Using Max-Plus Algebra for the Evaluation of Stochastic Process Algebra Prefixes

  • Lucia Cloth
  • Henrik Bohnenkamp
  • Boudewijn Haverkort
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2165)


In this paper, the concept of complete finite prefixes for process algebra expressions is extended to stochastic models. Events are supposed to happen after a delay that is determined by random variables assigned to the preceding conditions. Max-plus algebra expressions are shown to provide an elegant notation for stochastic prefixes not containing any decisions. Furthermore, they allow for the computation of performance measures. The derivation of the so called k-th occurrence times is shown in detail.


Cycle Time Event Class Occurrence Time Recurrence Time Discrete Event System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    F. Baccelli, A. Jean-Marie, and Zhen Liu. A survey on solution methods for task graph models. In N. Gotz, U. Herzog, and M. Rettelbach, editors, Proc. of the QMIPS-Workshop on Formalism, Principles and State-of-the-art. Arbeitsberichte des IMMD 26(14). Universität Erlangen, 1993.Google Scholar
  2. 2.
    F. L. Baccelli, G. Cohen, G. J. Olsder, and J.-P. Quadrat. Synchronization and Linearity. An Algebra for Discrete Event Systems. John Wiley & Sons, 1992.Google Scholar
  3. 3.
    E. Brinksma, J.-P. Katoen, R. Langerak, and D. Latella. A stochastic causality-based process algebra. The Computer Journal, 38(7):552–565, 1995.CrossRefGoogle Scholar
  4. 4.
    L. Cloth. Complete finite prefix for stochastic process algebra. Master’s thesis, RWTH Aachen, Department of Computer Science, 2000. available at
  5. 5.
    J. Esparza, S. Romer, and W. Vogler. An improvement of McMillan’s unfolding algorithm. In T. Margaria and B. Steffen, editors, Proc. of TACAS’96, LNCS 1055, pages 87–106. Springer, 1996.Google Scholar
  6. 6.
    P. Glynn. A GSMP formalism for discrete event simulation. Proc. of the IEEE, 77(1):14–23, 1989.CrossRefGoogle Scholar
  7. 7.
    J.-P. Katoen. Quantitative and Qualitative Extensions of Event Structures. PhD thesis, Universiteit Twente, 1996.Google Scholar
  8. 8.
    J.-P. Katoen, E. Brinksma, D. Latella, and R. Langerak. Stochastic simulation of event structures. In M. Ribaudo, editor, Proc. of PAPM 1996, pages 21–40. C.L.U.T. Press, 1996.Google Scholar
  9. 9.
    R. Langerak and H. Brinksma. A complete finite prefix for process algebra. In CAV’99, LNCS 1663, pages 184–195. Springer, 1999.Google Scholar
  10. 10.
    K. L. McMillan. Symbolic Model Checking, chapter 9: A Partial Order Approach, pages 153–167. Kluwer, 1993.Google Scholar
  11. 11.
    V. Mertsiotakis and M. Silva. A throughput approximation algorithm for decision free processes. In M. Ribaudo, editor, Proc. of PAPM 1996, pages 161–178. C.L.U.T. Press, 1996.Google Scholar
  12. 12.
    G. Olsder, J. Resing, R. de Vries, M. Keane, and G. Hooghiemstra. Discrete event systems with stochastic processing times. IEEE Transactions on Automatic Control, 35(3):299–302, 1990.zbMATHCrossRefGoogle Scholar
  13. 13.
    T. C. Ruys, R. Langerak, J.-P. Katoen, D. Latella, and M. Massink. First passage time analysis of stochastic process algebra using partial orders. In T. Margaria and W. Yi, editors, Proc. of TACAS 2001, LNCS 2031, pages 220–235. Springer, 2001.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Lucia Cloth
    • 1
  • Henrik Bohnenkamp
    • 1
  • Boudewijn Haverkort
    • 1
  1. 1.Department of Computer ScienceLaboratory for Performance Evaluation and Distributed SystemsAachen

Personalised recommendations