SUMMARY
Under the assumption that each branch’ capacity of the network is deterministic, the quickest path problem is to find a path sending a specific of data from the source to the sink such that the transmission time is minimized. However, in many real-life networks such as computer systems, the capacity of each branch is stochastic with a transmission accurate rate. Such a network is named a stochastic computer network. Hence, we try to compute the probability that d units of data can be sent through the stochastic computer network within both the time and accuracy rate constraints according to a routing scheme. Such a probability is a performance indicator to provide to managers for improvement. This paper mainly proposes an efficient algorithm to find the minimal capacity vector meeting such requirements. The system reliability with respect to a routing scheme then can be calculated.