Finding shortest path in a combined exponential-gamma probability distribution arc length

We propose a dynamic programme to find the shortest path in a network having exponential and gamma probability distributions as arc lengths. Two operators of sum and comparison need to be adapted for the proposed dynamic programme. Convolution approach is used to sum any two probability distributions being employed in the dynamic programme. Generally, stochastic shortest path problems are treated using expected values of the arc probabilities, but in the proposed method using distributed observed past data as arc lengths, an integrated value is obtained as the shortest path length. The objective of this paper is to extend the shortest path problem in dynamic and stochastic networks where link travel times are defined as gamma or exponential probability distributions.