Abstract
With the advance of technology, a large amount of information required to be computed become more and more complex. The level of information complexity can be regarded as a network system. Network reliability plays an important role in both practical and theoretic aspects. Hence, network reliability becomes a popular issue for many researches to involve in. However, network reliability evaluation is a highly complex problem, also seen as NP-hard problems. In the past, the quickest path network problem was based on only one commodity, and the multi-commodity flow problems were solved by assuming that the arcs of the flow network are deterministic. However, the capacity of each arc is stochastic in many real-life networks. The weighted multi-commodity multistate-flow quickest-path network (WMMQN) is a novel network composed of multistate components (arcs) capable of transmitting different types of commodities where capacity weight varies with arcs which come along with their own lead time. This paper proposes a simple algorithm to calculate the probability that a flow network with a source node satisfies a specified demand Dp=(d1,d2,…,dp) at the sink node within T units of time, where dq is the demand of commodity q. Such a probability is called the multi-commodity reliability and is dependent on the capacities of arcs. An example is given to illustrate how to generate all lower boundary points for (Dp; T) so as to compute the multi-commodity reliability.