Yıl: 2020 Cilt: 33 Sayı: 4 Sayfa Aralığı: 749 - 764 Metin Dili: İngilizce DOI: 10.35378/gujs.669616 İndeks Tarihi: 16-06-2021

A Mathematical Model Using Time Elements for Timed-Arc Petri Nets

Öz:
In this work, a novel graphical and mathematical model is introduced for Timed-Arc Petri Nets. In this model, operation durations related to events are associated with arcs as firing durations. Time elements are introduced on the arcs of the model for monitoring tokens in operation durations (firing durations) of firing processes (events). In the model, the status of the system is represented as states consisting of remaining time vector for indicating the status of time elements and marking vector for indicating the status of places' state information. This feature of states allows to obtain reachability set enhanced with the time information and the timed reachability graph of the system. In this work, behavioral properties of the proposed model are also defined. Moreover, via considering real world systems, behavioral properties are analyzed and performance of the model is compared with Stretched Petri Nets which is a recently proposed type of Timed Petri Nets.
Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • [1] Cassandras, C., Lafortune, S., “Introduction to discrete event systems (second edition)”, Springer US, (2008).
  • [2] Zhou, M.C., DiCesare, F., “Petri net synthesis for discrete event control of manufacturing systems”, Springer US, (1993).
  • [3] Proth, J.M., Xie, X., “Petri nets a tool for design and management of manufacturing systems”, Wiley, (1996).
  • [4] Ho, Y. (Editor), “Discrete event dynamic systems: analyzing complexity and performance in the modern world”, IEEE Press, (1992).
  • [5] Zuberek, W.M., Timed Petri nets - definitions, properties, and applications”, Microelectronics and Reliability, 31(4): 627-644, (1991).
  • [6] Bowden, F., “A brief survey and synthesis of the roles of time in Petri nets”, Mathematical and Computer Modelling, 31: 55-68, (2000).
  • [7] Nielsen, M., Sassone, V., Srba, J., “Properties of distributed timed-arc Petri nets”, Proceedings of the 21th International Conference on Foundations of Software Technology and Theoretical Computer Science, 2245: 280–291, (2001).
  • [8] Akshay, S., Helouet, L., Phawade, R., “Combining free choice and time in Petri nets”, Journal of Logical and Algebraic Methods in Programming, 110: 1-29, (2020).
  • [9] Capkovic, F., “Modeling and control of discrete-event systems with partial non-determinism using Petri nets”, Acta Polytechnica Hungarica, 17(4): 47-66, (2020).
  • [10] Lefebvre, D., Daoui, C., “Control design for bounded partially controlled TPNs using timed extended reachability graphs and MDP”, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 50(6): 2273-2283, (2020).
  • [11] Li, L., Basile, F., Li, Z.W., “A reduced computation of state space to enforce GMECs and deadlockfreeness on TPN systems”, Proceedings of the 15th IFAC International Workshop on Discrete Event System, (2020).
  • [12] Wang, J., “Time Petri nets, theory and application”, Kluwer, (1998).
  • [13] Aybar, A., Iftar, A., “Deadlock avoidance controller design for timed Petri nets using stretching”, IEEE Systems Journal, 2(2): 178-188, (2008).
  • [14] Abdulla, P., Nylen, A., “Timed petri nets and BQOs”, Proceedings of the 22th International Conference on Application and Theory of Petri Nets, 53-70, (2001).
  • [15] Bolognesi, T., Lucidi, F., Trigila, S., “From timed Petri nets to timed lotos”, Proceedings of the 10th International Symposium on Protocol Specification, Testing and Verification, 395–408, (1990).
  • [16] Hanisch, H., “Analysis of place/transition nets with timed-arcs and its application to batch process control”, Proceedings of the 14th International Conference on Application and Theory of Petri Nets, 282-299, (1993).
  • [17] Jacobsen, L., Jacobsen, M., Moller, M.H., Srba, J., “Verification of timed-arc Petri nets”, Proceedings of the 37th International Conference on Current Trends in Theory and Practice of Computer Science, 6543: 46-72, (2011).
  • [18] Walter, W., “Timed petri-nets for modelling and analyzing protocols with real-time characteristics”, Proceedings of the 3rd IFIP International Workshop on Protocol Specification, Testing and Verification, 149-159, (1983).
  • [19] Bowden, F., “The modelling and analysis of command and control decision processes using extended time Petri nets: Chapter 6 Super-Class (Ph.D. thesis)”, University of Adelaide, (2001).
  • [20] Zhu, J., Denton, R., “Timed Petri nets and their application to communication protocol specification”, Proceedings of the 21th International Conference on Century Military Communications - What's Possible?' Military Communications, 195-199, (1988).
  • [21] Yufka, A., Ozkan, H.A., Aybar, A., “A formal method and novel graphical representation for deterministic timed-arc Petri nets”, Proceedings of the National Conference on Otomatik Kontrol Ulusal Toplantisi, 209-213, (2016).
  • [22] Yufka, A., Ozkan, H.A., Aybar, A., “Timed arc Petri nets: the time-element approach”, Proceedings of the 10th International Conference on Electrical and Electronics Engineering, 794-798, (2017).
  • [23] Yufka, A., Ozkan, H.A., Aybar, A., “Modeling basic components of railway systems using timed arc Petri nets”, Proceedings of the 5th International Conference on Control, Decision and Information Technologies, 427-432, (2018).
  • [24] Yufka, A., Ozkan, H.A., Aybar, A., “Timed arc Petri nets: the impulsive approach”, Proceedings of the 5th International Conference on Control, Decision and Information Technologies, 409-414, (2018).
