Extend the quickest path problem to the system reliability evaluation for a stochastic-flow network

From the point of view of quality management, it is an important issue to reduce the transmission time in the network. The quickest path problem is to find the path in the network to send a given amount of data from the source to the sink such that the transmission time is minimized. Traditionally, this problem assumed that the capacity of each arc in the network is deterministic. However, the capacity of each arc is stochastic due to failure, maintenance, etc. in many real-life networks. This paper proposes a simple algorithm to evaluate the probability that d units of data can be sent from the source to the sink through the stochastic-flow network within T units of time. Such a probability is called the system reliability. The proposed algorithm firstly generates all lower boundary points for (d,T) and the system reliability can then be computed in terms of such points.