Calculation of minimal capacity vectors through k minimal paths under budget and time constraints

Abstract

Abstract Reducing the transmission time is an important issue for a flow network to transmit a given amount of data from the source to the sink. The quickest path problem thus arises to find a single path with minimum transmission time. More specifically, the capacity of each arc is assumed to be deterministic. However, in many real-life networks such as computer networks and telecommunication networks, the capacity of each arc is stochastic due to failure, maintenance, etc. Hence, the minimum transmission time is not a fixed number. Such a network is named a stochastic-flow network. In order to reduce the transmission time, the network allows the data to be transmitted through k minimal paths simultaneously. Including the cost attribute, this paper evaluates the probability that d units of data can be transmitted under both time threshold T and budget B . Such a probability is called the system reliability. An efficient algorithm is proposed to generate all of lower boundary points for ( d , T , B ), the minimal capacity vectors satisfying the demand, time, and budget requirements. The system reliability can then be computed in terms of such points. Moreover, the optimal combination of k minimal paths with highest system reliability can be obtained.