analysis of a cone-based distributed topology control algorithm for wireless multi-hop networks l....
TRANSCRIPT
![Page 1: Analysis of a Cone-Based Distributed Topology Control Algorithm for Wireless Multi-hop Networks L. Li, J. Y. Halpern Cornell University P. Bahl, Y. M](https://reader035.vdocuments.net/reader035/viewer/2022070305/5514765b550346b0158b5305/html5/thumbnails/1.jpg)
Analysis of a Cone-Based Distributed Topology Control
Algorithm for Wireless Multi-hop Networks
L. Li, J. Y. HalpernCornell University
P. Bahl, Y. M. Wang, and R. WattenhoferMicrosoft Research, Redmond
![Page 2: Analysis of a Cone-Based Distributed Topology Control Algorithm for Wireless Multi-hop Networks L. Li, J. Y. Halpern Cornell University P. Bahl, Y. M](https://reader035.vdocuments.net/reader035/viewer/2022070305/5514765b550346b0158b5305/html5/thumbnails/2.jpg)
The Aladdin Home Networking System
PowerlineNetwork
PhonelineEthernet
LAN
HomeGateway
AlertRouter
IM
WirelessSensorNetwork
![Page 3: Analysis of a Cone-Based Distributed Topology Control Algorithm for Wireless Multi-hop Networks L. Li, J. Y. Halpern Cornell University P. Bahl, Y. M](https://reader035.vdocuments.net/reader035/viewer/2022070305/5514765b550346b0158b5305/html5/thumbnails/3.jpg)
OUTLINE• Motivation
• Bigger Picture and Related Work
• Basic Cone-Based Algorithm– Summary of Two Main Results– Properties of the Basic Algorithm
• Optimizations– Properties of Asymmetric Edge Removal
• Performance Evaluation
![Page 4: Analysis of a Cone-Based Distributed Topology Control Algorithm for Wireless Multi-hop Networks L. Li, J. Y. Halpern Cornell University P. Bahl, Y. M](https://reader035.vdocuments.net/reader035/viewer/2022070305/5514765b550346b0158b5305/html5/thumbnails/4.jpg)
• Example of No Topology Control with maximum transmission radius R (maximum connected node set)
High energy consumption High interference Low throughput
Motivation for Topology Control
![Page 5: Analysis of a Cone-Based Distributed Topology Control Algorithm for Wireless Multi-hop Networks L. Li, J. Y. Halpern Cornell University P. Bahl, Y. M](https://reader035.vdocuments.net/reader035/viewer/2022070305/5514765b550346b0158b5305/html5/thumbnails/5.jpg)
Network may partition
• Example of No Topology Control with smaller transmission radius
![Page 6: Analysis of a Cone-Based Distributed Topology Control Algorithm for Wireless Multi-hop Networks L. Li, J. Y. Halpern Cornell University P. Bahl, Y. M](https://reader035.vdocuments.net/reader035/viewer/2022070305/5514765b550346b0158b5305/html5/thumbnails/6.jpg)
Global connectivity Low energy consumption Low interference High throughput
• Example of Topology Control
![Page 7: Analysis of a Cone-Based Distributed Topology Control Algorithm for Wireless Multi-hop Networks L. Li, J. Y. Halpern Cornell University P. Bahl, Y. M](https://reader035.vdocuments.net/reader035/viewer/2022070305/5514765b550346b0158b5305/html5/thumbnails/7.jpg)
Bigger Picture and Related Work
Routing
MAC / Power-controlled MAC
SelectiveNode
Shutdown
TopologyControl
Relative Neighborhood Graphs, Gabriel graphs, Sphere-of-Influence graphs, -graphs, etc.
[GAF][Span]
[Hu 1993][Ramanathan & Rosales-Hain 2000][Rodoplu & Meng 1999][Wattenhofer et al. 2001]
ComputationalGeometry
[MBH 01][WTS 00]
![Page 8: Analysis of a Cone-Based Distributed Topology Control Algorithm for Wireless Multi-hop Networks L. Li, J. Y. Halpern Cornell University P. Bahl, Y. M](https://reader035.vdocuments.net/reader035/viewer/2022070305/5514765b550346b0158b5305/html5/thumbnails/8.jpg)
Basic Cone-Based Algorithm (INFOCOM 2001)
• Assumption: receiver can determine the direction of sender – Directional antenna community: Angle of
Arrival problem
• Each node u broadcasts “Hello” with increasing power (radius)
• Each discovered neighbor v replies with “Ack”.
![Page 9: Analysis of a Cone-Based Distributed Topology Control Algorithm for Wireless Multi-hop Networks L. Li, J. Y. Halpern Cornell University P. Bahl, Y. M](https://reader035.vdocuments.net/reader035/viewer/2022070305/5514765b550346b0158b5305/html5/thumbnails/9.jpg)
Cone-Based Algorithm with Angle
Need a neighbor in every -cone.
Can I stop?
