The probable lack of some arcs and nodes in the stochastic networks is considered in this paper, and its effect is shown as the arrival probability from a given source node to a given sink node. A discrete time Markov chain with an absorbing state is established in a directed acyclic network. Then, the probability of transition from the initial state to the absorbing state is computed. It is assumed to have some wait states, if there is a physical connection but not any immediate communication between two nodes. The Numerical results show, the critical nodes and arcs are detected by the proposed method and it can be used to anticipate probable congestion in communication and transportation networks.
Shirdel, G. H., & Abdolhosseinzadeh, M. (2014). Arrival probability in the stochastic networks with an established discrete time Markov chain. Journal of Mathematical Modeling, 2(1), 74-89.
MLA
Gholam Hassan Shirdel; Mohsen Abdolhosseinzadeh. "Arrival probability in the stochastic networks with an established discrete time Markov chain". Journal of Mathematical Modeling, 2, 1, 2014, 74-89.
HARVARD
Shirdel, G. H., Abdolhosseinzadeh, M. (2014). 'Arrival probability in the stochastic networks with an established discrete time Markov chain', Journal of Mathematical Modeling, 2(1), pp. 74-89.
VANCOUVER
Shirdel, G. H., Abdolhosseinzadeh, M. Arrival probability in the stochastic networks with an established discrete time Markov chain. Journal of Mathematical Modeling, 2014; 2(1): 74-89.
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