so on. This paper mainly focus on the study of modeling technology for dynamic workflow, as well as the transition rules of realizing workflow instance migration.
Firstly, this paper proposes Place-Programmed Petri Nets (PPPN) and Transition-Programmed Petri nets (TPPN) which respectively aim at workflows constrained by resources and stochastic workflows. Based on these, we consider places which have local storage described by variables (or attributes), and propose the definition of Programmed Petri Nets. This paper further describes its transition firing rule, and proves equivalence between PPPN and colored Petri nets. After that, we propose the definition of Programmed Workflow Nets (PWN) by modifying the definition of PPN, and deeply analyze dynamic mechanism of PWN.
Secondly, we propose the definition of rewriting nets based on PWN and its rewriting rules. The models and rules of rewriting nets based on PWN can realize all operations of various changing modes, and can alter the support characteristics, which can compares existing process management technology from the view of systems, of the changes of control flows. There are two ways to change the business processes of rewriting nets based on PWN. One is to change the programming functions of PWN, the other is to change the structure of current business process in order to improve the performance of the system, or to add, delete and update service in order to adapt environments and the change of business requirements. For the sake of dealing the transition of instances in runtime, we propose some definitions such as conservative state, and prove some properties.
Lastly, we introduce stochastic network calculus on account of the stochastic workflows including dynamic services composition. We apply arrival curves and service curves to analyze the delay bounds and backlog bounds of services composition based on communication network. It can be concluded the QoS evaluation of dynamic services composition under stochastic service guarantee. Meanwhile, we analyze the performance of two scenarios through instance simulation.
工作流的动态变化主要包括业务流程变动、实例迁移、工作流演进等,本文主要研究建模动态工作流的技术,以及实现工作流实例迁移的跃迁规则。
首先,本文针对具有资源约束的工作流、具有随机性的工作流分别提出了动态库所Petri网(DPPN)和变迁可编程Petri网(TPPN)。在此基础上,我们考虑具有由变量(或属性)描述的本地存储的库所,提出了可编程Petri网(PPN),详述了它的变迁发生规则,并给出了PPN与高级Petri网等价的构造性证明。然后,通过修改PPN得到了可编程工作流网(PWN)的定义,并深入分析了PWN的动态变化机制。
然后,我们将网重写系统结合PWN得出了基于PWN的重写网的定义和重写规则。PWN重写网的模型和规则能够实现各种变化模式的所有操作,并且能够改变控制流变化的支持特征。其中,支持特征能够从系统的角度对比现有的过程管理技术。有两种方式可以改变重写网的业务流程：(1)改变PWN的编程函数。(2)通过改变现有业务流程的结构来改进当前系统的性能或添加、删除和更新服务以适应环境和业务需求的变化。为处理运行实例的跃迁,提出了守恒状态等的定义,并证明了某些性质。
最后,针对包含动态服务组合的工作流的随机性,我们引入随机网络演算,用到达曲线和服务曲线,分析基于网络的服务组合中的时延和数据积压界限。由此可以得出随机服务保障下动态服务组合的QoS评价,并通过系统模拟与实例来分析两种情景下的性能。
Along with the rapid development of computer technology, cloud computing and economic globalization, workflow technology is currently being applied in quite diverse domains. However, the factors of change are present in some degree and form in process in almost all domains. It means that organizations or enterprises need to adjust their activities to deal with these factors in the execution of business processes. In order to adapt the increasingly fierce competition, dynamic changeable market environment and personalized user requirements, the dynamics, flexibility and adaptability of workflow systems must be improved. These characteristics not only bring to enterprises huge economic efficiency, but also provide a huge challenge to workflow models. For example, process instances are usually deviating from the pre-defined processes in runtime and loosing the control. How to handle the transition of the workflow instance in runtime, guarantee the transformed process which can not only realize the original target, but also avoid running detached and so on, become an urgent problem to be solved.
