Symbolically Quantifying Response Time in Stochastic Models Using Moments and Semirings View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2018

AUTHORS

Hugo Bazille , Eric Fabre , Blaise Genest

ABSTRACT

We study quantitative properties of the response time in stochastic models. For instance, we are interested in quantifying bounds such that a high percentage of the runs answers a query within these bounds. To study such problems, computing probabilities on a state-space blown-up by a factor depending on the bound could be used, but this solution is not satisfactory when the bound is large. In this paper, we propose a new symbolic method to quantify bounds on the response time, using the moments of the distribution of simple stochastic systems. We prove that the distribution (and hence the bounds) is uniquely defined given its moments. We provide optimal bounds for the response time over all distributions having a pair of these moments. We explain how to symbolically compute in polynomial time any moment of the distribution of response times using adequately-defined semirings. This allows us to compute optimal bounds in parametric models and to reduce complexity for computing optimal bounds in hierarchical models. More... »

PAGES

403-419

References to SciGraph publications

  • 2003-06-24. Symbolic Synthesis of Finite-State Controllers for Request-Response Specifications in IMPLEMENTATION AND APPLICATION OF AUTOMATA
  • 2014. Accelerating Parametric Probabilistic Verification in QUANTITATIVE EVALUATION OF SYSTEMS
  • 2016. Generalized Method of Moments for Stochastic Reaction Networks in Equilibrium in COMPUTATIONAL METHODS IN SYSTEMS BIOLOGY
  • 2005. Symbolic and Parametric Model Checking of Discrete-Time Markov Chains in THEORETICAL ASPECTS OF COMPUTING - ICTAC 2004
  • 2008. Introduction to Discrete Event Systems in NONE
  • 2015. Adaptive Moment Closure for Parameter Inference of Biochemical Reaction Networks in COMPUTATIONAL METHODS IN SYSTEMS BIOLOGY
  • 2011. The Complexity of Request-Response Games in LANGUAGE AND AUTOMATA THEORY AND APPLICATIONS
  • Book

    TITLE

    Foundations of Software Science and Computation Structures

    ISBN

    978-3-319-89365-5
    978-3-319-89366-2

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-319-89366-2_22

    DOI

    http://dx.doi.org/10.1007/978-3-319-89366-2_22

    DIMENSIONS

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