Topology Control and Its Effects in Wireless Networks

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Topology Control and Its Effectsin Wireless
Networks

• Ning Li, Jennifer Hou, and Lui Sha
• Department of Computer Science
• University of Illinois at Urbana-Champaign
• nli,jhou,lrs_at_cs.uiuc.edu

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Topology Control

• Intuitive power-saving methods in wireless
  networks
• Energy Power ? Working Time
• Reduce the working time sleep/wake up (IEEE
  802.11 PSM).
• Reduce the transmission power Topology Control.
• Problem Formulation
• Objective to reduce the transmission power and
  increase network capacity.
• Input a set of nodes in the 2D plane.
• Output the transmission range (power) for each
  node to form the appropriate neighbor relation.
• Topology control can achieve
• Global connectivity
• Lower energy consumption
• Less MAC-level contention/interference
• Higher network capacity

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Why Topology Control?
(1) No Topology Control
(2) With Topology Control
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Topology Control Layer
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Design Guidelines for Topology Control Algorithms

• The network connectivity should be preserved,
  especially for static wireless networks.
• Algorithms should be distributed, i.e., each node
  should make decisions on its own.
• To be more resistant to the impact of mobility,
  the algorithm should depend only on local
  information, e.g., information collected within
  one hop.
• Bi-directional links are preferred, so as to
  facilitate link level acknowledgments and the
  medium access control mechanisms such as RTS/CTS
  in IEEE 802.11.
• It is also desirable that the node degree in the
  topology derived under the algorithm is small.

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LMST Local Minimum Spanning Tree

• Visible Neighborhood the set of nodes that node
  u can reach by using its maximal transmission
  power.
• Information Collection Each node periodically
  broadcasts a Hello message to its visible
  neighborhood using its maximal transmission
  power.
• Topology Construction
• Each node independently obtains its local MST
  spanning the visible neighborhood (the tree
  should be unique).
• Each node only takes the one-hop, on-tree nodes
  as its neighbors in the final topology.
• The network topology under LMST is all the nodes
  and their individually perceived neighbor
  relations.

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LMST Example
w3
w2
w4
w1
w5
u
w6
w7
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Uni-Directional Links
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LMST Properties

• The final topology G0 is a connected graph (with
  some links being uni-directional).
• To make the topology bi-directional, we can apply
  
• Addition add extra links into G0 so that all
  uni-directional links become bi-directional
• Removal delete all uni-directional links in G0.
• Both approaches result in connected graphs with
  bi-directional links.
• LMST Properties
• The resulting topology preserves the
  connectivity.
• After removal of asymmetric links, all links are
  bi-directional and the connectivity is still
  preserved.
• The degree of any node is bounded by 6.

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Degree Bound

• Degree the number of neighbors a node has
• The degree of any node in Go is bounded by 6.
• cone(u,a,v) region that lies between OA and OB,
  where angle COA angle COB a/2.

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Degree Bound
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Proof of Connectivity

• Define a weight function such that each edge has
  a distinct weight.
• Prove by induction that any pair of nodes of
  distance at most r are connected
• Basis the pair of nodes on the shortest edge are
  connected.
• Induction on the node pairs in an ascending order
  of the weight. It can be proved that any pair of
  nodes are connected by shorter edges from the
  topology by LMST.
• Prove that any pair of nodes in the topology by
  LMST are connected.

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Dealing with Mobility
r vmax t
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Performance Evaluation

• Traffic Independent Metrics
• Average node degree
• Average link length
• Average radius
• Traffic Dependent Metrics
• Transmissions per packet
• Energy efficiency

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Simulation Results (1)
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Simulation Results (2)
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Average Degree
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Simulation Results (3)

• Simulation Setup
• n nodes are randomly distributed in a rectangular
  area.
• n/2 nodes are sources and the others are
  destinations.
• Two types of traffic CBR and TCP/FTP.
• Routing protocol AODV

Transmissions per packet
CBR Traffic
TCP/FTP Traffic
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Simulation Results (4)
CBR Traffic
TCP/FTP Traffic
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LMST Summary

• A localized topology control algorithm for
  wireless multihop networks which
• Preserves global connectivity
• Ensures bi-directional links
• Has a bounded number of neighbors
• Provides higher capacity and energy efficiency.

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Existing Work

• Assumptions
• Static multi-hop wireless network.
• Homogeneous Network the maximal transmission
  power (transmission range) for each node is the
  same.
• Transmission power can be adjusted.
• The area that the transmission of a node u can
  cover is a disk centered at u.
• Each node is able to determine its own position
  via GPS or other positioning techniques.
• Existing Work
• RM Relay-Region Based Approach, 1999
• CBTC Cone-Based Topology Control, 2000
• RNG, 2002
• COMPOW/CLUSTERPOW, 2002/2003

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RMRelay Region Based Approach
(b) Enclosure.
(a) Relay Region.
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CBTC(?)Cone-Based Topology Control

• Need a neighbor in every ?-cone.

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RNG Relative Neighborhood Graph