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Stochastic Approximation of Global Reachability Probabilities of Markov Population Models

  • Luca Bortolussi
  • Roberta Lanciani
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8721)

Abstract

Complex computer systems, from peer-to-peer networks to the spreading of computer virus epidemics, can often be described as Markovian models of large populations of interacting agents. Many properties of such systems can be rephrased as the computation of time bounded reachability probabilities. However, large population models suffer severely from state space explosion, hence a direct computation of these probabilities is often unfeasible. In this paper we present some results in estimating these probabilities using ideas borrowed from Fluid and Central Limit approximations. We consider also an empirical improvement of the basic method leveraging higher order stochastic approximations. Results are illustrated on a peer-to-peer example.

Keywords

Stochastic model checking reachability hitting times fluid approximation central limit approximation linear noise approximation 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Luca Bortolussi
    • 1
    • 2
  • Roberta Lanciani
    • 3
  1. 1.DMGUniversity of TriesteItaly
  2. 2.CNR/ISTIPisaItaly
  3. 3.IMT LuccaItaly

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