On transmission time through k minimal paths of a capacitated-flow network

The quickest path problem is to minimize the transmission time for sending a specified amount of data through a single minimal path. Two deterministic attributes are involved herein; the capacity and the lead time. However, in many real-life networks such as computer systems, urban traffic systems, etc., the arc capacity should be multistate due to failure, maintenance, etc. Such a network is named a capacitated-flow network. The minimum transmission time is thus not a fixed number. This paper is mainly to evaluate system reliability that d units of data can be transmitted through k minimal paths under time constraint T. A simple algorithm is proposed to generate all minimal capacity vectors meeting the demand and time constraints. The system reliability is subsequently computed in terms of such vectors. The optimal k minimal paths with highest system reliability can further be derived.