QUICK RELIABILITY ASSESSMENT OF TWO-COMMODITY TRANSMISSION THROUGH A CAPACITATED-FLOW NETWORK

Each arc in a capacitated-flow network has discrete and multiple-valued random capacities. Many studies evaluated the probability named system reliability herein that the maximum flow from source to sink is no less than a demand d for a capacitated-flow network. Such studies only considered commodities of a same type transmitted throughout the network. Many real-world systems allow commodities of multiple types to be transmitted simultaneously, especially in the case that different type of commodity consumes the arc's capacity differently. For simplicity, this article assesses the system reliability for a two-commodity case as follows. Given the demand (d(1), d(2)), where d(1) and d(2) are the demands of commodity 1 and 2 at the sink, respectively, an algorithm is proposed to find out all lower boundary points for (d(1), d(2)). The system reliability can be computed quickly in terms of such points. The computational complexity of the proposed algorithm is also analyzed.