k-Terminal Reliability of Ad Hoc Networks Considering the Impacts of Node Failures and Interference

The ad hoc network is an emerging wireless communication technology. Recently, the reliability of ad hoc networks has attracted increasing attention in the literature. In this paper, the reliability of such networks is analyzed by incorporating the impacts of node failures and interference, because node failures usually obstruct the achievement of the intended function of a network, and interference is a key factor that degenerates the communication quality. We consider a general case that an ad hoc network is functional if at least k arbitrary nodes are operational and connected. Accordingly, two novel reliability indices, the generalized k-terminal reliability and the average generalized k-terminal reliability, are proposed, and their calculation methods are provided based on the Laplace transformation technique and the graph theory. For optimizing the design of an ad hoc network, a multiobjective optimization problem is investigated to maximize the reliability level and minimize the cost. The optimization problem is handled by the weighted sum method, and the most suitable solution is selected by the fuzzy satisfying approach. Finally, a numerical example is given to demonstrate the application of the proposed methods.