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On Topology Control and Non-Uniform Node Deployment in Ad Hoc Networks

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On Topology Control and Non-Uniform Node Deployment in Ad Hoc Networks National Technical University of Athens (NTUA) School of Electrical & Computer Engineering – PowerPoint PPT presentation

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Title: On Topology Control and Non-Uniform Node Deployment in Ad Hoc Networks


1
On Topology Control and Non-Uniform Node
Deployment in Ad Hoc Networks
  • National Technical University of Athens (NTUA)
  • School of Electrical Computer Engineering
  • Network Management Optimal Design Lab
    (NETMODE)
  • Vasileios Karyotis, Alexandros Manolakos and
    Symeon Papavassiliou
  • IEEE PWN 10 (PERCOM10 workshop)
  • Mannheim - Germany, Thursday, April 02, 2010

2
Outline
  • Topology Control (TC) in wireless networks
  • Impact of non-uniform node distributions on TC
  • Randomized Topology Control approach
  • Nearest Random Neighbors (NRN)
  • Analysis-enhancements of NRN (e-NRN)
  • Performance evaluation/comparison
  • Discussion

3
Ad Hoc Network System Model
  • Network graph G(V,E) with n nodes
  • Notation shown in table
  • Homogeneous initial network
  • For all nodes, initially
  • No energy constraints considered
  • Deterministic trans. power attenuation model
  • Two nodes are connected whenever each one lies in
    the others transmission radius ? RGG approach

4
Topology Control TC (I)(introduction)
  • Connectivity/energy consumption critical in
    wireless, multi-hop networks
  • Topology Control is a variant of Power Control
    for multi-hop networks
  • Power Control ? PHY layer
  • Topology Control ? NET layer
  • Underlying graph G(V,E) induced graph G?(V?,E?)
  • Trans. range implicitly controlled by varying
    trans. power
  • Open/closed feedback control mechanism

5
Topology Control TC (II)(objectives
tradeoffs)
  • Objectives
  • Capacity increase ? via spatial reuse
  • Energy consumption reduction
  • Connectivity maintenance
  • Environmental adaptation
  • All nice things come. (not to an end!)
  • ..as tradeoffs in engineering...

6
Topology Control TC (III)(classification
common practice)
  • Numerous approaches/classifications
  • PHY-MAC-NET
  • Centralized/distributed
  • Homogeneous/heterogeneous
  • Energy-oriented
  • Interference-oriented ? structural properties
  • Connectivity-oriented
  • Always preserving
  • Preserving with high probability (w.h.p.)
  • Impact of mobility has been considered
  • Effect of RWP mobility model
  • Little attention/consideration on impact of
    realistic spatial densities
  • Uniform or modified uniforms employed globally
  • Explicitly
  • implicitly

7
K-Neigh Topology Control Protocol
  • Proposed by Blough, Leoncini, Resta and Santi
    (2006), 4
  • Focus on physical degree
  • Number of nodes within trans. range of a node
  • Parameter K is deterministic pre-decided
  • Preserves connectivity w.h.p.
  • Nodes (stationary) initially broadcast ID with
    max. power
  • Based on responses ? neighbors in increasing
    distance order
  • The first K selected new neighbors
  • Trans. radius adapted properly
  • K9 ideal value (empirically) ? both high
    connectivity, low av. physical node degree
  • Optional pruning stage (power-aware triangle
    inequality)
  • Distributed asynchronous operation

8
The beta(a,ß) Distribution
  • Model for non-uniform node deployments
  • Continuous probability distribution, restricted
    in 0,1
  • Depends on two parameters a, ß (shape parameters)
  • pdf
    cdf

9
Impact of Non-uniform Node Distributions
  • Symmetric, non-uniform in 2D ? connectivity drops
  • Worse for dense networks
  • In 3D ? higher K required to ensure 95
    connectivity
  • K9 works for planar uniform scenarios only
  • Mobility ? non-uniform spatial density (2D/3D),
    5
  • Similar complications as above

10
Randomized Topology Control
  • Traditional TC approaches inefficient for both
  • 3D arrangements
  • Non-uniform arrangements
  • Strict connectivity requirements may pose harsh
    constraints
  • Sacrifice some small percentage connectivity for
    efficiency
  • Need to reduce node degree, but
  • balance the cost of degree reduction
    nevertheless

