Reliability Evaluation of Stochastic-Flow Network under Quickest Path and System Capacity Constraints

This paper proposes an algorithm to evaluate the probability that d units of data can be sent from the source node to the sink node through a valid group of paths on a network. The conditions of transmission are such that the transmission time of each path belonging to this valid group of paths does not exceed the specified upper bound T, and that the maximal capacity of that path is not less than the specified lower bound Cs (the required system capacity). Such a probability, which is called the system reliability, is denoted by R(d,Cs,T). Based on minimal paths, the algorithm generates all the lower boundary points for (d,Cs,T), and the system reliability can then be calculated in terms of all the lower boundary points for (d,Cs,T) by applying the inclusion-exclusion rule