On performance evaluation for a multistate network under spare routing

This paper focuses on a multistate network composed of multistate edges to study the relationship between transmission reliability and spare routing. In the network, each edge has several possible capacities and may fail due to failure, maintenance, etc. Hence, the minimum transmission time to send a given amount of data is not a fixed number. The spare routing is a transmission rule which indicates the first and the second priority pairs of minimal paths. The second one takes charge of the transmission duty if the first one is out of order. We evaluate the probability that the required amount of data can be sent through a pair of minimal paths simultaneously under both time threshold and budget constraint. Such a probability is named transmission reliability which can be regarded as a performance index to measure the transmission capability of a multistate network. An efficient solution procedure is thus proposed to generate all lower boundary points meeting the constraints. The transmission reliability is calculated in terms of such points.