Stochastic Timed Automata

  • Christos G. Cassandras
  • Stéphane Lafortune
Part of the The Kluwer International Series on Discrete Event Dynamic Systems book series (DEDS, volume 11)


In practice, systems always operate in environments which are constantly plagued by uncertainty. This is especially true in dealing with DES, which, by their nature, often involve unpredictable human actions and machine failures. The process of resource sharing (which provides an important motivation for studying DES) is inherently characterized by such unpredictability: changing user demand, computer breakdowns, inconsistencies in human decision making, etc. While the untimed (or logical) models considered in Chapters 2 to 4 do account for “all possible behaviors” of the system, their use is limited to logical (or qualitative) performance objectives. Deterministic timed models of the type considered in Chapter 5 certainly contribute to our basic understanding of some quantitative properties of the dynamic behavior of a system (for instance, the periodic behavior of systems that can be modeled as marked graphs). But their use is limited since models with deterministic clock structures only capture a single timed string of events (or states), or, in other words, a single sample path of the system. If we are to develop either descriptive or prescriptive techniques for evaluating performance and for “optimally” controlling timed DES with respect to quantitative performance measures and in the presence of uncertainty, more refined models that incorporate stochastic elements are required.


Service Time Poisson Process Queue Length Sample Path Interarrival Time 
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.


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Selected References

Review of Probability and Stochastic Processes

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Queueing Models

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Stochastic Timed Automata

  1. Glynn, P., “A GSMP Formalism for Discrete Event Systems,” Proceedings of the IEEE, Vol. 77, No. 1, pp. 14–23, 1989.CrossRefGoogle Scholar
  2. Ho, Y.C., and X. Cao, Perturbation Analysis of Discrete Event Dynamic Systems, Kluwer Academic Publishers, Boston, 1991.zbMATHCrossRefGoogle Scholar
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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Christos G. Cassandras
    • 1
  • Stéphane Lafortune
    • 2
  1. 1.Boston UniversityUSA
  2. 2.The University of MichiganUSA

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