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Hitting Times in Markov Chains with Restart and their Application to Network Centrality

Author

Listed:
  • Konstantin Avrachenkov

    (Inria Sophia Antipolis)

  • Alexey Piunovskiy

    (University of Liverpool)

  • Yi Zhang

    (University of Liverpool)

Abstract

Motivated by applications in telecommunications, computer science and physics, we consider a discrete-time Markov process with restart. At each step the process either with a positive probability restarts from a given distribution, or with the complementary probability continues according to a Markov transition kernel. The main contribution of the present work is that we obtain an explicit expression for the expectation of the hitting time (to a given target set) of the process with restart. The formula is convenient when considering the problem of optimization of the expected hitting time with respect to the restart probability. We illustrate our results with two examples in uncountable and countable state spaces and with an application to network centrality.

Suggested Citation

  • Konstantin Avrachenkov & Alexey Piunovskiy & Yi Zhang, 2018. "Hitting Times in Markov Chains with Restart and their Application to Network Centrality," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1173-1188, December.
    • Handle: RePEc:spr:metcap:v:20:y:2018:i:4:d:10.1007_s11009-017-9600-5
    DOI: 10.1007/s11009-017-9600-5
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    References listed on IDEAS

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    1. Maurer, Sebastian M. & Huberman, Bernardo A., 2001. "Restart strategies and Internet congestion," Journal of Economic Dynamics and Control, Elsevier, vol. 25(3-4), pages 641-654, March.
    2. Nummelin, Esa & Tuominen, Pekka, 1982. "Geometric ergodicity of Harris recurrent Marcov chains with applications to renewal theory," Stochastic Processes and their Applications, Elsevier, vol. 12(2), pages 187-202, March.
    3. Søren Asmussen & Pierre Fiorini & Lester Lipsky & Tomasz Rolski & Robert Sheahan, 2008. "Asymptotic Behavior of Total Times for Jobs That Must Start Over if a Failure Occurs," Mathematics of Operations Research, INFORMS, vol. 33(4), pages 932-944, November.
    4. Miquel Montero & Axel Masó-Puigdellosas & Javier Villarroel, 2017. "Continuous-time random walks with reset events," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 90(9), pages 1-10, September.
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    Cited by:

    1. Dmitrii Silvestrov & Sergei Silvestrov & Benard Abola & Pitos Seleka Biganda & Christopher Engström & John Magero Mango & Godwin Kakuba, 2021. "Perturbed Markov Chains with Damping Component," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 369-397, March.

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