an implementation framework for trajectory-based routing in ad hoc networks murat yuksel, ritesh...
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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