No! There’s an -gap!
![Page 10: Analysis of a Cone-Based Distributed Topology Control Algorithm for Wireless Multi-hop Networks L. Li, J. Y. Halpern Cornell University P. Bahl, Y. M](https://reader035.vdocuments.net/reader035/viewer/2022070305/5514765b550346b0158b5305/html5/thumbnails/10.jpg)
Notation
• E = { (u,v) V x V: v is a discovered neighbor by node u}– G
= (V, E)
– E may not be symmetric
• (B,A) in E but (A,B) not in E
R A B 70
60
50
= 145
![Page 11: Analysis of a Cone-Based Distributed Topology Control Algorithm for Wireless Multi-hop Networks L. Li, J. Y. Halpern Cornell University P. Bahl, Y. M](https://reader035.vdocuments.net/reader035/viewer/2022070305/5514765b550346b0158b5305/html5/thumbnails/11.jpg)
Two symmetric sets
• E+ = { (u,v): (u,v) E or (v,u) E }
– Symmetric closure of E
– G+ = (V, E
+ )
• E- = { (u,v): (u,v) E and (v,u) E }
– Asymmetric edge removal
– G- = (V, E
- )
![Page 12: Analysis of a Cone-Based Distributed Topology Control Algorithm for Wireless Multi-hop Networks L. Li, J. Y. Halpern Cornell University P. Bahl, Y. M](https://reader035.vdocuments.net/reader035/viewer/2022070305/5514765b550346b0158b5305/html5/thumbnails/12.jpg)
Summary of Two Main Results
• Let GR = (V, ER), ER = { (u,v): d(u,v) R }
• Connectivity Theorem– If 150, then G
+ preserves the connectivity of GR and the bound is tight.
• Asymmetric Edge Theorem– If 120, then G
- preserves the connectivity of GR and the bound is tight.
![Page 13: Analysis of a Cone-Based Distributed Topology Control Algorithm for Wireless Multi-hop Networks L. Li, J. Y. Halpern Cornell University P. Bahl, Y. M](https://reader035.vdocuments.net/reader035/viewer/2022070305/5514765b550346b0158b5305/html5/thumbnails/13.jpg)
The Why-150 Lemma
150 = 90 + 60
![Page 14: Analysis of a Cone-Based Distributed Topology Control Algorithm for Wireless Multi-hop Networks L. Li, J. Y. Halpern Cornell University P. Bahl, Y. M](https://reader035.vdocuments.net/reader035/viewer/2022070305/5514765b550346b0158b5305/html5/thumbnails/14.jpg)
Both circles have max radius R
A
N
B
• Counterexample for = 150 +
Properties of the Basic Algorithm
![Page 15: Analysis of a Cone-Based Distributed Topology Control Algorithm for Wireless Multi-hop Networks L. Li, J. Y. Halpern Cornell University P. Bahl, Y. M](https://reader035.vdocuments.net/reader035/viewer/2022070305/5514765b550346b0158b5305/html5/thumbnails/15.jpg)
Both circles have max radius R
A
W
N
K
J
B
Y
WAN = 150 WAK = 150
• Counterexample for = 150 +
![Page 16: Analysis of a Cone-Based Distributed Topology Control Algorithm for Wireless Multi-hop Networks L. Li, J. Y. Halpern Cornell University P. Bahl, Y. M](https://reader035.vdocuments.net/reader035/viewer/2022070305/5514765b550346b0158b5305/html5/thumbnails/16.jpg)
Both circles have max radius R
A
N
B W
K
J
Y
WAN = 150 WAK = 150 Z
X 150 < WAX < α
d(A,X) < R < d(X,B)
• Counterexample for = 150 +
![Page 17: Analysis of a Cone-Based Distributed Topology Control Algorithm for Wireless Multi-hop Networks L. Li, J. Y. Halpern Cornell University P. Bahl, Y. M](https://reader035.vdocuments.net/reader035/viewer/2022070305/5514765b550346b0158b5305/html5/thumbnails/17.jpg)
For 150 ( 5/6 )• Connectivity Lemma
– if d(A,B) = d R and (A,B) E+, there must be a
pair of nodes, one red and one green, with distance less than d(A,B).
A B W
Y
Z
X
d
![Page 18: Analysis of a Cone-Based Distributed Topology Control Algorithm for Wireless Multi-hop Networks L. Li, J. Y. Halpern Cornell University P. Bahl, Y. M](https://reader035.vdocuments.net/reader035/viewer/2022070305/5514765b550346b0158b5305/html5/thumbnails/18.jpg)
Connectivity Theorem
• Order the edges in ER by length and induction
on the rank in the ordering
– For every edge in ER, there’s a corresponding path in G
+ .
• If 150, then G+ preserves the
connectivity of GR and the bound is tight.