The dynamic changes of workflow mainly include process changes, instance migration and workflow evolution and so on. This paper mainly focus on the study of modeling technology for dynamic workflow, as well as the transition rules of realizing workflow instance migration.
Firstly, this paper proposes Place-Programmed Petri Nets (PPPN) and Transition-Programmed Petri nets (TPPN) which respectively aim at workflows constrained by resources and stochastic workflows. Based on these, we consider places which have local storage described by variables (or attributes), and propose the definition of Programmed Petri Nets. This paper further describes its transition firing rule, and proves equivalence between PPPN and colored Petri nets. After that, we propose the definition of Programmed Workflow Nets (PWN) by modifying the definition of PPN, and deeply analyze dynamic mechanism of PWN.
Secondly, we propose the definition of rewriting nets based on PWN and its rewriting rules. The models and rules of rewriting nets based on PWN can realize all operations of various changing modes, and can alter the support characteristics, which can compares existing process management technology from the view of systems, of the changes of control flows. There are two ways to change the business processes of rewriting nets based on PWN. One is to change the programming functions of PWN, the other is to change the structure of current business process in order to improve the performance of the system, or to add, delete and update service in order to adapt environments and the change of business requirements. For the sake of dealing the transition of instances in runtime, we propose some definitions such as conservative state, and prove some properties.
Lastly, we introduce stochastic network calculus on account of the stochastic workflows including dynamic services composition. We apply arrival curves and service curves to analyze the delay bounds and backlog bounds of services composition based on communication network. It can be concluded the QoS evaluation of dynamic services composition under stochastic service guarantee. Meanwhile, we analyze the performance of two scenarios through instance simulation.
引文
1. WFMC. Workflow Management Coalition Terminology and Glossary(WFMC-TC-1011)[M]. Brussels:Workflow Management Coalition,1996:1-65.
2. WFMC. Workflow Management Coalition:The Workflow Reference Model. http://www.wfnc.org,1995.
3. W.M.P. van der Aalst. The Application of Petri Nets to Workflow Management [J]. The Journal of Circuit, System and Computers,1998,8(1):21-66.
4. W.M.P. van der Aalst. Verification of workflow nets[J]. Proceedings of 18th international Conference,1997,12(48):407-426.
5. A Ferseha. Qualitative and Quantitative Ailalysis of Business Workflow Using Generalized Stochastic petri Nets[J]. Proeeeding of 1994 Conference on workflow management challenges, Paradigms and Produets,1994:222-234.
6. N.R. Adam, V. Ailuri, W.K. Huang. Modeling and Analysis of Workflow Using Petri Nets[J]. Journal of Intelligent Information Systems,1998,33(10):1-29.
7. E. Badouel, J. Oliver. Reconfigurable Nets, a Class of High Level Petri Nets Supporting Dynamic Changes within Workflow Systems[M]. Publication Internet: IRISAPI 1163,1998:1-23.
8. W.M.P. van der Aalst, Arthur H.M., ter Hofstede. Verification of Workflow Task Structures:A Petri-Net-Based Approach[J]. Information Systems,2000,25(1):43-69.
9. 曹化工,杨曼红.基于对象Petri网的工作流过程定义[J].计算机辅助设计与图形学学报,2001,13(1)：15-18.
10.李建强,范玉顺.基于Petri网化简方法的工作流模型验证[J].信息与控制,2001,30(6)：492-497.
11.高军,王海洋.基于对象模型工作流的失败处理与失败恢复[J].软件学报,2001,12(5)：776-782.
12.刘婷,林闯,刘卫东.基于时间Petri网的工作流系统模型的线性推理[J],电子学报,2002,30(2)：245-248.
13.庞善臣.工作流的Petri网建模及模型分析[M],山东：山东科技大学,2004.
14.庞善臣,蒋昌俊.一种基于不变量结构分解的工作流性能分析方法[J].计算机学报, 2010,33(10)：908-918.
15. Raya, Halevi Y. Integrated communication and control systems:part Ⅰ-analysis and part Ⅱ-design consideration[J]. ASME J of Dynamic System Measurement & Control,1988: 367-381.
