Original scientific paper
https://doi.org/10.17535/crorr.2016.0003
The critical node problem in stochastic networks with discrete-time Markov chain
Gholam Hassan Shirdel
orcid.org/0000-0003-2759-4606
; Department of Mathematics, Faculty of Basic Science, University of Qom, Qom, Iran
Mohsen Abdolhosseinzadeh
; Department of Mathematics, Faculty of Basic Science, University of Qom, Qom, Iran
Abstract
The length of the stochastic shortest path is defined as the arrival probability from a source node to a destination node. The uncertainty of the network topology causes unstable connections between nodes. A discrete-time Markov chain is devised according to the uniform distribution of existing arcs where the arrival probability is computed as a finite transition probability from the initial state to the absorbing state. Two situations are assumed, departing from the current state to a new state, or waiting in the current state while expecting better conditions. Our goal is to contribute to determining the critical node in a stochastic network, where its absence results in the greatest decrease of the arrival probability. The proposed method is a simply application for analyzing the resistance of networks against congestion and provides some crucial information of the individual nodes. Finally, this is illustrated using networks of various topologies.
Keywords
stochastic network; discrete-time Markov chain; arrival probability; critical node problem
Hrčak ID:
157347
URI
Publication date:
5.4.2016.
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