Challenges in Geographic Routing:
Sparse Networks, Obstacles, and Traffic
Provisioning
Brad Karp
Berkeley, CA
[email protected]
DIMACS Pervasive Networking Workshop
21 May, 2001
Motivating Examples
Vast wireless network of mobile temperature sensors, floating on
the ocean’s surface: Sensor Networks
Metropolitan-area network comprised of customer-owned and
-operated radios: Rooftop Networks
Challenges in Geographic Routing
Brad Karp
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1
Scalability through Geography
How should we build networks with a mix of these characteristics?
Mobility
Scale (number of nodes)
Lack of static hierarchical structure
Use geography in system design to achieve scalability. Examples:
Greedy Perimeter Stateless Routing (GPSR): scalable
geographic routing for mobile networks [Karp and Kung, 2000]
GRID Location Service (GLS): a scalable location database for
mobile networks [Li et al., 2000]
Geography-Informed Energy Conservation [Xu et al., 2001]
Challenges in Geographic Routing
Brad Karp
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Outline
Motivation
GPSR Overview
GPSR’s Performance on Sparse Networks: Simulation Results
Planar Graphs and Radio Obstacles: Challenge and Approaches
Geographic Traffic Provisioning and Engineering
Conclusions
Challenges in Geographic Routing
Brad Karp
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GPSR: Greedy Forwarding
Nodes learn immediate neighbors’ positions through
beacons/piggybacking on data packets: only state required!
Locally optimal, greedy forwarding choice at a node:
Forward to the neighbor geographically closest to the
destination
D
x
y
Challenges in Geographic Routing
Brad Karp
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Greedy Forwarding Failure: Voids
When the intersection of a node’s circular radio range and the
circle about the destination on which the node sits is empty of
nodes, greedy forwarding is impossible
Such a region is a void:
D
v
z
void
w
y
x
Challenges in Geographic Routing
Brad Karp
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Node Density and Voids
Existing and Found Paths, 1340 m x 1340 m Region
1.1
1
Fraction of paths
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
Fraction existing paths
Fraction paths found by greedy
0.1
0
50
100
150
200
Number of nodes
250
300
The probability that a void region occurs along a route increases as
nodes become more sparse
Challenges in Geographic Routing
Brad Karp
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GPSR: Perimeter Mode for Void Traversal
D
x
Traverse face closer to D along xD by right-hand rule, until reaching
the edge that crosses xD
Repeat with the next closer face along xD, &c.
Forward greedily where possible, in perimeter mode where not
Challenges in Geographic Routing
Brad Karp
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Challenge: Sparse Networks
Greedy forwarding approximates shortest paths closely on dense
networks
Perimeter-mode forwarding detours around planar faces; not
shortest-path
Greedy forwarding clearly robust against packet looping under
mobility
Perimeter-mode forwarding less robust against packet looping on
mobile networks; faces change dynamically
Perimeter mode really a recovery technique for greedy forwarding
failure; greedy forwarding has more desirable properties
How does GPSR perform on sparser networks, where perimeter
mode is used most often?
