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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

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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

IEEE PWN ’10 (PERCOM’10 workshop)

Mannheim - Germany, Thursday, April 02, 2010

NETMODE (Network Management & Optimal Design Lab)

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

- 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)

- 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)

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)

- 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

- 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(α,β) Distribution

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

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NETMODE (Network Management & Optimal Design Lab)

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

- 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)

- 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

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

NETMODE (Network Management & Optimal Design Lab)

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)

- 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

- 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)

- 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)

- 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)

- 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)

- 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)

- 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)

- 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 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)

- 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

- 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)

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