16. M.Y. CHOW, Y. Tipsuwan. Network-based control systems:a tutorial[C]. Proceeding of the 27th Annual Conference of IEEE on Industrial Electronics Society,2001:257-261.
17. A. Stothert, I. Macleod. Effect of timing jitter on distributed computer control system performance[C]. Proceeding of the 15th IFAC Workshop on Distributed Computer Control, 1998.
18. G.C. Walsh, O. Beldiman, L.G. Bushnell. Stability analysis of networked control system[C]. Proceeding of American Control Conference, 1999:2876-2880.
19. L. Vaquero, L. Rodero Marino, J. Caceres, et al. A break in the clouds:towards a cloud definition[J]. SIGCOMM Computer Communication Review,2009,39(1): 50-55.
20. J. Geelan. Twenty one experts define cloud computing.http://virtualization.sys-con.com/node/612375,2008.
21. R. Buyya, C.S. Yeo, S. Venugopal. Market-oriented cloud computing:Vision, hype, and reality for delivering it services as computing utilities[C]. Proceedings of the 2009 9th IEEE/ACM International Symposium on Cluster Computing and the Grid, 2009.
22.张杰.基于虚拟执行规则的工作流演进技术与实现[M],山东：山东科技大学,2009.
23. W.M.P van der Aalst, A.H.M ter Hofstede, B. Kiepuszewski, et al. Workflow Patterns[J]. Distributed and Parallel Databases,2003,14(1):5-51.
24. C Ellis, K Keddara, G Rozenberg. Dynamic Change within Workflow Systems[C]. Proceeding of the Conference on Organizational Computing Systems,1995:10-21.
25. G De Michelis, C.A Ellis. Computer Supported Cooperative Work and Petri Nets. Germany:Dagstuhl Castle,1996.
26. A Asperti, N Busi. Mobile Petri Nets[D]. Italy:University of Bologna,1996.
27. R Milner, J Parrow, D Walker. A calculus of mobile processes[J]. Information and Computation,1992,100(1):1-77.
28. C Fournet, G Gonthier. The reflexive chemical abstract machine and the join-calculus[C]. Proceeding of the 23rd ACM Symposium on Principle of Programming Languages,1996.
29. C Fournet, G Gonthier, J.J Levy. et al. A Calculus of Mobile Agents[J]. Proceedings of CONCUR,1996,1119:406-421.
30. R Valk. Self-Modifying Nets, a Natural Extension of Petri Nets[J]. Proceedings of Icalp,1978,62:464-476.
31. R Valk. Generalizations of Petri Nets[J]. Proceedings of MFCS,1981,118:140-155.
32. E Badouel, Darondeau. Stratified Petri Nets[J]. Proceedings of FCT,1997,12(79): 117-128.
33. E Badouel, M Llorens, J Oliver. Modeling Concurrent Systems:Reconfigurable Nets[J]. Proceedings of Parallel and Distributed Processing Techniques and Applications,2003,4:1568-1574.
34. T Murata. Petri Nets:Properties, Analysis and Applications[J]. Proceedings of IEEE, 1989,77(4):541-580.
35. J L Peterson. Petri net Theory and the Modeling of Systems[D]. New Jersey: Englewood Cliffs,1981.
36. P. Baldan. Modeling Concurrent Computations:From Contextual Petri Nets to Graph Grammars[D]. Italy:Univ. of Pisa,2000.
37. A Corradini. Concurrent Computing From Petri Nets to Graph Grammars. http://www.elsevier.nl/locate/entcs/volume2.html,1995:1-15.
38. Dirk A Taubner. Finite representations of CCS and TCSP programs by automata and Petri nets[M]. New York:Springer Verlag,1993.
39. J G Kobielus. Workflow Strategies[M]. Foster City:IDG Book WorldWide,1997.
40.罗海滨,范玉顺,吴登.工作流技术综述[J].软件学报,2000,11(7)：899-907.
