Node Distribution of a New Scalable Mobility Model for Ad Hoc Wireless Networks Sheeraz Ahmad IIT Kanpur Mentor : Dr. Carl Baum

Outline Background of Mobility Models Random Way Point Model Motivation Introduction to New Model Node Distribution for New Model Outage Probability Comparison between Theoretical and Simulation Results Conclusion

Background of Mobility Models Mobility Models are required to describe the motion of mobile nodes. To track real motion, long time observation and statistical averaging can be used. For quick simulation, models like Random Way Point and Markov Model are used.

Random Way Point Model Choose two points uniformly in given region. Choose a random velocity. Start moving towards the second point with this velocity. After node reaches there, choose another point and repeat the process.

Motivation Node distribution for RWP is non-uniform; nodes tend to spend more time in the ‘middle’. Due to this RWP is not scalable, i.e. if we try to increase the size of the region this ‘edge effect’ becomes more prominent. Again due to the non-uniformity network performance becomes location dependent. Compelling need to come up with models which give uniform or nearly uniform distribution.

Introduction to New Model Instead of the interior the points are chosen on the boundary. The process progresses by choosing the angle subtended by the path at the center from the distribution :1/4*sin(| |/2) a r

Node Distribution for New Model = sub-segment length within r-circle = = total length within a-circle Probability that node lies within a circle of radius r = = (which is uniform)

We apply similar reasoning to donut geometry for following cases: 1. Donut 1 : where only such are chosen such that path does not collide with inner circle. 2. Donut 2 : where only such are chosen such that path always collides with inner circle and after collision the node reflects back. b a

Extending the same logic we get the node distribution as : Donut 1: Donut 2:

Outage Probability Probability that a node is deprived of connection (call it ). We assume outage for a node if it has no other node present within a distance d. x a d

For circle geometry we get = Outage probability ( ) =

For donut geometry we get = Outage probability ( ) =

Comparison between Theoretical and Simulation Results

Conclusion A new mobility model was suggested and was applied to three different scenarios. Theoretical expressions for node distribution of all three were derived which agree very closely with simulations. Node distribution for circle is uniform and for donut 1 is nearly uniform. By using these two in conjunction we can get a scalable mobility model. Performance criteria are MODEL SENSITIVE.

References “Stationary Distributions for the Random Waypoint Mobility Model” by William Navidi and Tracy Camp. “Random Waypoint Considered Harmful” by J. Yoon et al. “Understanding the Simulation of Mobility Models with Palm Calculus” by Jean-Yves Le Boudec

Acknowledgements Dr. Carl Baum Dr. Noneaker and Dr. Xu Rahul, Josh and other graduate students Fellow SURE participants SURE Program, Clemson University

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