Challenges in Geographic Routing
Brad Karp
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Simulation Environment
ns-2 with wireless extensions [Broch et al., 1998]: full 802.11 MAC,
physical propagation; allows comparison of results
Topologies and Workloads:
Nodes
Region
Density
CBR Flows
50
1500 m 300 m
1 node / 9000 m2
30
1 node / 9000 m2
30
1 node / 35912 m2
30
200
50
3000 m 600 m
1340 m 1340 m
Simulation Parameters:
Pause Time: 0, 30, 60, 120 s
Motion Rate: [1, 20] m/s
GPSR Beacon Interval: 1.5 s
Data Packet Size: 64 bytes
CBR Flow Rate: 2 Kbps
Simulation Length: 900 s
Challenges in Geographic Routing
Brad Karp
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Packet Delivery Success Rate (50, 200; Dense)
1
Fraction data pkts delivered
0.9
0.8
0.7
0.6
0.5
0.4
DSR (200 nodes)
GPSR (200 nodes), B = 1.5
DSR (50 nodes)
GPSR (50 nodes), B = 1.5
0.3
0.2
0
Challenges in Geographic Routing
20
40
Brad Karp
60
Pause time (s)
80
100
120
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Packet Delivery Success Rate (50; Sparse)
1
Fraction data pkts delivered
0.95
0.9
0.85
0.8
0.75
DSR (50 nodes)
GPSR (50 nodes), B = 1.5
GPSR (50 nodes), B = 1.5, Greedy Only
0.7
0
Challenges in Geographic Routing
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40
Brad Karp
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Pause time (s)
80
100
120
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Path Length (50; Dense)
DSR
120
DSR
60
GPSR
DSR
30
Pause Time
Routing Algorithm
GPSR
GPSR
DSR
0
GPSR
0.0
0.2
0.4
0.6
0.8
1.0
Fraction of delivered pkts
0
1
2
3
4
>= 5
Hops Longer than Optimal
Challenges in Geographic Routing
Brad Karp
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Path Length (50 nodes, Sparse)
DSR
120
DSR
60
GPSR
DSR
30
Pause Time
Routing Algorithm
GPSR
GPSR
DSR
0
GPSR
0.0
0.2
0.4
0.6
0.8
1.0
Fraction of delivered pkts
0
1
2
3
4
>= 5
Hops Longer than Optimal
Challenges in Geographic Routing
Brad Karp
[email protected]
13
Outline
Motivation
GPSR Overview
GPSR’s Performance on Sparse Networks: Simulation Results
Planar Graphs and Radio Obstacles: Challenge and Approaches
Geographic Traffic Provisioning and Engineering
Conclusions
Challenges in Geographic Routing
Brad Karp
[email protected]
14
Network Graph Planarization
Relative Neighborhood Graph (RNG) [Toussaint, ’80] and Gabriel
Graph (GG) [Gabriel, ’69] are long-known planar graphs
Assume an edge exists between any pair of nodes separated by
less than a threshold distance (i.e., the nominal radio range)
RNG and GG can be constructed using only neighbors’ positions,
and both contain the Euclidean MST!
w
w
u
v
RNG
Challenges in Geographic Routing
u
v
GG
Brad Karp
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Planarized Graphs: Example
200 nodes, placed uniformly at random on a 2000-by-2000-meter
region; radio range 250 meters
Full Network
Challenges in Geographic Routing
GG Subgraph
Brad Karp
RNG Subgraph
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Challenge: Radio-Opaque Obstacles and
Planarization
Obstacles violate assumption that neighbors determined purely by
distance:
Full Network
GG and RNG Subgraph
In presence of obstacles, planarization can disconnect
destinations!
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Brad Karp
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Coping with Obstacles
Eliminate edges only in presence of mutual witnesses; edge
endpoints must agree
Full Graph
Mutual GG
Mutual RNG
Prevents disconnection, but doesn’t planarize completely
Forward through a randomly chosen partner node (location)
Compensate for variable path loss with variable transmit power
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Brad Karp
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Traffic Concentration Demands Provisioning
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If we assume uniform traffic distribution, flows tend to cross the
center of the network
All link capacities symmetric!
Challenges in Geographic Routing
Brad Karp
[email protected]
19
Geographic Network Provisioning
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In a dense wireless network, position is correlated with capacity
Symmetric link capacity and dense connectivity
Route congested flows’ packets through a randomly chosen point
Challenges in Geographic Routing
Brad Karp
[email protected]
20
Conclusions
On sparse networks, GPSR delivers packets robustly, most of
which take paths of near-shortest length
Non-uniform radio ranges complicate planarization; variable-power
radios and random-partner proxying may help
Geographically routed wireless networks support a new,
geographic family of traffic engineering strategies, that leverage
spatial reuse to alleviate congestion
Use of geographic information offers diverse scaling benefits in
pervasive network systems
Challenges in Geographic Routing
Brad Karp
[email protected]
21