Discrete Event Dynamic Systems

, Volume 18, Issue 1, pp 91–109 | Cite as

Minimizing Place Capacities of Weighted Event Graphs for Enforcing Liveness

  • Olivier Marchetti
  • Alix Munier-Kordon


This paper addresses the problem of minimizing place capacities of weighted event graphs in order to enforce liveness. Necessary and sufficient conditions of the solution existence are derived. Lower bounds of place capacities while preserving liveness are established and a polynomial algorithm is proposed to determine an initial marking leading to these lower bounds while preserving the liveness.


Petri nets Liveness Buffer requirement Manufacturing 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Adé M (1997) Data memory minimization for synchronous data flow graphs emulated on dsp-fpga targets. PhD Thesis, Université Catholique de LouvainGoogle Scholar
  2. Adé M, Lauwereins R, Peperstraete JA (1994) Buffer memory requirements in dsp applications. In: IEEE 5th international workshop on rapid system prototyping. Grenoble, France, pp 108–123Google Scholar
  3. Bhattacharyya SS, Murthy PK, Lee EA (1999) Synthesis of embedded software from synchronous dataflow specifications. J VLSI Signal Process (21):151–166Google Scholar
  4. Čubrić M, Panangaden P (1993) Minimal memory schedules for dataflow networks. In: CONCUR ’93, 4th international conference on concurrency theory. Lecture notes in computer science, vol 715, pp 368–383Google Scholar
  5. Chrzastowski-Wachtel P, Raczunas M (1993) Liveness of weighted circuits and the diophantine problem of Frobenius. FCT, pp 171–180Google Scholar
  6. Gaubert S (1990) An algebraic method for optimizing resources in timed event graphs. In: 9th Conference on analysis and optimization of systems. Lecture notes in computer science, vol 144, pp 957–966Google Scholar
  7. Giua A, Piccaluga A, Seatzu C (2002) Firing rate optimization of cyclic timed event graphs. Automatica 38(1):91–103MATHCrossRefMathSciNetGoogle Scholar
  8. Hillion H, Proth J-M (1989) Performance evaluation of a job-shop system using timed event graph. IEEE Trans Automat Contr 34(1):3–9MATHCrossRefMathSciNetGoogle Scholar
  9. Karp RM (1972) Reducibility among combinatorial problems. In: Miller RE, Thatcher JW (eds) Complexity of computer computations. Plenum, pp 85–103Google Scholar
  10. Karp RM, Miller RE (1966) Properties of a model for parallel computations: determinacy, termination, queueing. SIAM 14(63):1390–1411MATHMathSciNetGoogle Scholar
  11. Lee EA, Messerschmitt DG (1987a) Static scheduling of synchronous data flow programs for digital signal processing. IEEE Trans Comput C-36(1):24–35Google Scholar
  12. Lee EA, Messerschmitt DG (1987b) Synchronous data flow. IEEE Proc IEEE 75(9):1235–1245CrossRefGoogle Scholar
  13. Laftit S, Proth J-M, Xie X (1992) Optimization of invariant criteria for event graphs. IEEE Trans Automat Contr 37(5):547–555MATHCrossRefMathSciNetGoogle Scholar
  14. Murthy PK, Bhattacharyya SS, Lee EA (1997) Joint minimization of code and data for synchonous dataflow programs. J Formal Methods Syst Des 11(1):41–70CrossRefGoogle Scholar
  15. Marchetti O, Munier-Kordon A (2004) A sufficient condition for the liveness of weighted event graphs. Research report, LIP6, Laboratoire d’Informatique de Paris 6. Available at
  16. Munier A (1993) Régime asymptotique optimal d’un graphe d’événements temporisé: application à un probléme d’assemblage. RAIRO 27(5):171–180Google Scholar
  17. Munier A (1996) The basic cyclic scheduling problem with linear precedence constraints. Discret Appl Math 64(3):219–238MATHCrossRefMathSciNetGoogle Scholar
  18. Murthy PM (1996) Scheduling techniques for synchronous and multidimensional synchronous dataflow. PhD Thesis, University of California at BerkeleyGoogle Scholar
  19. Sauer N (2003) Marking optimization of weighted marked graphs. Discret Event Dyn Syst 13(3):245–262MATHCrossRefMathSciNetGoogle Scholar
  20. Teruel E, Chrzastowski P, Colom JM, Silva M (1992) On weighted T-Systems. In: Jensen K (ed) Application and theory of Petri nets, vol 616. Springer, pp 348–367Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Laboratoire d’Informatique de Paris 6–Département SoCUniversité Pierre et Marie CurieParis Cedex 05France

Personalised recommendations