Topology Control Murat Demirbas SUNY Buffalo Uses slides from Y.M. Wang and A. Arora.
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Transcript of Topology Control Murat Demirbas SUNY Buffalo Uses slides from Y.M. Wang and A. Arora.
Topology Control
Murat Demirbas
SUNY Buffalo
Uses slides from
Y.M. Wang
and A. Arora
2
• High density deployment is common
• Even with minimal sensor coverage, we get a high density communication network (radio range > typical sensor range)
• Energy constraints
• When not easily replenished
• High interference
• Many nodes in communication range
We will look at selecting high-quality links as part of routing!
Why Control Communications Topology
3
Problem Statement(s)
1. Choose a transmit-power level whereby network is connected
• per node or same for all nodes
• with per node there is the issue of avoiding asymmetric links
• cone-based algorithm:
node u transmits with the minimum power ρu s.t. there is at least one neighbor in every
cone of angle x centered at u
2. Find an MCDS, i.e. a minimum subset of nodes that is both:
Set cover
Connected
4
Problem Statement(s)
3. Find a minimum subset of nodes that provides some density
in each geographic region connectivity we’ll look at the examples of SPAN, GAF, CEC
Sub-problems:
• Prune asymmetric links• Tolerate node perturbations• Load balance
5
Outline
• Cone-based algorithm
• SPAN
• GAF-CEC
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
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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
8
• 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
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Network may partition
• Example of No Topology Control with smaller transmission radius
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Global connectivity Low energy consumption Low interference High throughput
• Example of Topology Control
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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]
12
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”.
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Cone-Based Algorithm with Angle
Need a neighbor in every -cone.
Can I stop?
No! There’s an -gap!
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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
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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
- )
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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.
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The Why-150 Lemma
150 = 90 + 60
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Both circles have max radius R
A
N
B
• Counterexample for = 150 +
Properties of the Basic Algorithm
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Both circles have max radius R
A
W
N
K
J
B
Y
WAN = 150 WAK = 150
• Counterexample for = 150 +
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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 +
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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
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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.
23
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
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Properties of Asymmetric Edge Removal
• Counterexample for = 120 +
R A B
60+/3
60
60-/3
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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
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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.
27
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
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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
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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
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• 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
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• 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
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Outline
• Cone-based algorithm
• SPAN
• GAF-CEC
33
SPAN
• Goal: preserve fairness and capacity & still provide energy savings
• SPAN elects “coordinators” from all nodes to create backbone topology
• Other nodes remain in power-saving mode and periodically check if they should
become coordinators
• Tries to minimize # of coordinators while preserving network capacity
• Depends on an ad-hoc routing protocol to get list of neighbors & the
connectivity matrix between them
• Runs above the MAC layer and “alongside” routing
35
Coordinator Election & Announcement
• Rule: if 2 neighbors of a non-coordinator node cannot reach each other
(either directly or via 1 or 2 coordinators), node becomes coordinator
• Announcement contention is resolved by delaying coordinator
announcements with a randomized backoff delay
• delay = ((1 – Er/Em) + (1 – Ci/(Ni pairs)) + R)*Ni*T
Er/Em: energy remaining/max energy
Ni: number of neighbors for node i
Ci: number of connected nodes through node i
R: Random[0,1]
T: RTT for small packet over wireless link
36
Coordinator Withdrawal
• Each coordinator periodically checks if it should withdraw as a coordinator
• A node withdraws as coordinator if each pair of its neighbors can reach each other
directly of via some other coordinators
• To ensure fairness, after a node has been a coordinator for some period of time, it
withdraws if every pair of nodes can reach each other through other neighbors (even
if they are not coordinators)
• After sending a withdraw message, the old coordinator remains active for a “grace
period” to avoid routing loses until the new coordinator is elected
38
Performance Results
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Outline
• Cone-based algorithm
• SPAN
• GAF-CEC
40
GAF/CEC: Geographical Adaptive Fidelity
• Each node uses location information (provided by some orthogonal
mechanism) to associate itself to a virtual grid
• All nodes in a virtual grid must be able to communicate to all nodes
in an adjacent grid
• Assumes a deterministic radio range, a global coordinate system
and global starting point for grid layout
• GAF is independent of the underlying ad-hoc routing protocol
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Virtual Grid Size Determination
• r: grid size, R: deterministic radio range
• r2 + (2r)2 <= R2
• r <= R/sqrt(5)
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Parameters settings
• enat: estimated node active time
• enlt: estimated node lifetime
• Td,Ta, Ts: discovery, active,
and sleep timers
• Ta = enlt/2
• Ts = [enat/2, enat]
• Node ranking:
Active > discovery (only one node active per grid)
Same state, higher enlt --> higher rank (longer expected time first)
Node ids to break ties
43
Performance Results
44
CEC
• Cluster-based Energy Conservation
• Nodes are organized into overlapping clusters
• A cluster is defined as a subset of nodes that are mutually
reachable in at most 2 hops
45
Cluster Formation
• Cluster-head Selection: longest lifetime of all its neighbors
(breaking ties by node id)
• Gateway Node Selection:
primary gateways have higher priority
gateways with more cluster-head neighbors have higher priority
gateways with longer lifetime have higher priority
46
Network Lifetime