1. Generated Waypoint Efficiency: The efficiency considered here is defined as follows: As can be seen from the graph, for the obstruction radius values (200, 400, 600, 800) considered here, the lowest efficiency is around 30% and this is not going to slow down the simulation significantly considering the fact that the program can generate waypoints at a very rapid pace. Steady State Distribution: Although the distribution of nodes is not quite uniform, it does depend on the size of the obstruction. As can be seen from the graph, the peak value shifts to the right as the obstruction radius is increased. The area considered for the movement of nodes is a circle of radius 1000 meters. The inner circle represents obstructions and its radius can be varied. The obstruction can affect mobility as well as communication. Constant velocity model (10 meters/sec) is used. Node distribution is sampled every 1 second. A waypoint in this model is described by Radius (R) and Angle (Θ). R and Θ are independent Random Variables. To distribute R and Θ uniformly over the 2D space, generate a Uniform Random Variable (U) using Mersenne Twister algorithm and obtain R and Θ using the following density functions: Rahul Amin Dr. Carl Baum A New Class of Mobility Models for Ad Hoc Wireless Networks v1v1 v3v3 v2v2 0 3 1 2 Effects of obstructions can be incorporated using this mobility model. The size of obstruction is flexible and can be adjusted to user’s needs. SURE 2006 An overall area of weakness in research on wireless ad- hoc (peer-to-peer) networks is in the area of mobility modeling. Perhaps the most widely used model, called the random waypoint model, has nodes picking future destinations, or waypoints, according t o a two- dimensional uniform distribution over a fixed area. Nodes move in a straight line at a fixed velocity from waypoint to waypoint. A new random velocity (also uniform) is chosen when a new destination is chosen. Random Waypoint Model is too idealistic. Nodes can move freely throughout the area without any restrictions. In a real-world scenario, there are certain areas that might obstruct a node’s mobility and communication ability. The main goal behind this research is to study the effects of these obstructions. Background Motivation 0 1 2 2 3 3 4 5 6 6 New Model – The Basics New Model – The Details The name of this model is Boundary Prevention Model. Node smartly predicts if it is going to collide with the obstruction during its travel from current waypoint to the next waypoint. If a collision is predicted, then the node does not travel to the next waypoint. Instead, it discards that waypoint and generates a new waypoint and checks again if it is going to collide with the obstruction trying to travel to this new waypoint. If it predicts that it is not going to collide, then the node continues its travel to this waypoint. But if it is going to collide again, then it keeps on generating waypoints until it finds one that it is going to be able to travel to without any collision. In the figure to the right, waypoints 2, 3 and 6 had to be regenerated since the node detected that if it tried to travel to those waypoints, a collision with obstruction would occur. Collision Prediction Calculations To predict if a node is going to collide with the obstruction, a simple geometric problem is considered. Equation (i) represents the equation of a circle centered at (0,0) with radius r. Equation (ii) represents the equation that describes a line that is going to pass through points (x 1, y 1 ) and (x 2, y 2 ). Equation (ii) is substituted in Equation (i) and it is expanded to get a simple quadratic equation in the form ax 2 + bx 2 + c = 0. This quadratic equation is solved to see if any real solutions between 0 and 1 exist. If they do, then the node knows that if it tries to travel to the next waypoint, it is going to run into the obstruction. Model Properties A partition is inability of any one node to be able to connect to any other node for a given distribution through routing. The maximum hop distance used is ½ R = 500 meters. Kruskal’s minimum spanning tree algorithm is used to determine partitions. As can be noticed, the two graphs are very similar indicating that the nodes are distributed in such a way that even if the nodes aren’t allowed to communicate over the obstruction, they are doing almost as good as when they are allowed to communicate over the obstruction. Mobility Blocking, No Communication Blocking Mobility & Communication Blocking Probability of Partition Effects of Route Update Delay on Required Power The average required power is the sum of the required power to travel between each source-destination pair divided by the total number of source-destination pairs. The power required to travel between any given link between two nodes is proportional to the distance of the link squared. The lowest cost path between source- destination pair is found using Dijkstra’s shortest path algorithm. The maximum hop distance used was 2R = 2000 meters. This was done so that no partitions could occur in any given distribution. The obstruction represented only mobility blocking and not communication blocking. As can be seen from the graph, the average required power decreases as the number of nodes is increased. But the average required power is eventually going to level off. Average Required Power Per Node Number of Nodes = 30. Update Period: The amount of time between updates to the routing metrics. Before this update occurs, a source node keeps on using the old routes to reach a destination node. As the update period increases, required power increases Conclusions Future Work Run simulations for Boundary Collision model which has the same basic properties as the Boundary Prevention Model, but differs in the fact that instead of predicting collision, the node travels until it collides with the obstruction boundary. Compare the results for Boundary Collision model with Boundary Prevention Model. Incorporate Markov velocity model in the current model which would allow different nodes to travel at different velocities. Create multiple obstructions with different radii and study its effects. Change the path metrics for choosing the routes for obtaining minimum required power. Currently, all the links are squared since power is assumed to be proportional to distance squared. What can be done is when the link passes through the obstruction, the part that passes through the obstruction can be cubed instead of being squared. This would be basically studying the effects of partial communication blocking over certain areas. This partial communication area in our case would be represented by the inner circle obstruction. Uniform 2D Boundary Prevention Distribution Distribution