41. W.M.P. van der Aalst. Three Good reasons for Using a Petri-net-based Workflow management System[C]. Proceedings of the International Working Conference on Information and Process ltegration in Enterprises,1996:179-201.
42. WFMC. The workflow reference model[M]. Brussels:Workflow Management Coalition, 1995.
43. C A Ellis, G J Nutt. Modeling and enactment of workflow systems[C]. Lecture Notes in Computer Science,1993,10:1-16.
44. M Papazogbu, A Delis, A Bouguettaya et al. Class library support for workflow environments and applications[J]. IEEE Transactions on Computers,1997.46(6): 673-686.
45. W.M.P. van der Aalst. Structural characterizations of sound workflow nets[M]. Eindhoven: Eindhoven University of Technology,1996.
46.杜玉越,蒋昌俊.基于工作流网的实时协同系统模拟技术[J].计算机学报,2004,27(4)：471-481.
47. A Carl, Petri. Communication with Automata[M]. New York:Griffiss Air Force Base, 1966.
48. K Jensen. Coloured Petri nets:basic concepts, analysis methods, and practical use[M]. New York:Springer Verlag,1992.
49. M K Molloy. Performance analysis using stochastic Petri nets[J]. IEEE Transaction On. Computers,1962,31(9):913-917.
50 L Chuang, D C Marinesc(?). Stoekistie high-level Petri nets and applications[J]. IEEE Transaction On Computers,1988,37(7):815-825.
51. J J P Tsai, S J Yang, Y H Chang. Timing Constrant Petri Nets and Their Application to Schedulability Analysis of Rea-Time System Specifications[J]. IEEE Transaction On Software Engineering,1995,21(1):32-49.
52.C G Looney. Fuzzy Petri Nets for Rule-Based Decision making[J]. IEEE Transaction On Systems,1988,18(1):178-183.
53. Lopez Benitez. Petri net based performance evaluation of distributed homogeneous task systems[J]. IEEE Transaction On Reliability,2000,49(2):188-198.
54. Z W Li, M C Zhou. Elementary siphons of Petri nets and their application to deadlock prevention in flexible manufacturing systems[J]. IEEE Transaction On Systems,2004, 34(1):38-51.
55. J Q Li, Y S Fan, M C Zhou. Performance modeling and analysis of workflow[J]. IEEE Transaction on Systems, Man and Cybernetics,2004,34(2):179-193.
56. T Murata. Petri nets:Properities. analysis and applications[J]. Proceeding of the IEEE, 1989,77(4):541-580.
57.吴哲辉.有界Petri网活性和公平性的分析与实现[J].计算机学报,1989,12(4)：267-278.
58.蒋昌俊.离散事件动态系统的PN机理论[M].北京：科学出版社,2000.
59.袁崇义. Petri网原理[M].北京：电子工业出版社,1998.
60.吴哲辉. Petri网行为描述、性质分析与系统模拟[M].北京：机械工业出版社,2003.
61. G K Janssens, B W Jan Verelst. B Weyn. Techniques for modeling workflows and their support for reuse[C]. Business Process Management,2000,1806:343-375.
62. W.M.P. van der Aalst. The application of Petri nets to workflow management[J]. The Journal of Circuits, System and Computers,1998,8(1):21-66.
63. J Li, Y Fan, and M C Zhou. Timing constraint workflow nets for workflow analysis[J]. IEEE Transaction on System, Man and Cybern,2003,33(2):179-193.
64. S Ling, H Schmidt. Time Petri nets for workflow modeling and analysis[C]. Proceeding of IEEE International Conference on System, Man and Cybernetics,2000,4:3039-3044.
65.吴哲辉.Petri网导论[M].北京：机械工业出版社,2006.
66. Y Y Du, C J Jiang, M C Zhou. Modeling and Analysis of Real-Time Cooperative Systems Using Petri Nets[J]. IEEE Transactions on Systems, Man and Cybernetics,2007,37(5): 643-654.
