An Implementation Framework for

Trajectory-Based Routing in Ad Hoc Networks

Murat Yuksel, Ritesh Pradhan, Shivkumar Kalyanaraman

Electrical, Computer, and Systems Engineering Department

Rensselaer Polytechnic Institute, Troy, NY

June 22, 2004 IEEE ICC’04 2

Outline Motivation Overview of Trajectory-Based Routing

(TBR) Bezier Curves for TBR Forwarding Algorithms for TBR Long/Complex Trajectories Contributions Future Work

June 22, 2004 IEEE ICC’04 3

Motivation

Wireless ad hoc networks An emerging part of our

technology, e.g. laptops, PDAs, watches, cars, …

Very scarce resources e.g. capacity, power, memory

Traffic engineering requires flexibility in routing:

Multi-path capability Major issues:

Ad hoc nature of nodes Mobility

Dynamic topology causes continuous update to routing tables.

TE is essential for ad hoc networks

Proactive routing does NOT work!

TE in ad hoc n

etwork

s require

new routin

g building block

s

June 22, 2004 IEEE ICC’04 4

Motivation (cont’d) Why TBR is a viable routing building block for TE?

Multi-path capability in a wireless, multi-hop, ad hoc environment

Possible application to p2p with virtual geographic locations

June 22, 2004 IEEE ICC’04 5

Motivation (cont’d)

Application-specific requirements

particularly important for sensor networks

Area of interest: Take pictures of the lake Measure temperature

around an experimental area

Area of disinterest: Route secure info around

the unsafe area Route more traffic

around the congested area

June 22, 2004 IEEE ICC’04 6

Overview of TBR Source Routing (SR):

Source inserts all the route into each packet, e.g. SBR, DSR.

Very flexible for applications, but causes too large packet headers.

Greedy Routing (GR): Each packet is forwarded to the neighbor closest to

the destination, e.g. FACE, Greedy Perimeter Stateless Routing (GPSR), Cartesian Routing (CR).

Fixed-size, short packet headers, but not flexible for applications.

Trajectory-Based Routing (TBR): Proposed by a group from Rutgers University. Represents the whole path as a parametric curve

and encodes it into each packet.

June 22, 2004 IEEE ICC’04 7

Overview of TBR (cont’d) TBR is a geographic routing protocol, and requires a

positioning service TBR is a middle-ground between SR and GR.

Since a parametric curve can form any path (e.g. circle, straight line, curly lines), it gives more flexibility for the source to define the path. – similar to SR

Since the intermediate nodes decode the trajectory, they do not have to keep state. – similar to GR

Source Routing

i.e. flex, large header

Greedy Routing

i.e. no header or state, but no flex

Trajectory-Based Routing

June 22, 2004 IEEE ICC’04 8

Overview of TBR (cont’d) So, how does it work?

What happens when a packet travels in the network?

S

DDATADATA

How to encode the trajectory into packets’ headers?

June 22, 2004 IEEE ICC’04 9

source

destination

Control pt -2

Control pt -1

Bezier Curves for TBR Can we use Bezier curves? Cubic Bezier curves:

2 control pts + source + destination

easy to handle. Represented in parametric

form:

t is the time parameter.Q(0) is the

source point

Q(1) is the destination

point

June 22, 2004 IEEE ICC’04 10

Bezier Curves for TBR (cont’d)

If (x0,y0), (x1,y1), (x2,y2) and (x3,y3) are known, then the

constant vectors A, B & C can be calculated as:

Given that: Each packet header contains locations of source (x0,y0),

destination (x3,y3) and control points (x1,y1), (x2,y2). Each node maintains neighbor table.

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. What is a viable forwarding strategy?

June 22, 2004 IEEE ICC’04 11

Forwarding Algorithms for TBR

Terminology: di = closest distance of node Ni to the curve ti = time parameter at the point where node Ni

is closest to the curve – time of node Ni

The time ti of node Ni can also be interpreted as projection of the node on the curve.

neighbor of Ni = nodes that are in transmission range of Ni and have a time greater than ti.

d i

N i

T raj ectoryQ (t)

Q (t i)

June 22, 2004 IEEE ICC’04 12

Forwarding Algorithms for TBR (cont’d)

Closest-To-Curve (CTC) - to the neighbor with smallest distance to the curve.

Least Advancement on Curve (LAC) – to the neighbor with smallest time on the curve.

Random - randomly forward to one the neighbors

T ransmissionRange of N 0

d1

d6 d7

d8

d9

d3

d5

d4

d0

d2

N 5

N 3

N 0

N 7

N 1

N 8

N 4

N 9

N 2

N 6

t 0t 6

t 3

t 5t 9

t 4t 8

t 7

t 2t 1

Q (t )

June 22, 2004 IEEE ICC’04 13

Forwarding Algorithms for TBR (cont’d)

Several other algorithms are possible.. CTC-LAC – to the neighbor with smallest time but

also stands within a predefined distance from the curve.

Most Advancement on Curve (MAC) – to the neighbor with largest time.

