Abstract
A genetic algorithm is presented to find the arrival probability in a directed acyclic network with stochastic parameters, that gives more reliability of transmission flow in delay sensitive networks. Some sub-networks are extracted from the original network, and a connection is established between the original source node and the original destination node by randomly selecting some local source and the local destination nodes. The connections are sorted according to their arrival probabilities and the best established connection is determined with the maximum arrival probability. There is an established discrete time Markov chain in the network. The arrival probability to a given destination node from a given source node in the network is defined as the multi-step transition probability of the absorbtion in the final state of the established Markov chain. The proposed method is applicable on large stochastic networks, where the previous methods were not. The effectiveness of the proposed method is illustrated by some numerical results with perfect fitness values of the proposed genetic algorithm.
Highlights
Established connections in networks should be reliable to transmit flow from a source node to a destination node especially in delay sensitive networks
Our criterion to evaluation of the connections from the source node toward the destination node in the network is presented as the arrival probability, which is obtained by the established discrete time Markov chain (DTMC) in the network
The arrival probability from a given source node to a given destination node was computed according to the probability of transition from the initial state to the absorbing state by multi-step transition probability in DTMC
Summary
Established connections in networks should be reliable to transmit flow from a source node to a destination node especially in delay sensitive networks. Our criterion to evaluation of the connections from the source node toward the destination node in the network is presented as the arrival probability, which is obtained by the established discrete time Markov chain (DTMC) in the network. The maximum arrival probability from a given source node to a given destination node is computed according to known discrete distribution probabilities of leaving or waiting in nodes, and a DTMC stochastic process is used to model the problem rather than dynamic programming or stochastic programming. The established discrete time Markov chain Kulkarni (1986), Azaron and Modarres (2005) considered an acyclic directed network They produced a CTMC and in each transition from one state to another possibly more than one node can be added.
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