Most existing work on survivability in mobile ad-hoc networks(MANETs) focuses on two dimensional(2D) networks.However,many real applications run in three dimensional(3D) networks,e.g.,climate and ocean monitoring,and air defense systems.The impact on network survivability due to node behaviors was presented,and a quantitative analysis method on survivability was developed in 3D MANETs by modeling node behaviors and analyzing 3D network connectivity.Node behaviors were modeled by using a semi-Markov process.The node minimum degree of 3D MANETs was discussed.An effective approach to derive the survivability of k-connected networks was proposed through analyzing the connectivity of 3D MANETs caused by node misbehaviors,based on the model of node isolation.The quantitative analysis of node misbehaviors on the survivability in 3D MANETs is obtained through mathematical description,and the effectiveness and rationality of the proposed approach are verified through numerical analysis.The analytical results show that the effect from black and gray attack on network survivability is much severer than other misbehaviors.