67. M Llorens, J Oliver. Structural and Dynamic Changes in Concurrent Systems: Reconfigurable Petri Nets. IEEE Computer Society,2004,53(9):1147-1158.
68. B Weber, S Rinderle, M Reichert. Change Support in Process Aware. Information Systems, 2008,66(3):438-466.
69. S H Ryu, F Casati, H Skogsrud et al. Supporting the Dynamic Evolution of Web Service Protocols in Service-Oriented Architectures. ACM Transactions on the Web,2008,2(2): 1-43.
70. B Benatallah, F Casati. Distributed and Parallel Database[M]. Springer issues on Web, 2002.
71. Y M Jiang, Y Liu. Stochastic Network Calculus[M]. Springer issues on Web,2008.
72. C S Chang. Performance Guarantees in Communication Networks. New York:Springer Verlag,2000.
2. WFMC. Workflow Management Coalition:The Workflow Reference Model. http://www.wfnc.org,1995.
3. W.M.P. van der Aalst. The Application of Petri Nets to Workflow Management [J]. The Journal of Circuit, System and Computers,1998,8(1):21-66.
4. W.M.P. van der Aalst. Verification of workflow nets[J]. Proceedings of 18th international Conference,1997,12(48):407-426.
5. A Ferseha. Qualitative and Quantitative Ailalysis of Business Workflow Using Generalized Stochastic petri Nets[J]. Proeeeding of 1994 Conference on workflow management challenges, Paradigms and Produets,1994:222-234.
6. N.R. Adam, V. Ailuri, W.K. Huang. Modeling and Analysis of Workflow Using Petri Nets[J]. Journal of Intelligent Information Systems,1998,33(10):1-29.
7. E. Badouel, J. Oliver. Reconfigurable Nets, a Class of High Level Petri Nets Supporting Dynamic Changes within Workflow Systems[M]. Publication Internet: IRISAPI 1163,1998:1-23.
8. W.M.P. van der Aalst, Arthur H.M., ter Hofstede. Verification of Workflow Task Structures:A Petri-Net-Based Approach[J]. Information Systems,2000,25(1):43-69.
9. 曹化工,杨曼红.基于对象Petri网的工作流过程定义[J].计算机辅助设计与图形学学报,2001,13(1)：15-18.
10.李建强,范玉顺.基于Petri网化简方法的工作流模型验证[J].信息与控制,2001,30(6)：492-497.
11.高军,王海洋.基于对象模型工作流的失败处理与失败恢复[J].软件学报,2001,12(5)：776-782.
12.刘婷,林闯,刘卫东.基于时间Petri网的工作流系统模型的线性推理[J],电子学报,2002,30(2)：245-248.
13.庞善臣.工作流的Petri网建模及模型分析[M],山东：山东科技大学,2004.
14.庞善臣,蒋昌俊.一种基于不变量结构分解的工作流性能分析方法[J].计算机学报, 2010,33(10)：908-918.
15. Raya, Halevi Y. Integrated communication and control systems:part Ⅰ-analysis and part Ⅱ-design consideration[J]. ASME J of Dynamic System Measurement & Control,1988: 367-381.
16. M.Y. CHOW, Y. Tipsuwan. Network-based control systems:a tutorial[C]. Proceeding of the 27th Annual Conference of IEEE on Industrial Electronics Society,2001:257-261.
17. A. Stothert, I. Macleod. Effect of timing jitter on distributed computer control system performance[C]. Proceeding of the 15th IFAC Workshop on Distributed Computer Control, 1998.
18. G.C. Walsh, O. Beldiman, L.G. Bushnell. Stability analysis of networked control system[C]. Proceeding of American Control Conference, 1999:2876-2880.
19. L. Vaquero, L. Rodero Marino, J. Caceres, et al. A break in the clouds:towards a cloud definition[J]. SIGCOMM Computer Communication Review,2009,39(1): 50-55.
