Flow Generation for Stochastic-flow Networks with Demands as Real Number

Network reliability is concerned with the probability that the predetermined demand from multiple sources can be transmitted through the stochastic-flow network (SFN) successfully. The minimal capacity vectors (MCVs) which are the minimally required capacity for each arc are used to network reliability calculation. Every MCV is transformed from the flow vectors satisfying predetermined demands based on minimal paths (MPs). However, the demands are set as integers for flow vector generation in the previous studies. In fact, demand might be the positive real number in the practical transmission. In this paper, a concept of the minimal transmission unit is proposed to search the flow vectors for demands as the positive real number. It can reduce the range of the flow search. Then an algorithm for flow vector generation is developed to efficiently deal with demands as the positive real number. A simple case shows that the proposed algorithm is reasonable.