Trajectory-Based Forwarding Mechanisms for Ad-Hoc Sensor Networks Murat Yuksel, Ritesh Pradhan, Shivkumar Kalyanaraman Electrical, Computer, and Systems Engineering Department Rensselaer Polytechnic Institute, Troy, NY

Rensselaer Polytechnic Institute, Troy, NY2 Outline Motivation Overview of Trajectory-Based Routing (TBR) Bezier curves for TBR Forwarding algorithms for TBR Long trajectories Simulation results Future work

Rensselaer Polytechnic Institute, Troy, NY3 Motivation There may be several cases where shortest- path routing is not suitable for the application: To measure some parameters for a river To obtain terrain knowledge of a hostile area To use safer locations for important data transmissions Such application-specific requirements are particularly important for sensor networks

Rensselaer Polytechnic Institute, Troy, NY4 Motivation (cont’d) Example: Consider a battlefield with east-side of mountains being friendly area. Application can request to: obtain view of “west-side of the mountains” transmit secure information to allied soldiers through “east-side of the mountains”

Rensselaer Polytechnic Institute, Troy, NY5 Overview of TBR Source Routing (SR) Source inserts entire route into each packet, e.g. SBR, DSR. Very flexible for applications, but causes too large packet headers. Greedy Routing (GR) Assuming a positioning service, each packet is forwarded to the neighbor closest to the destination, e.g. GPSR, CR. Fixed-size, short packet headers, but not flexible for applications. Trajectory-Based Routing (TBR) Proposed by Nath and Niculescu from Rutgers University. Represents the whole path as a parametric curve and encodes it into each packet. Geographic routing protocol, and requires positioning service.

Rensselaer Polytechnic Institute, Troy, NY6 Overview of TBR (cont’d) What happens when a packet travels in the network? Source encodes the trajectory into the packet’s header. All nodes forward the packet based on a predefined forwarding strategy. After packet arrival, the intermediate nodes decode the trajectory and forwards the packet along the trajectory. The packet gets forwarded until it reaches the destination or is dropped. TBR is a middle-ground between SR and GR. Since a parametric curve can form any path (e.g. circle, straight line, oscillatory lines), it gives more flexibility to define the path. – similar to SR Since nodes decode the trajectory, i.e. stateless – similar to GR One important issue is “how should we encode the trajectory into packets’ headers”?

Rensselaer Polytechnic Institute, Troy, NY7 source destination Control pt -2 Control pt -1 Bezier Curves for TBR We propose to encode paths by using Bezier curves. Cubic Bezier curves (2 control pts + source + destination) are easy to handle. A Cubic Bezier curve is represented in parametric form: Q(0) is the source point, and Q(1) is the destination point.

Rensselaer Polytechnic Institute, Troy, NY8 Bezier Curves for TBR (cont’d) If (x 0,y 0 ), (x 1,y 1 ), (x 2,y 2 ) and (x 3,y 3 ) are known, then the constant vectors A, B & C can be calculated as: Each packet header contains locations of source (x 0,y 0 ), destination (x 3,y 3 ) and control points (x 1,y 1 ), (x 2,y 2 ). So, when a packet arrives, each node: Decodes the trajectory by performing the above calculations Figures out which neighbor to forward the packet, based on forwarding strategy.

Rensselaer Polytechnic Institute, Troy, NY9 Forwarding Algorithms for TBR Terminology: d i = closest distance of node N i to the trajectory curve t i = value of the time parameter at the point where node N i is closest to the curve – residual of node N i The residual t i of node N i can also be interpreted as projection of the node on the curve. neighbor of N i = set of nodes that are in transmission range of N i and have a residual greater than t i.

Rensselaer Polytechnic Institute, Troy, NY10 Forwarding Algorithms for TBR (cont’d) Closest-To- Curve (CTC) - node forwards to its neighbor closest to the curve. Least Advancement on Curve (LAC) – node forwards to its neighbor with least advancement on the curve. Random - node randomly forwards to one of its neighbor

Rensselaer Polytechnic Institute, Troy, NY11 Forwarding Algorithms for TBR (cont’d) CTC-LAC – node forwards to its neighbor with LAC but is also close to the curve (within a predefined distance). Most Advancement on Curve (MAC) – node forwards to its neighbor which is nearest to the destination. Failure of CTC and MAC Failure of LAC

Rensselaer Polytechnic Institute, Troy, NY12 Forwarding Algorithms for TBR (cont’d) Lowest Deviation from Curve (LDC) – node forwards to its neighbor with lowest deviation from curve. Calculation of areas is computationally intensive. Can be approximated by numerical techniques.

Rensselaer Polytechnic Institute, Troy, NY13 Long Trajectories For a generalized long trajectory We brake the trajectory into multiple cubic Bezier curves. Before data traffic, source performs signaling and sends a probe packet that include all the control points (more than two) for the trajectory and starting locations of the smaller cubic Bezier curves (i.e. Intermediate Point (IP) ). Nodes close to an IP will contend for being a Special Intermediate Node (SIN).

Rensselaer Polytechnic Institute, Troy, NY14 Long Trajectories (cont’d) SINs (i.e. I 1, I 2 below) do special forwarding. They remove info about last curve’s control points and replaces it with that of the next piece’s control points from packet’s header and inserts the next one’s control points. Rest of the nodes fwd packets to nodes that are closest to curve and you advance least on curve. Curve 3 D Curve 1 Curve 2 S I1I1 I2I2

Rensselaer Polytechnic Institute, Troy, NY15 Simulation Results Used NS-2 Number of nodes – 50, 100, 150, 200. Area – 250mX500m Three different trajectories: Circular Zigzag – Single-piece Zigzag -- Multi-piece No mobility yet

Rensselaer Polytechnic Institute, Troy, NY16 Simulation Results (cont’d) A long trajectory composed of two concatenated cubic Bezier curves

Rensselaer Polytechnic Institute, Troy, NY17 Simulation Results (cont’d) Deviation of various forwarding strategies from the circular trajectory

Rensselaer Polytechnic Institute, Troy, NY18 Simulation Results (cont’d) Normalized path length in various forwarding strategies applied on the circular trajectory

Rensselaer Polytechnic Institute, Troy, NY19 Simulation Results (cont’d) Deviation of various forwarding strategies from the single-piece zigzag trajectory

Rensselaer Polytechnic Institute, Troy, NY20 Simulation Results (cont’d) Normalized path length in various forwarding strategies applied on the single-piece zigzag trajectory

Rensselaer Polytechnic Institute, Troy, NY21 Simulation Results (cont’d) Deviation from the trajectory and normalized path length for the multi- piece zigzag trajectory with CTC-LAC forwarding strategy

Rensselaer Polytechnic Institute, Troy, NY22 Future Work Extensive simulation of multi-piece case Amount of state maintained at SINs Strategies for selecting SINs Simulation with various mobility patterns Analysis of success rate (i.e. % reaching destination) for the forwarding strategies Resilience strategies to increase success rate

Rensselaer Polytechnic Institute, Troy, NY23 Thank you !!