20. J. Geelan. Twenty one experts define cloud computing.http://virtualization.sys-con.com/node/612375,2008.
21. R. Buyya, C.S. Yeo, S. Venugopal. Market-oriented cloud computing:Vision, hype, and reality for delivering it services as computing utilities[C]. Proceedings of the 2009 9th IEEE/ACM International Symposium on Cluster Computing and the Grid, 2009.
22.张杰.基于虚拟执行规则的工作流演进技术与实现[M],山东：山东科技大学,2009.
23. W.M.P van der Aalst, A.H.M ter Hofstede, B. Kiepuszewski, et al. Workflow Patterns[J]. Distributed and Parallel Databases,2003,14(1):5-51.
24. C Ellis, K Keddara, G Rozenberg. Dynamic Change within Workflow Systems[C]. Proceeding of the Conference on Organizational Computing Systems,1995:10-21.
25. G De Michelis, C.A Ellis. Computer Supported Cooperative Work and Petri Nets. Germany:Dagstuhl Castle,1996.
26. A Asperti, N Busi. Mobile Petri Nets[D]. Italy:University of Bologna,1996.
27. R Milner, J Parrow, D Walker. A calculus of mobile processes[J]. Information and Computation,1992,100(1):1-77.
28. C Fournet, G Gonthier. The reflexive chemical abstract machine and the join-calculus[C]. Proceeding of the 23rd ACM Symposium on Principle of Programming Languages,1996.
29. C Fournet, G Gonthier, J.J Levy. et al. A Calculus of Mobile Agents[J]. Proceedings of CONCUR,1996,1119:406-421.
30. R Valk. Self-Modifying Nets, a Natural Extension of Petri Nets[J]. Proceedings of Icalp,1978,62:464-476.
31. R Valk. Generalizations of Petri Nets[J]. Proceedings of MFCS,1981,118:140-155.
32. E Badouel, Darondeau. Stratified Petri Nets[J]. Proceedings of FCT,1997,12(79): 117-128.
33. E Badouel, M Llorens, J Oliver. Modeling Concurrent Systems:Reconfigurable Nets[J]. Proceedings of Parallel and Distributed Processing Techniques and Applications,2003,4:1568-1574.
34. T Murata. Petri Nets:Properties, Analysis and Applications[J]. Proceedings of IEEE, 1989,77(4):541-580.
35. J L Peterson. Petri net Theory and the Modeling of Systems[D]. New Jersey: Englewood Cliffs,1981.
36. P. Baldan. Modeling Concurrent Computations:From Contextual Petri Nets to Graph Grammars[D]. Italy:Univ. of Pisa,2000.
37. A Corradini. Concurrent Computing From Petri Nets to Graph Grammars. http://www.elsevier.nl/locate/entcs/volume2.html,1995:1-15.
38. Dirk A Taubner. Finite representations of CCS and TCSP programs by automata and Petri nets[M]. New York:Springer Verlag,1993.
39. J G Kobielus. Workflow Strategies[M]. Foster City:IDG Book WorldWide,1997.
40.罗海滨,范玉顺,吴登.工作流技术综述[J].软件学报,2000,11(7)：899-907.
41. W.M.P. van der Aalst. Three Good reasons for Using a Petri-net-based Workflow management System[C]. Proceedings of the International Working Conference on Information and Process ltegration in Enterprises,1996:179-201.
42. WFMC. The workflow reference model[M]. Brussels:Workflow Management Coalition, 1995.
43. C A Ellis, G J Nutt. Modeling and enactment of workflow systems[C]. Lecture Notes in Computer Science,1993,10:1-16.
44. M Papazogbu, A Delis, A Bouguettaya et al. Class library support for workflow environments and applications[J]. IEEE Transactions on Computers,1997.46(6): 673-686.
45. W.M.P. van der Aalst. Structural characterizations of sound workflow nets[M]. Eindhoven: Eindhoven University of Technology,1996.
