Combinatorial Fusion Analysis (CFA) and Applications - Dimacs
DIMACS Pervasive Networking Workshop Sparse Networks
Transcript of DIMACS Pervasive Networking Workshop Sparse Networks
Challenges in Geographic Routing:Sparse Networks, Obstacles, and Traffic
Provisioning
Brad Karp
Berkeley, CA
DIMACS Pervasive Networking Workshop21 May, 2001
Motivating Examples
Vast wireless network of mobile temperature sensors, floating onthe ocean’s surface: Sensor Networks
Metropolitan-area network comprised of customer-owned and-operated radios: Rooftop Networks
Challenges in Geographic Routing Brad Karp [email protected] 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): scalablegeographic routing for mobile networks [Karp and Kung, 2000]
� GRID Location Service (GLS): a scalable location database formobile networks [Li et al., 2000]
� Geography-Informed Energy Conservation [Xu et al., 2001]
Challenges in Geographic Routing Brad Karp [email protected] 2
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] 3
GPSR: Greedy Forwarding
Nodes learn immediate neighbors’ positions throughbeacons/piggybacking on data packets: only state required!
Locally optimal, greedy forwarding choice at a node:
Forward to the neighbor geographically closest to thedestination
y
x
D
Challenges in Geographic Routing Brad Karp [email protected] 4
Greedy Forwarding Failure: Voids
When the intersection of a node’s circular radio range and thecircle about the destination on which the node sits is empty ofnodes, greedy forwarding is impossible
Such a region is a void:
D
v z
w
x
y
void
Challenges in Geographic Routing Brad Karp [email protected] 5
Node Density and Voids
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
0 50 100 150 200 250 300
Fra
ctio
n o
f p
ath
s
Number of nodes
Existing and Found Paths, 1340 m x 1340 m Region
Fraction existing pathsFraction paths found by greedy
The probability that a void region occurs along a route increases asnodes become more sparse
Challenges in Geographic Routing Brad Karp [email protected] 6
GPSR: Perimeter Mode for Void Traversal
D
xTraverse face closer to D along xD by right-hand rule, until reachingthe 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 [email protected] 7
Challenge: Sparse Networks
Greedy forwarding approximates shortest paths closely on densenetworks
Perimeter-mode forwarding detours around planar faces; notshortest-path
Greedy forwarding clearly robust against packet looping undermobility
Perimeter-mode forwarding less robust against packet looping onmobile networks; faces change dynamically
Perimeter mode really a recovery technique for greedy forwardingfailure; greedy forwarding has more desirable properties
How does GPSR perform on sparser networks, where perimetermode is used most often?
Challenges in Geographic Routing Brad Karp [email protected] 8
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
200 3000 m � 600 m 1 node / 9000 m2 30
50 1340 m � 1340 m 1 node / 35912 m2 30
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 [email protected] 9
Packet Delivery Success Rate (50, 200; Dense)
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 20 40 60 80 100 120
Fra
ctio
n d
ata
pkt
s d
eliv
ered
Pause time (s)
DSR (200 nodes)GPSR (200 nodes), B = 1.5
DSR (50 nodes)GPSR (50 nodes), B = 1.5
Challenges in Geographic Routing Brad Karp [email protected] 10
Packet Delivery Success Rate (50; Sparse)
0.7
0.75
0.8
0.85
0.9
0.95
1
0 20 40 60 80 100 120
Fra
ctio
n d
ata
pkt
s d
eliv
ered
Pause time (s)
DSR (50 nodes)GPSR (50 nodes), B = 1.5
GPSR (50 nodes), B = 1.5, Greedy Only
Challenges in Geographic Routing Brad Karp [email protected] 11
Path Length (50; Dense)
0.0 0.2 0.4 0.6 0.8 1.0Fraction of delivered pkts
GPSR
DSR
GPSR
DSR
GPSR
DSR
GPSR
DSR
0.0 0.2 0.4 0.6 0.8 1.0Fraction of delivered pkts
0
30
60
120
Pau
se Tim
e
0.0 0.2 0.4 0.6 0.8 1.0Fraction of delivered pkts
Ro
uti
ng
Alg
ori
thm
Hops Longer than Optimal
Ro
uti
ng
Alg
ori
thm
0 1 2 3 4 >= 5
Challenges in Geographic Routing Brad Karp [email protected] 12
Path Length (50 nodes, Sparse)
0.0 0.2 0.4 0.6 0.8 1.0Fraction of delivered pkts
GPSR
DSR
GPSR
DSR
GPSR
DSR
GPSR
DSR
0.0 0.2 0.4 0.6 0.8 1.0Fraction of delivered pkts
0
30
60
120
Pau
se Tim
e
0.0 0.2 0.4 0.6 0.8 1.0Fraction of delivered pkts
Ro
uti
ng
Alg
ori
thm
Hops Longer than Optimal
Ro
uti
ng
Alg
ori
thm
0 1 2 3 4 >= 5
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 GabrielGraph (GG) [Gabriel, ’69] are long-known planar graphs
Assume an edge exists between any pair of nodes separated byless 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!
u v
w
RNG
u v
w
GG
Challenges in Geographic Routing Brad Karp [email protected] 15
Planarized Graphs: Example
200 nodes, placed uniformly at random on a 2000-by-2000-meterregion; radio range 250 meters
Full Network GG Subgraph RNG Subgraph
Challenges in Geographic Routing Brad Karp [email protected] 16
Challenge: Radio-Opaque Obstacles andPlanarization
Obstacles violate assumption that neighbors determined purely bydistance:
Full Network GG and RNG Subgraph
In presence of obstacles, planarization can disconnectdestinations!
Challenges in Geographic Routing Brad Karp [email protected] 17
Coping with Obstacles
Eliminate edges only in presence of mutual witnesses; edgeendpoints 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
Challenges in Geographic Routing Brad Karp [email protected] 18
Traffic Concentration Demands Provisioning
������
������
��������
����
������������
��������
����
������������
��������
����
���
���
������
������
��������
����
������������
������
������
���
���
���
���
������
������
������
������
���
���
���
���
������
������
������
������
���
���
������������
������
������
���
���
������������
������
������
���
���
���
���
������
������
������
������
���
���
���
���
���
���
���
���
���
���
����
����
���
���
���
���
���
���
������
������
��������
����
������������
��������
����
����
����
����
����
���
���
���
���
����
����
���
���
If we assume uniform traffic distribution, flows tend to cross thecenter of the network
All link capacities symmetric!
Challenges in Geographic Routing Brad Karp [email protected] 19
Geographic Network Provisioning
������
������
��������
����
������������
��������
����
������������
��������
����
���
���
������
������
��������
����
������������
������
������
���
���
���
���
������
������
������
������
���
���
���
���
������
������
������
������
���
���
������������
������
������
���
���
������������
������
������
���
���
���
���
������
������
������
������
���
���
���
���
���
���
���
���
���
���
����
����
���
���
���
���
���
���
������
������
��������
����
������������
��������
����
����
����
����
����
���
���
���
���
����
����
���
���
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 ofwhich take paths of near-shortest length
Non-uniform radio ranges complicate planarization; variable-powerradios and random-partner proxying may help
Geographically routed wireless networks support a new,geographic family of traffic engineering strategies, that leveragespatial reuse to alleviate congestion
Use of geographic information offers diverse scaling benefits inpervasive network systems
Challenges in Geographic Routing Brad Karp [email protected] 21