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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 Network Management & Optimal Design Lab (NETMODE) Vasileios Karyotis , Alexandros Manolakos and Symeon Papavassiliou

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on topology control and non uniform node deployment in ad hoc networks

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 (PERCOM’10 workshop)

Mannheim - Germany, Thursday, April 02, 2010

NETMODE (Network Management & Optimal Design Lab)

outline
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

NETMODE (Network Management & Optimal Design Lab)

ad hoc network system model
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 other’s transmission radius  RGG approach

NETMODE (Network Management & Optimal Design Lab)

topology control tc i introduction
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 graphG΄(V΄,E΄)
  • Trans. range implicitly controlled by varying trans. power
  • Open/closed feedback control mechanism

NETMODE (Network Management & Optimal Design Lab)

topology control tc ii objectives tradeoffs
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...

NETMODE (Network Management & Optimal Design Lab)

topology control tc iii classification common practice
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

NETMODE (Network Management & Optimal Design Lab)

k neigh topology control protocol
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
    • K=9 ideal value (empirically)  both high connectivity, low av. physical node degree
    • Optional pruning stage (power-aware triangle inequality)
  • Distributed & asynchronous operation

NETMODE (Network Management & Optimal Design Lab)

the beta distribution
The beta(α,β) Distribution
  • Model for non-uniform node deployments
  • Continuous probability distribution, restricted in [0,1]
  • Depends on two parameters α, β(shape parameters)

pdfcdf

NETMODE (Network Management & Optimal Design Lab)

impact of non uniform node distributions
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
    • K=9 works for planar uniform scenarios only
  • Mobility  non-uniform spatial density (2D/3D), [5]
    • Similar complications as above

NETMODE (Network Management & Optimal Design Lab)

randomized topology control
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

NETMODE (Network Management & Optimal Design Lab)

nearest random neighbors nrn
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

NETMODE (Network Management & Optimal Design Lab)

initial k neigh nrn topology comparison
Initial, K-Neigh, NRN Topology Comparison

100 nodes in [0,1]2 following normal/manhattan-like β(2,2) distributions

NETMODE (Network Management & Optimal Design Lab)

nrn topology properties
NRN Topology Properties

Node degree p.m.f

Average node degree

Variance of node degree

Network av. Node degree Variance of network node

degree

NETMODE (Network Management & Optimal Design Lab)

enhanced nearest random neighbors e nrn
Enhanced-Nearest Random Neighbors (e-NRN)
  • Plain NRN suffers in sparse topologies
  • Solution  protect low degree nodes
  • Threshold degree value dmin
    • If node degree >= dmin  perform NRN
    • othw. do not change degree value
  • Combination of NRN and magic number

NETMODE (Network Management & Optimal Design Lab)

numerical results
Numerical Results
  • Node distribution in [0,1]2 or [0,1]3
  • Values of initial max. trans. radius in the [0,1]2 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

NETMODE (Network Management & Optimal Design Lab)

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

NETMODE (Network Management & Optimal Design Lab)

e nrn performance ii
e-NRN Performance (II)
  • Average physical node degree performance in [0,1]2
  • e-NRN guarantees low physical degree even in rather dense topologies
  • Both NRN/e-NRN guarantee connectivity in dense networks

NETMODE (Network Management & Optimal Design Lab)

e nrn vs k neigh i
e-NRN vs. K-Neigh (I)
  • Series of comparisons for various settings
  • K-Neigh w. pruning stage
  • K=9=dmin
  • Comparison in uniform 2D deployments
  • Connectivity drops for K-Neigh  tolerable in this scenario

NETMODE (Network Management & Optimal Design Lab)

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

NETMODE (Network Management & Optimal Design Lab)

e nrn vs k neigh iii
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

NETMODE (Network Management & Optimal Design Lab)

e nrn vs k neigh iv
e-NRN vs. K-Neigh (IV)
  • Comparison in β(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

NETMODE (Network Management & Optimal Design Lab)

e nrn vs k neigh quantitative summary
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 dmin=6 in both uniform/non-uniform networks

NETMODE (Network Management & Optimal Design Lab)

e nrn vs k neigh qualitative summary
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

NETMODE (Network Management & Optimal Design Lab)

summary of work
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

NETMODE (Network Management & Optimal Design Lab)

slide25
Thanks for your attention

Questions?

NETMODE (Network Management & Optimal Design Lab)