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An improved approach for marking optimization of timed weighted marked graphs

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Abstract

Timed weighted marked graphs are a mathematical formalism suitable to model automated manufacturing systems in which synchronization and bulk services and arrivals appear, such as assembly lines and kanban systems. In this paper, we aim to develop practically efficient methods for the marking optimization of timed weighted marked graphs, a problem which consists in finding an initial resource assignment to minimize the cost of resources under a given requirement on the cycle time. Starting with a live initial marking, we first compute the critical places of a timed weighted marked graph by exploring an equivalent model called timed marked graph. Then, we develop an analytical method to identify the critical circuit of the system to which tokens will be iteratively added. Application to a real manufacturing system is finally provided, which shows that the developed approach is significantly more efficient than the existing ones.

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Notes

  1. As stated in [13], the problem has a solution iffb ≥ max{xi ⋅ δi, ti ∈ T}, where xi is the component of minimal T-semiflow corresponding to transition ti and δi is the fixed delay time of transition ti.

References

  • Bhattacharyya S, Murthy P, Lee E (1999) Synthesis of embedded software from synchronous dataflow specifications. J VLSI Signal Process 21(2):151–166

    Article  Google Scholar 

  • Campos J, Chiola G, Silva M (1991) Ergodicity and throughput bounds of Petri nets with unique consistent firing count vector. IEEE Trans Software Eng 17 (2):117–125

    Article  MathSciNet  Google Scholar 

  • Cottenceau B, Hardouin L, Boimond JL (2014) Modeling and control of weight-balanced timed event graphs in dioids. IEEE Trans Autom Control 59 (5):1219–1231

    Article  MathSciNet  Google Scholar 

  • Ghamarian AH, Geilen MCW, Stuijk S, Basten T, Moonen AJM, Bekooij MJG, Theelen BD, Mousavi MR (2006) Throughput analysis of synchronous data flow graph. In: Proc. 6th Int appl concur syst design, pp 25–36

  • Giua A, Piccaluga A, Seatzu C (2002) Firing rate optimization of cyclic timed event graphs. Automatica 38(1):91–103

    Article  MathSciNet  Google Scholar 

  • Govindarajan R, Gao GR (1995) Rate-optimal schedule for multi-rate dsp computations. J VLSI Signal Process 9(3):211–232

    Article  Google Scholar 

  • Gurobi (2018) Optimization Gurobi. [Online]. Available: http://www.gurobi.com/

  • He Z, Li ZW, Giua A (2014) Marking optimization of deterministic timed weighted marked graphs. In: Proc. 10th IEEE int. conf. autom. sci. eng.. Taipei, pp 413–418

  • He Z, Li ZW, Giua A (2017a) Cycle time optimization of deterministic timed weighted marked graphs by transformation. IEEE Trans Control Syst Technol 25 (4):1318–1330

    Article  Google Scholar 

  • He Z, Li ZW, Giua A (2017b) Optimization of deterministic timed weighted marked graphs. IEEE Trans Autom Sci Eng 14(2):1084–1095

    Article  Google Scholar 

  • He Z, Li ZW, Giua A (2018) Performance optimization for timed weighted marked graphs under infinite server semantics. IEEE Trans Autom Control 63(8):2573–2580

    Article  MathSciNet  Google Scholar 

  • Lafit S, Proth JM, Xie XL (1991) Marking optimization in timed event graphs. In: Proc. Int conf. appl. theory Petri nets. Springer, Berlin, pp 281–300

  • Lee E, Messerschmitt D (1987) Synchronous data flow. Proc IEEE 75 (9):1235–1245

    Article  Google Scholar 

  • Liu M, Wang SG, Zhou MC, Liu D, Al-Ahmari A, Wu NQ, Li ZW (2017) Deadlock and liveness characterization for a class of generalized Petri nets. Infor Sci 420:403–416

    Article  Google Scholar 

  • Ma ZY, Li ZW, Giua A (2015) Design of optimal Petri net controllers for disjunctive generalized mutual exclusion constraints. IEEE Trans Autom Control 60 (7):1774–1785

    Article  MathSciNet  Google Scholar 

  • Ma ZY, Li ZW, Giua A (2017) Characterization of admissible marking sets in Petri nets with conflicts and synchronizations. IEEE Trans Autom Control 62 (3):1329–1341