CTC-MAC – to the neighbor with highest time but also stands within a predefined distance from the curve.

Failure cases are possible..

June 22, 2004 IEEE ICC’04 14

Forwarding Algorithms for TBR (cont’d)

Failure of LAC

d2

d1

d3

d4

d0

N 3

N 2

N 4

N 1

t 0

t 3

t 1

t 4

t 2

Q (t )

N 0d2

d1

d3

d4

d0

N 3

N 2

N 4

N 1

t 0

t 3

t 1

t 4

t 2

Q (t )

N 0

June 22, 2004 IEEE ICC’04 15

Forwarding Algorithms for TBR (cont’d) Failure of CTC and MAC

d2

d1

d3

d5

d4

d0

N 5

N 3

N 2 N 4

N 1

t 0

t 3

t 5t 1

t 4

t 2

Q (t )

N 0

d2

d1

d3

d5

d4

d0

N 5

N 3

N 2 N 4

N 1

t 0

t 3

t 5t 1

t 4

t 2

Q (t )

N 0

June 22, 2004 IEEE ICC’04 16

d2

d3

N 3

N 2

t 0

t 3

t 1t 2

Q (t )

d1

N 0

N 1

d2

Forwarding Algorithms for TBR (cont’d)

Lowest Deviation from Curve (LDC) – node forwards to its neighbor with lowest deviation from curve.

d2

d3

N 3

N 2

t 0

t 3

t 1t 2

Q (t )

d1

N 0

N 1

d2 d2

d3

N 3

N 2

t 0

t 3

t 1t 2

Q (t )

d1

N 0

N 1

d2 d2

d3

N 3

N 2

t 0

t 3

t 1t 2

Q (t )

d1

N 0

N 1

d2

Deviation = deviated area from the curve per unit curve distance, i.e.:

ii

iiii

tt

tQtQNNArea

1

11 ))(),(,,(

June 22, 2004 IEEE ICC’04 17

t 0

Q (t)

(x 0, y0)

N i

N 0

(x i, y i)

t i

Forwarding Algorithms for TBR (cont’d)

Lowest Deviation from Curve (LDC) – Area calculations are computationally intensive. Can be approximated by numerical techniques.

Slice the area by parallel lines – similar to Riemann Sums in numerical integration

t 0

t i < t 0+9dt

Q (t)

(x 0, y0)

t 0+dt

t 0+2dt

(x 1, y1)(x 2, y2)

(x 3, y3)

t 0+3dt

N i

N 0

(x i, y i)

(x 4, y4)(x 5, y5)

(x 6, y6)

t 0+6dtt 0+5dtt 0+4dt

t 0+7dt

t 0+8dt

June 22, 2004 IEEE ICC’04 18

Simulation Results NS-2 Area –

250mX500m Different

trajectories: Circular Zigzag

No mobility yet

June 22, 2004 IEEE ICC’04 19

Simulation Results (cont’d) Deviation from the circular trajectory

June 22, 2004 IEEE ICC’04 20

Simulation Results (cont’d) Normalized path length on the circular trajectory

June 22, 2004 IEEE ICC’04 21

Simulation Results (cont’d)

Deviation from the zigzag trajectory

June 22, 2004 IEEE ICC’04 22

Long/Complex Trajectories How to encode long/complex curves?

longer curve larger packet header

IP1

IP2

Split the curve into simpler pieces: Each piece could be represented by a

cubic Bezier curve The complete trajectory is

concatenation of the pieces.

Source performs signaling and sends a control packet that include:

end locations of the cubic Bezier curves, i.e. Intermediate Point (IP)

all the control points

The nodes closest to the IPs will be the Special Intermediate Nodes (SINs).

DS

I1

I2

June 22, 2004 IEEE ICC’04 23

Long/Complex Trajectories How to encode long/complex curves?

longer curve larger packet header

IP1

IP2D

S

I1

I2

SINs (i.e. I1, I2) do special forwarding. Store the next Bezier curve’s control points Update the packet headers with that of the

next Bezier curve’s control points

C1

C2

C3 C4

C5

C6

SD

C5C6C3

C4IP2

SD

June 22, 2004 IEEE ICC’04 24

Contributions Our contributions:

An architecture to deploy TBR for long/complex trajectories.

A locally optimal forwarding strategy: Lowest Deviation from Curve (LDC)

A method of encoding/decoding trajectories by using Cubic Bezier curves.

A simulation-based evaluation of several forwarding strategies.

June 22, 2004 IEEE ICC’04 25

Future Work

Our ongoing work on TBR: A testbed deployment in RPI-CWN. Calculation of optimal curve to avoid certain spots. Finding optimal route for a given trajectory with

global topology knowledge. Future work on TBR:

Optimal split of long/complex trajectories. Analysis of the signaling overhead in mobile

environments. Hybrid trajectory encoding techniques: frequency

and space-time Resilience techniques for different forwarding

strategies.

June 22, 2004 IEEE ICC’04 26

Thank you!

THE END