1. An Implementation Framework for Trajectory-Based Routing in Ad-Hoc Networks Murat Yuksel, Ritesh Pradhan and Shivkumar Kalyanaraman Rensselaer Polytechnic Institute ICC 2004

2. Outline Introduction Using Bezier Curves for TBR Greedy forwarding Algorithm for TBR Simulation Conclusion

3. Introduction Trajectory-Based Routing (TBR)  Source based routing Source encodes trajectory to traverse and embeds it into each packet  Greedy forwarding Forward packet follow its trajectory

4. Introduction Source Destination

5. Using Bezier Curves for TBR Cubic Bezier Curves

6. Using Bezier Curves for TBR A Cubic Bezier Curve is represented as:  t = 0, presents the source point of curve  t = 1, presents the destination point of curve

7. Using Bezier Curves for TBR Source(x 0,y 0 ) Destination(x 3,y 3 ) Control point1(x 1,y 1 ) Control point2(x 2,y 2 )

8. Using Bezier Curves for TBR Source  Encode the complete trajectory into each packet, by putting Source, destination, and two control points Intermediate nodes  Decode the complete trajectory Solve the equation system  Forwarding the packet follows the trajectory as much as possible

9. Using Bezier Curves for TBR If the curve will much more number of control points than two  Encode each control point would make the header bulky One way to define long trajectories is to split into smaller pieces  Cubic Bezier curves

10. Using Bezier Curves for TBR Middle point

11. Using Bezier Curves for TBR Source sends a probe packet to find the closest nodes of the middle points  Special Intermediate Node (SIN) Recode the control points for the next cubic Bezier curve in the trajectory

12. Using Bezier Curves for TBR Control pt1-1 Control pt1-2 SIN1 Control pt2-1 Control pt2-2 SIN2 Control pt3-1 Control pt3-2

13. Greedy forwarding Algorithm for TBR Random Closest to Curve (CTS) Least Advancement on Curve (LAC) Hybrid of CTC and LAC (CTC-LAC) Most Advancement on Curve (MAC) Lowest Deviation form Curve (LDC)

14. Greedy forwarding Algorithm for TBR Closest Point on the Bezier Curve One of roots of this equation will be the point on the Bezier curve Q(t) nearest to the node N i

15. Greedy forwarding Algorithm for TBR Terminology Q (t i ) :Residual point of N i t i :the parameter at the curve point closet to N i d i : residual distance

16. Greedy forwarding Algorithm for TBR Random  Select the next node randomly

17. Greedy forwarding Algorithm for TBR Closest to Curve (CTS)  Select the next node which is closest to the curve

18. Greedy forwarding Algorithm for TBR Closest to Curve (CTS)  Error – violation of the trajectory

19. Greedy forwarding Algorithm for TBR Least Advancement on Curve (LAC)  Forward to the node whose residual lies right next to the residual of the current node

20. Greedy forwarding Algorithm for TBR Hybrid of CTC and LAC (CTC-LAC)  Define a tolerable residual distance D  Select the node : d i < D and the smallest residual t i

21. Greedy forwarding Algorithm for TBR Most Advancement on Curve (MAC)  Select the farthest node along the curve

22. Greedy forwarding Algorithm for TBR Most Advancement on Curve (MAC)  Error – violation of the trajectory

23. Greedy forwarding Algorithm for TBR Lowest Deviation form Curve (LDC)  Select the minimize ratio R i Riemann sums

24. Simulation Ns-2 simulator Transmission range 5m Do not include mobility in our simulations Nodes are randomly distributed over a rectangular area 250mX500m

25. Simulation

27. Conclusion We proposed to use Bezier curve for trajectories in TBR  Enable routing of data packets  Keeping the packet header size constant