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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

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

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  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 (PERCOM’10 workshop) Mannheim - Germany, Thursday, April 02, 2010 NETMODE (Network Management & Optimal Design Lab)

  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 NETMODE (Network Management & Optimal Design Lab)

  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 other’s transmission radius  RGG approach NETMODE (Network Management & Optimal Design Lab)

  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 graphG΄(V΄,E΄) • Trans. range implicitly controlled by varying trans. power • Open/closed feedback control mechanism NETMODE (Network Management & Optimal Design Lab)

  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... NETMODE (Network Management & Optimal Design Lab)

  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 NETMODE (Network Management & Optimal Design Lab)

  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 • 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)

  8. 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)

  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 • 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)

  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 NETMODE (Network Management & Optimal Design Lab)

  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 NETMODE (Network Management & Optimal Design Lab)

  12. 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)

  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 NETMODE (Network Management & Optimal Design Lab)

  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 >= dmin  perform NRN • othw. do not change degree value • Combination of NRN and magic number NETMODE (Network Management & Optimal Design Lab)

  15. 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)

  16. 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)

  17. 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)

  18. 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)

  19. 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)

  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 NETMODE (Network Management & Optimal Design Lab)

  21. 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)

  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 dmin=6 in both uniform/non-uniform networks NETMODE (Network Management & Optimal Design Lab)

  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 NETMODE (Network Management & Optimal Design Lab)

  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 NETMODE (Network Management & Optimal Design Lab)

  25. Thanks for your attention Questions? NETMODE (Network Management & Optimal Design Lab)

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