![Page 19: Analysis of a Cone-Based Distributed Topology Control Algorithm for Wireless Multi-hop Networks L. Li, J. Y. Halpern Cornell University P. Bahl, Y. M](https://reader035.vdocuments.net/reader035/viewer/2022070305/5514765b550346b0158b5305/html5/thumbnails/19.jpg)
Optimizations
• Shrink-back operation– “Boundary nodes” can shrink radius as
long as not reducing cone coverage
• Asymmetric edge removal– If 120, remove all asymmetric edges
• Pairwise edge removal– If < 60, remove longer edge e2
e1
e2
A B
C
![Page 20: Analysis of a Cone-Based Distributed Topology Control Algorithm for Wireless Multi-hop Networks L. Li, J. Y. Halpern Cornell University P. Bahl, Y. M](https://reader035.vdocuments.net/reader035/viewer/2022070305/5514765b550346b0158b5305/html5/thumbnails/20.jpg)
Properties of Asymmetric Edge Removal
• Counterexample for = 120 +
R A B
60+/3
60
60-/3
![Page 21: Analysis of a Cone-Based Distributed Topology Control Algorithm for Wireless Multi-hop Networks L. Li, J. Y. Halpern Cornell University P. Bahl, Y. M](https://reader035.vdocuments.net/reader035/viewer/2022070305/5514765b550346b0158b5305/html5/thumbnails/21.jpg)
For 120 ( 2/3 )• Asymmetric Edge Lemma
– if d(A,B) R and (A,B) E, there must be a pair of nodes, W or X and node B, with distance less than d(A,B).
A B
W
X
![Page 22: Analysis of a Cone-Based Distributed Topology Control Algorithm for Wireless Multi-hop Networks L. Li, J. Y. Halpern Cornell University P. Bahl, Y. M](https://reader035.vdocuments.net/reader035/viewer/2022070305/5514765b550346b0158b5305/html5/thumbnails/22.jpg)
Asymmetric Edge Theorem
• Two-step inductions on ER and then on E
– For every edge in ER , if it becomes an asymmetric edge in G , then there’s a corresponding path consisting of only symmetric edges.
• If 120, then G- preserves the
connectivity of GR and the bound is tight.
![Page 23: Analysis of a Cone-Based Distributed Topology Control Algorithm for Wireless Multi-hop Networks L. Li, J. Y. Halpern Cornell University P. Bahl, Y. M](https://reader035.vdocuments.net/reader035/viewer/2022070305/5514765b550346b0158b5305/html5/thumbnails/23.jpg)
Performance Evaluation
• Simulation Setup– 100 nodes randomly placed on a
1500m-by-1500m grid. Each node has a maximum transmission radius 500m.
• Performance Metrics– Average Radius– Average Node Degree
![Page 24: Analysis of a Cone-Based Distributed Topology Control Algorithm for Wireless Multi-hop Networks L. Li, J. Y. Halpern Cornell University P. Bahl, Y. M](https://reader035.vdocuments.net/reader035/viewer/2022070305/5514765b550346b0158b5305/html5/thumbnails/24.jpg)
Average Radius
0
100
200
300
400
500
600
Basic With opt1 Withopt1&2
With allopts
Ave
rag
e ra
diu
s
Max power
150-deg
120-deg
![Page 25: Analysis of a Cone-Based Distributed Topology Control Algorithm for Wireless Multi-hop Networks L. Li, J. Y. Halpern Cornell University P. Bahl, Y. M](https://reader035.vdocuments.net/reader035/viewer/2022070305/5514765b550346b0158b5305/html5/thumbnails/25.jpg)
Average Node Degree
0
5
10
15
20
25
30
Basic With opt1 Withopt1&2
With allopts
Ave
rag
e n
od
e d
egre
e
Max power
150-deg
120-deg
![Page 26: Analysis of a Cone-Based Distributed Topology Control Algorithm for Wireless Multi-hop Networks L. Li, J. Y. Halpern Cornell University P. Bahl, Y. M](https://reader035.vdocuments.net/reader035/viewer/2022070305/5514765b550346b0158b5305/html5/thumbnails/26.jpg)
• In response to mobility, failures, and node additions
• Based on Neighbor Discovery Protocol (NDP) beacons– Joinu(v) event: may allow shrink-back
– Leaveu(v) event: may resume “Hello” protocol
– AngleChangeu(v) event: may allow shrink-back or resume “Hello” protocol
• Careful selection of beacon power
Reconfiguration
![Page 27: Analysis of a Cone-Based Distributed Topology Control Algorithm for Wireless Multi-hop Networks L. Li, J. Y. Halpern Cornell University P. Bahl, Y. M](https://reader035.vdocuments.net/reader035/viewer/2022070305/5514765b550346b0158b5305/html5/thumbnails/27.jpg)
• Distributed cone-based topology control algorithm that achieves maximum connected node set– If we treat all edges as bi-directional
• 150-degree tight upper bound– If we remove all unidirectional edges
• 120-degree tight upper bound
• Simulation results show that average radius and node degree can be significantly reduced
Summary