On the Probability of K-Connectivity in Wireless Ad Hoc Networks Under Different Mobility Models

Abstract

We compare the probability of k-Connectivity of an ad hoc network under Random Way Point (RWP), City Section and Manhattan mobility models. A Network is said to be k-Connected if there exists at least k edge disjoint paths between any pair of nodes in that network at any given time and velocity. Initially, for each of the three mobility models, the movement of the each node in the ad hoc network at a given velocity and time are captured and stored in the Node Movement Database (NMDB). Using the movements in the NMDB, the location of the node at a given time is computed and stored in the Node Location Database (NLDB). A weighted graph is created using the location of the nodes from NLDB, which is converted into a residual graph. The k-Connectivity of this residual graph is obtained by running Ford-Fulkerson’s algorithm on it. Ford Fulkerson’s algorithm computes the maximum flow of a network by recording the flows assigned to different routes from each node to all the other nodes in the network. When run for a particular source-destination pair (s, d) pair on a residual network graph with unit edge weights as capacity, the maximum flow determined by Ford-Fulkerson’ algorithm is the number of edge disjoint s-d paths on the network graph. Simulations show that the RWP model yields the highest probability of k-Connectivity compared to City Section and Manhattan mobility models for a majority of different node densities and velocities considered. Simulation results also show that, for all the three mobility models, as the k value increases, the probability of k-Connectivity decreases for a given density and velocity and as the density increases the probability of k-Connectivity increases.