    Article  MathSciNet  Google Scholar 

  • Marchetti O, Munier A (2010) Complexity results for weighted timed event graphs. Discrete Optim 7(3):166–180

    Article  MathSciNet  Google Scholar 

  • Millo JV, De Simone R (2012) Periodic scheduling of marked graphs using balanced binary words. Theor Comput Sci 458:113–130

    Article  MathSciNet  Google Scholar 

  • Munier A (1992) Régime asymptotique optimal d’un graphe d’événements temporisé généralisé: Application à un problème d’assemblage. RAIRO-APII 27:487–513

    MATH  Google Scholar 

  • Murata T (1989) Petri nets: properties, analysis and applications. Proc IEEE 77 (4):541–580

    Article  Google Scholar 

  • Nakamura M, Silva M (1999a) Cycle time computation in deterministically timed weighted marked graphs. In: Proc. 7th IEEE int conf emerg technol factory autom, vol 2, pp 1037–1046

  • Nakamura M, Silva M (1999b) An iterative linear relaxation and tabu search approach to minimum initial marking problems of timed marked graphs. In: Proc. European control conf, pp 985–990

  • Sauer N (2003) Marking optimization of weighted marked graphs. Discrete Event Dyn Syst 13(3):245–262

    Article  MathSciNet  Google Scholar 

  • Sessego F, Giua A, Seatzu C (2008) HYPENS: a Matlab tool for timed discrete, continuous and hybrid Petri nets. In: Proc. Int conf appl theor Petri nets, pp 419–428

    Chapter  Google Scholar 

  • Sriram S, Bhattacharyya SS (2009) Embedded multiprocessors: scheduling and synchronization. CRC Press, Boca Raton

    Google Scholar 

  • Stuijk S, Geilen M, Basten T (2006) Exploring trade-offs in buffer requirements and throughput constraints for synchronous dataflow graphs. In: Proc. 43rd Design autom. conf., pp 899–904

  • Teruel E, Chrzastowski-Wachtel P, Colom JM, Silva M (1992) On weighted T-systems. Appl Theory Petri Nets 616:348–367

    MathSciNet  Google Scholar 

  • Tong Y, Li ZW, Seatzu C, Giua A (2016) On the equivalence of observation structures for Petri net generators. IEEE Trans Autom Control 61(9):2448–2462

    Article  MathSciNet  Google Scholar 

  • Tong Y, Li ZW, Seatzu C, Giua A (2018) Current-state opacity enforcement in discrete event systems under incomparable observations. Discrete Event Dyn Syst 28 (2):161–182

    Article  MathSciNet  Google Scholar 

  • van Schuppen JH, Silva M, Seatzu C (2012) Control of discrete-event systems-automata and Petri net perspectives. Lect Notes Control Inf Sci Springer 433:319–340

    MATH  Google Scholar 

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Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant Nos. 61803246, 61703321, and 61472295, the Science and Technology Development Fund, MSAR, under Grant No. 122/2017/A3, and the Natural Science Foundation of Shaanxi University of Science and Technology under Grant Nos. 2016BJ-15 and 2017BJ-39.

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Authors and Affiliations

  1. College of Mechanical and Electrical Engineering, Shaanxi University of Science and Technology, Xi’an, 710021, China

    Zhou He & Miao Liu

  2. School of Electro-Mechanical Engineering, Xidian University, Xi’an, 710071, China

    Ziyue Ma & Zhiwu Li

  3. Institute of Systems Engineering, Macau University of Science and Technology, Taipa, 999078, Macao

    Zhiwu Li

  4. Department of Electrical and Electronic Engineering, University of Cagliari, Cagliari, 09124, Italy

    Alessandro Giua

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  1. Zhou He
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  2. Miao Liu
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  3. Ziyue Ma
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  4. Zhiwu Li
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  5. Alessandro Giua
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Correspondence to Zhiwu Li.

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This article belongs to the Topical Collection: Special Issue on Smart Manufacturing - A New DES Frontier

Guest Editors: Rong Su and Bengt Lennartson

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He, Z., Liu, M., Ma, Z. et al. An improved approach for marking optimization of timed weighted marked graphs. Discrete Event Dyn Syst 29, 127–143 (2019). https://doi.org/10.1007/s10626-019-00278-w

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