Network Reliability of a Time-Based Multistate Network Under Spare Routing With $p$ Minimal Paths

This paper constructs a time-based multistate network composed of multistate edges to study network reliability. Each edge involves three attributes: variable capacity, lead time, and cost. The transmission time from the source to the sink is thus not fixed. Two problems are discussed in this paper. First, we evaluate the probability that the given amount of data can be sent through minimal paths simultaneously under both time threshold, and budget constraint. Such a probability we term network reliability. It can be treated as a performance index to measure the transmission ability of a complex multistate system. Then, the calculation procedures are proposed to make solution. To enhance network reliability, the network administrator decides the spare routing in advance to indicate the first and the second priority minimal paths. The second path will be responsible for the transmission duty if the first fails. The second problem is addressed to evaluate network reliability according to the spare routing.