Abstract
The quickest path problem is to find a path to send a given amount of data from the source node to the sink node with minimum transmission time. In order to conform to the real world systems such as distribution systems and supply chain management system, we assume the capacity of each arc is stochastic (multi-state). In this study, (1) we propose a new algorithm to evaluate the probability that d units of data can be sent from the source node to the sink node through the multi-state quickest path flow network within T units of time. The proposed algorithm based on the k shortest paths algorithm only has less time complexity than the best-known algorithms which were required to solve the NP-hard problem to find all minimal paths in advance. (2) Add cost constraint and extend the problem to evaluate the probability that d units of data can be sent from the source node to the sink node through the multi-state quickest path flow network within time (T) and total cost (c) constraints. Two examples is given to illustrate how multi-state quickest path flow network reliability is evaluated using the proposed algorithm.