Research On The Problem Of Diameter-Constrained Active Network Reliability

With the rapid development of communication technology and computer network, network reliability model is widely used in industry, communication and transportation systems. As an important parameter of network, the evaluation of network reliability is highly significant. Combined graph theory and probabilistic statistics theory, this paper mainly investigates the diameter-constrained active network reliability model, and obtains some useful conclusions as follows:1. As regards the diameter-constrained ST network, calculation expressions of network reliability are given when parameter D=1and D=2, and a new method of reducing network is provided for the case of D=3. As for D≥3, new reliability recursive bounds are given.2. As for the diameter-constrained SKT network, firstly, decision theorem about irrelevant edges in ST networks is extended, and some decision theorems about irrelevant edges and nodes are got in diameter-constrained SKT network. Then irrelevant edges reduction algorithm and factoring decomposition algorithm based on diameter-constrained are listed, an example is used to demonstrate the effectiveness of the algorithms. Finally, in special case when D=2in SKT network, the concepts of stratified graph and isomorphic graph are introduced, a new method of reducing networks is proposed, and it can greatly improve the efficiency of nodes and edges’reduction in a network.3. Regarding the diameter-constrained SKT network, firstly, the definitions of D-K node-cut set and minimal D-K node-cut set are proposed, and then make some demonstrations about the existence of a SKT network’s minimal D-K node-cut sets. Finally, this paper gives a new way to get the upper bound of a SKT network, and Arpanet is used to verify the effectiveness of the given upper bound.