46.杜玉越,蒋昌俊.基于工作流网的实时协同系统模拟技术[J].计算机学报,2004,27(4)：471-481.
47. A Carl, Petri. Communication with Automata[M]. New York:Griffiss Air Force Base, 1966.
48. K Jensen. Coloured Petri nets:basic concepts, analysis methods, and practical use[M]. New York:Springer Verlag,1992.
49. M K Molloy. Performance analysis using stochastic Petri nets[J]. IEEE Transaction On. Computers,1962,31(9):913-917.
50 L Chuang, D C Marinesc(?). Stoekistie high-level Petri nets and applications[J]. IEEE Transaction On Computers,1988,37(7):815-825.
51. J J P Tsai, S J Yang, Y H Chang. Timing Constrant Petri Nets and Their Application to Schedulability Analysis of Rea-Time System Specifications[J]. IEEE Transaction On Software Engineering,1995,21(1):32-49.
52.C G Looney. Fuzzy Petri Nets for Rule-Based Decision making[J]. IEEE Transaction On Systems,1988,18(1):178-183.
53. Lopez Benitez. Petri net based performance evaluation of distributed homogeneous task systems[J]. IEEE Transaction On Reliability,2000,49(2):188-198.
54. Z W Li, M C Zhou. Elementary siphons of Petri nets and their application to deadlock prevention in flexible manufacturing systems[J]. IEEE Transaction On Systems,2004, 34(1):38-51.
55. J Q Li, Y S Fan, M C Zhou. Performance modeling and analysis of workflow[J]. IEEE Transaction on Systems, Man and Cybernetics,2004,34(2):179-193.
56. T Murata. Petri nets:Properities. analysis and applications[J]. Proceeding of the IEEE, 1989,77(4):541-580.
57.吴哲辉.有界Petri网活性和公平性的分析与实现[J].计算机学报,1989,12(4)：267-278.
58.蒋昌俊.离散事件动态系统的PN机理论[M].北京：科学出版社,2000.
59.袁崇义. Petri网原理[M].北京：电子工业出版社,1998.
60.吴哲辉. Petri网行为描述、性质分析与系统模拟[M].北京：机械工业出版社,2003.
61. G K Janssens, B W Jan Verelst. B Weyn. Techniques for modeling workflows and their support for reuse[C]. Business Process Management,2000,1806:343-375.
62. W.M.P. van der Aalst. The application of Petri nets to workflow management[J]. The Journal of Circuits, System and Computers,1998,8(1):21-66.
63. J Li, Y Fan, and M C Zhou. Timing constraint workflow nets for workflow analysis[J]. IEEE Transaction on System, Man and Cybern,2003,33(2):179-193.
64. S Ling, H Schmidt. Time Petri nets for workflow modeling and analysis[C]. Proceeding of IEEE International Conference on System, Man and Cybernetics,2000,4:3039-3044.
65.吴哲辉.Petri网导论[M].北京：机械工业出版社,2006.
66. Y Y Du, C J Jiang, M C Zhou. Modeling and Analysis of Real-Time Cooperative Systems Using Petri Nets[J]. IEEE Transactions on Systems, Man and Cybernetics,2007,37(5): 643-654.
67. M Llorens, J Oliver. Structural and Dynamic Changes in Concurrent Systems: Reconfigurable Petri Nets. IEEE Computer Society,2004,53(9):1147-1158.
68. B Weber, S Rinderle, M Reichert. Change Support in Process Aware. Information Systems, 2008,66(3):438-466.
69. S H Ryu, F Casati, H Skogsrud et al. Supporting the Dynamic Evolution of Web Service Protocols in Service-Oriented Architectures. ACM Transactions on the Web,2008,2(2): 1-43.
70. B Benatallah, F Casati. Distributed and Parallel Database[M]. Springer issues on Web, 2002.
71. Y M Jiang, Y Liu. Stochastic Network Calculus[M]. Springer issues on Web,2008.
72. C S Chang. Performance Guarantees in Communication Networks. New York:Springer Verlag,2000.