A Probability-Based Approach for Solving Shortest Path Problems in Gaussian Networks

A new approach to find the shortest path in Gaussian random networks is developed. The network's weights are assumed to be independent Gaussian variable with given mean and variance. First, Dijkastra's algorithm is used to find all possible paths from a source node to a destination node. Second, the weight for each path, sum of edges weights, is used and pairwise comparison between paths weight is computed in terms of probability. Analytical approach is presented to find the shortest path and two algorithms are proposed. Both algorithms require J - 1 steps to find the shortest path where J is the number of available paths in the network. Numerical analysis is also conducted to verify the analytical results where weights realizations are considered according to the pre-defined mean and variance. The numerical results have shown the tightness of the developed analytical algorithms. Furthermore, Different Network structures, in terms of number of nodes and edges, are also considered in the simulation.