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Formal Methods for the Design of Real-Time Systems

SFM-RT 2004: Formal Methods for the Design of Real-Time Systems pp 132–180Cite as

Real Time and Stochastic Time

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3185))

Abstract

We present a theory for the design and analysis of concurrent/distributed systems with real-time and stochastic time aspects. We start by presenting the model of Interactive Generalized Semi-Markov Processes (IGSMP): a compositional model for representing the class of stochastic processes known as Generalised Semi-Markov Processes (GSMPs), i.e. probabilistic timed systems where durations of delays are expressed by random variables with a general probability distribution. Technically, IGSMPs extend GSMPs with action transitions representing the ability of a process to interact with another process. Then, we introduce the calculus of Interactive Generalized Semi-Markov Processes, a stochastic process algebra which produces IGSMPs as semantic models of its terms. This is obtained by expressing the concurrent execution of delays through a simple probabilistic extension of Van Glabbeek and Vaandrageer’s ST semantics based on dynamic names. We also present observational equivalence over IGSMPs, we observe that it is a congruence for all the operators of the calculus and we produce an axiomatization for this equivalence which is complete over finite-state strongly guarded processes. Finally, we present a case study on queuing systems G/G/1/q.

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Author information

Authors and Affiliations

  1. Dipartimento di Scienze dell’Informazione, Università di Bologna, Mura Anteo Zamboni 7, 40127, Bologna, Italy

    Mario Bravetti

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  1. Mario Bravetti
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Editors and Affiliations

  1. Istituto di Scienze e Tecnologie dell’Informazione, Università di Urbino “Carlo Bo”, Italy

    Marco Bernardo

  2. Dipartimento di Matematica ed Informatica, University of Camerino, Via Madonna delle Carceri 9, 62032, Camerino, Italy

    Flavio Corradini

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Bravetti, M. (2004). Real Time and Stochastic Time. In: Bernardo, M., Corradini, F. (eds) Formal Methods for the Design of Real-Time Systems. SFM-RT 2004. Lecture Notes in Computer Science, vol 3185. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30080-9_5

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  • DOI: https://doi.org/10.1007/978-3-540-30080-9_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23068-7

  • Online ISBN: 978-3-540-30080-9

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