topology control
DESCRIPTION
Topology Control. Murat Demirbas SUNY Buffalo Uses slides from Y.M. Wang and A. Arora. Why Control Communications Topology. High density deployment is common Even with minimal sensor coverage, we get a high density communication network (radio range > typical sensor range) - PowerPoint PPT PresentationTRANSCRIPT
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.
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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.
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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
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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
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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
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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
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Performance Results
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Outline
• Cone-based algorithm
• SPAN
• GAF-CEC
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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
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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
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Network Lifetime