Reliability evaluation of a multistate network under routing policy

Multistate network is a stochastic network composed with multistate arcs in which each arc has several possible capacities and may fail due to failure, maintenance, etc. Different from the deterministic case, the minimum transmission time in a multistate network is not a fixed number. We evaluate the probability that a given amount of commodities can be sent through a pair of minimal paths simultaneously under the time constraint. Such a probability is named the system reliability. An efficient solution procedure is first proposed to calculate it. In order to enhance the system reliability, the network administrator decides the routing policy in advance to indicate the first and the second priority pairs of minimal paths. Subsequently, we evaluate the system reliability under the routing policy. An easy criterion is then proposed to derive an ideal routing policy with higher system reliability. We can treat the system reliability as a performance index to measure the transmission ability of a multistate network such as logistics, urban traffic, information, telecommunication systems, etc.