Quickest path problems in stochastic-flow networks with time constraint: A fast and reliable solution

Abstract

Quickest path problems (QPPs) have gained considerable attention of researchers in the last two decades due to their enormous applications in a variety of networks such as communication and transportation networks. Most of such networks are classified as stochastic flow network due to their changing states with time. Algorithms have been proposed in the literature to evaluate the probability that a specified amount of data could be transmitted from a source to the sink through a stochastic flow network within a given amount of time. In order to reduce the transmission time while maintaining system reliability, Lin [27, 28] has proposed using multiple disjoint paths for transmission of data/items by distributing the load into two or more segments. The algorithm presented in [26] efficiently solves the problem of finding the most reliable pair of paths among all available pairs from a source to the sink. However, the process of determining the most reliable pair of disjoint paths consumes considerable amount of time and it is practically non-feasible to wait for pair of disjoint paths with highest probability in order to transmit the data/items. In view of this, we have proposed a threshold of probability and pairs of paths that cross the threshold are considered for communication of data. Instead of a globally optimized solution, we focus on minimizing the time to compute the system reliability. We have also presented a comparison of the performance of the proposed method with the method presented in [27] for different graphs. The results show marked improvement in the system overhead for reliability computation without much compromise on the quality of service, since the pair satisfies a minimum reliability constraint. The method is particularly useful for applications involving large networks.