The critical node problem in stochastic networks with discrete-time Markov chain

• Main Authors: Gholam Hassan Shirdel, Mohsen Abdolhosseinzadeh
• Format: Article
• Language: English
• Published: Croatian Operational Research Society 2016-04-01
• Series: Croatian Operational Research Review
• Subjects: stochastic network; discrete-time Markov chain; arrival probability; critical node problem
• Online Access: http://hrcak.srce.hr/index.php?show=clanak&id_clanak_jezik=231896

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.