11
Nearest Random Neighbors (NRN)
  • Distributed, asynchronous and localized
  • Node degree ? random variable Xi
  • Nodes initially ranked in increasing distance
    order
  • New degree Xi is randomly an uniformly selected
    in 1,di
  • Neighbor subset determined according to distance
  • Trans. radius adaptation to reach the farthest
  • Pruning stage to remove asymmetric edges
  • Optional pruning stage as in K-Neigh (logical
    degree)
  • Randomness allows for more balanced neighbor
    selection
  • Differs from XTC, RTC

12
Initial, K-Neigh, NRN Topology Comparison
  • 100 nodes in 0,12 following normal/manhattan-lik
    e ß(2,2) distributions

13
NRN Topology Properties
  • Node degree p.m.f
  • Average node degree
  • Variance of node degree
  • Network av. Node degree Variance of
    network node

  • degree

14
Enhanced-Nearest Random Neighbors (e-NRN)
  • Plain NRN suffers in sparse topologies
  • Solution ? protect low degree nodes
  • Threshold degree value dmin
  • If node degree gt dmin ? perform NRN
  • othw. do not change degree value
  • Combination of NRN and magic number

15
Numerical Results
  • Node distribution in 0,12 or 0,13
  • Values of initial max. trans. radius in the
    0,12 deployment region to preserve 99
    connectivity
  • NRN/e-NRN performance evaluation
  • Comparison with K-Neigh
  • Average physical node degree
  • Connectivity
  • 1000 different scenarios for averaging

16
NRN Performance (I)
  • Connectivity of NRN
  • Problems of NRN in sparse networks
  • Addressed through e-NRN
  • dmin value required to achieve gt 95 connectivity
    e-NRN
  • e-NRN a global solution
  • NRN a good compromise for moderate-dense networks

17
e-NRN Performance (II)
  • Average physical node degree performance in
    0,12
  • e-NRN guarantees low physical degree even in
    rather dense topologies
  • Both NRN/e-NRN guarantee connectivity in dense
    networks

18
e-NRN vs. K-Neigh (I)
  • Series of comparisons for various settings
  • K-Neigh w. pruning stage
  • K9dmin
  • Comparison in uniform 2D deployments
  • Connectivity drops for K-Neigh ? tolerable in
    this scenario

19
e-NRN vs. K-Neigh (II)
  • Comparison in ß(2,2) 2D deployments
  • K-Neigh connectivity drops sharply
  • Best performance w.r.t. physical node degree
  • 2nd worse performance among analyzed topologies

20
e-NRN vs. K-Neigh (III)
  • Comparison in uniform 3D deployments
  • e-NRN maintains connectivity
  • K-Neigh drops connectivity below 95
  • Not sharply
  • Maintains physical node degree performance

21
e-NRN vs. K-Neigh (IV)
  • Comparison in ß(2,2) 3D deployments
  • K-Neigh exhibits worst connectivity performance
  • Retains best physical node degree performance
  • e-NRN achieves in all cases more than 99
    connectivity

22
e-NRN vs. K-Neigh (Quantitative Summary)
  • e-NRN always better in connectivity
  • Achieves more than 99 in all cases
  • K-Neigh better in physical node degree
  • In all cases less than 10, even 7
  • Non-uniform deployments seem to impact more
    K-Neigh performance than 3D
  • e-NRN can guarantee 95 connectivity with even
    dmin6 in both uniform/non-uniform networks

23
e-NRN vs. K-Neigh (Qualitative Summary)
  • No magic number
  • Adaptive
  • Connectivity-oriented
  • Close to best physical node degree performance
  • More robust to errors and failures

24
Summary of Work
  • Impact of non-uniform node distribution on TC
    mechanisms
  • Randomized TC approach to overcome them
  • NRN/e-NRN balance neighbor selection more
    efficiently
  • Maintain connectivity in arbitrary node
    deployments
  • 2D,3D, Mobile/fixed, uniform/non-uniform
  • Comparison with K-Neigh protocol
  • Better w.r.t. physical node degree performance
  • NRN/e-NRN maintain more than 99 connectivity

25
  • Thanks for your attention
  • Questions?
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