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

1NETMODE (Network Management & Optimal Design Lab)

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


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


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


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

Topology Control

G(V,E) G(V΄,E΄)


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!) All nice things come…. (not to an end!) ……..as tradeoffs in engineering.....as tradeoffs in engineering...

Topology Control

ConnectivityRobustness

QoS

Capacity increaseInterference reduction

Energy efficiency


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


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


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) pdf cdf


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


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


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


Initial, K-Neigh, NRN Topology Comparison

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


NRN Topology Properties

Node degree p.m.fAverage node degreeVariance of node degree

Network av. Node degree Variance of network node degree


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


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


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


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


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


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


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


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


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


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


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


Thanks for your attention

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

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