Reliability evaluation of a multistate network subject to time constraint under routing policy

A multistate network is a stochastic network composed of multistate arcs in which each arc has several possible capacities and may fail due to failure, maintenance, etc. The quality of a multistate network depends on how to meet the customer's requirements and how to provide the service in time. The system reliability, the probability that a given amount of data can be transmitted through a pair of minimal paths (MPs) simultaneously under the time constraint, is a proper index to evaluate the quality of a multistate network. An efficient solution procedure is first proposed to calculate it. In order to further enhance the system reliability, the network administrator decides the routing policy in advance to indicate the first and the second priority pairs of MPs. The second priority pair of MPs takes charge of the transmission duty if the first fails. The system reliability under the routing policy can be subsequently evaluated.