  • [25] Yufka, A., Ozkan, H.A., Aybar, A., “Reachability set algorithms for timed-arc Petri nets”, International Journal of Industrial Electronics and Electrical Engineering, 7(5): 36-45, (2019).
  • [26] Aybar, A., Iftar, A., “Supervisory controller design to enforce some basic properties in timed-transition Petri nets using stretching”, Nonlinear Analysis: Hybrid Systems, 6: 712-729, (2012).
  • [27] Aybar, A., Iftar, A., “Supervisory controller design for timed Petri nets”, Proceedings of the 1st International Conference on System of Systems Engineering, 59-64, (2006).
  • [28] Aybar, A., Iftar, A., “Supervisory controller design to enforce some basic properties in timed Petri nets”, Proceedings of the 13th IFAC International Symposium on Information Control Problems in Manufacturing, 940-945, (2009).
  • [29] Aybar, A., Iftar, A., “Representation of the state of timed-place Petri nets using stretching”, Proceedings of the 4th IFAC International Workshop on Discrete-Event System Design, 42(21): 72- 77, (2009).
  • [30] Aybar, A., Iftar, A., “Supervisory controller design to enforce basic properties in timed-place Petri nets”, Proceedings of the 6th IFAC International Conference on Management and Control of Production and Logistics, 46(24): 486-492, (2013).
  • [31] Yufka, A., “Timed-arc Petri nets modeling and forbidden state control approach: chapter 7 algorithms for timed-arc Petri nets (Ph.D. thesis)”, Eskisehir Technical University, (2019).
  • [32] Murata, T., “Petri nets - properties, analysis and applications”, Proceedings of the IEEE, 77(4): 541- 580, (1989).
  • [33] Aybar, A., Iftar, A., “Decentralized supervisory controller design to avoid deadlock in Petri nets”, International Journal of Control, 76(13): 1285-1295, (2003).
  • [34] Aybar, A., Iftar, A., Ozkan, H.A., “Centralized and decentralized supervisory controller design to enforce boundedness, liveness, and reversibility in Petri nets”, International Journal of Control, 78(8): 537-553, (2005).
APA YUFKA A, APAYDIN OZKAN H, AYBAR A (2020). A Mathematical Model Using Time Elements for Timed-Arc Petri Nets. , 749 - 764. 10.35378/gujs.669616
Chicago YUFKA Alpaslan,APAYDIN OZKAN HANIFE,AYBAR AYDIN A Mathematical Model Using Time Elements for Timed-Arc Petri Nets. (2020): 749 - 764. 10.35378/gujs.669616
MLA YUFKA Alpaslan,APAYDIN OZKAN HANIFE,AYBAR AYDIN A Mathematical Model Using Time Elements for Timed-Arc Petri Nets. , 2020, ss.749 - 764. 10.35378/gujs.669616
AMA YUFKA A,APAYDIN OZKAN H,AYBAR A A Mathematical Model Using Time Elements for Timed-Arc Petri Nets. . 2020; 749 - 764. 10.35378/gujs.669616
Vancouver YUFKA A,APAYDIN OZKAN H,AYBAR A A Mathematical Model Using Time Elements for Timed-Arc Petri Nets. . 2020; 749 - 764. 10.35378/gujs.669616
IEEE YUFKA A,APAYDIN OZKAN H,AYBAR A "A Mathematical Model Using Time Elements for Timed-Arc Petri Nets." , ss.749 - 764, 2020. 10.35378/gujs.669616
ISNAD YUFKA, Alpaslan vd. "A Mathematical Model Using Time Elements for Timed-Arc Petri Nets". (2020), 749-764. https://doi.org/10.35378/gujs.669616
APA YUFKA A, APAYDIN OZKAN H, AYBAR A (2020). A Mathematical Model Using Time Elements for Timed-Arc Petri Nets. Gazi University Journal of Science, 33(4), 749 - 764. 10.35378/gujs.669616
Chicago YUFKA Alpaslan,APAYDIN OZKAN HANIFE,AYBAR AYDIN A Mathematical Model Using Time Elements for Timed-Arc Petri Nets. Gazi University Journal of Science 33, no.4 (2020): 749 - 764. 10.35378/gujs.669616
MLA YUFKA Alpaslan,APAYDIN OZKAN HANIFE,AYBAR AYDIN A Mathematical Model Using Time Elements for Timed-Arc Petri Nets. Gazi University Journal of Science, vol.33, no.4, 2020, ss.749 - 764. 10.35378/gujs.669616
AMA YUFKA A,APAYDIN OZKAN H,AYBAR A A Mathematical Model Using Time Elements for Timed-Arc Petri Nets. Gazi University Journal of Science. 2020; 33(4): 749 - 764. 10.35378/gujs.669616
Vancouver YUFKA A,APAYDIN OZKAN H,AYBAR A A Mathematical Model Using Time Elements for Timed-Arc Petri Nets. Gazi University Journal of Science. 2020; 33(4): 749 - 764. 10.35378/gujs.669616
IEEE YUFKA A,APAYDIN OZKAN H,AYBAR A "A Mathematical Model Using Time Elements for Timed-Arc Petri Nets." Gazi University Journal of Science, 33, ss.749 - 764, 2020. 10.35378/gujs.669616
ISNAD YUFKA, Alpaslan vd. "A Mathematical Model Using Time Elements for Timed-Arc Petri Nets". Gazi University Journal of Science 33/4 (2020), 749-764. https://doi.org/10.35378/gujs.669616