1 / 23

A Uniform Continuum Model for the Scaling of Ad-Hoc Networks

A Uniform Continuum Model for the Scaling of Ad-Hoc Networks. Ernst W Grundke A Nur Zincir-Heywood Faculty of Computer Science Dalhousie University Halifax NS. www.cs.dal.ca/~grundke/ants/continuumModel.html. Acknowledgements. The Ant Colony: Nur Zincir-Heywood Allan Jost Owen Yue

shellie-morton
Download Presentation

A Uniform Continuum Model for the Scaling of Ad-Hoc Networks

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. A Uniform Continuum Model for the Scaling of Ad-Hoc Networks Ernst W GrundkeA Nur Zincir-Heywood Faculty of Computer ScienceDalhousie UniversityHalifax NS www.cs.dal.ca/~grundke/ants/continuumModel.html

  2. Acknowledgements The Ant Colony: Nur Zincir-Heywood Allan Jost Owen Yue Donald Morrison Nick Pilon Grundke & Zincir-Heywood, Dalhousie University: Uniform Continuum Model for Scaling

  3. In a mobile ad-hoc network, ... • … nodes move • … nodes enter & leave • … communication is short-range wireless • … hosts = routers • … node power is scarce What happens when such networks get large? Grundke & Zincir-Heywood, Dalhousie University: Uniform Continuum Model for Scaling

  4. A Continuum Model • Only the node density is known Grundke & Zincir-Heywood, Dalhousie University: Uniform Continuum Model for Scaling

  5. A Continuum Model • Only the node density is known • Think of nodes as “smeared out” Grundke & Zincir-Heywood, Dalhousie University: Uniform Continuum Model for Scaling

  6. A Uniform Model • Assume similar conditions everywhere: no edge effects X X Grundke & Zincir-Heywood, Dalhousie University: Uniform Continuum Model for Scaling

  7. Model • Continuum of nodes • Uniform: no edge effects • Simple, optimistic assumptions • Mathematically tractable: no simulation • Dimensionless parameters • Analytical results • Approximate at best • J. B. S. Haldane, 1928, “On being the right size” Grundke & Zincir-Heywood, Dalhousie University: Uniform Continuum Model for Scaling

  8. Network Geometry • Nearest neighbour distance d1 • Node density = 1/(r12) Node Voronoi cell r1 = d1/2 Grundke & Zincir-Heywood, Dalhousie University: Uniform Continuum Model for Scaling

  9. Network Geometry • N nodes • Max separation D • D = d1(N-1) D D+d1 Grundke & Zincir-Heywood, Dalhousie University: Uniform Continuum Model for Scaling

  10. Node Behaviour • Generate user data randomly: pT packets per unit time • Finite transmission range R:d1 R D • Forward user data packets B C A R Grundke & Zincir-Heywood, Dalhousie University: Uniform Continuum Model for Scaling

  11. Nodes Behaviour (cont.) • Motion: pW link events per unit time  = pW/pT (the walk/talk ratio) Grundke & Zincir-Heywood, Dalhousie University: Uniform Continuum Model for Scaling

  12. Nodes Behaviour (cont.) • Group of g nodes competing for a single channel:g =(R+r1)2/r12 • Finite transmission bandwidth:pW<b, pT<b in isolation, pW<b/g, pT<b/g in network Grundke & Zincir-Heywood, Dalhousie University: Uniform Continuum Model for Scaling

  13. Forwarding User Data Packets • Define forwarding overhead:  = mean hops per packet • Uniformity: data rate = pT(per node) • If packets travel D/2 in hops of R,  = (r1/R)(N-1) • Example: <5 requires N<121. Grundke & Zincir-Heywood, Dalhousie University: Uniform Continuum Model for Scaling

  14. Ceiling (Forwarding) pT < b/g pT/b< R/(r1(N1))  r12 /(R+r1)2= r1R/((R+r1)2(N1)) • Small range (R 2r1) is best; then pT/b< 0.22/(N1) • Example: If N=100 then pT/b < 2.5% • Applies regardless of routing & mobility Grundke & Zincir-Heywood, Dalhousie University: Uniform Continuum Model for Scaling

  15. Ceiling (Forwarding) pT/b< 0.22/(N1): N Max pT/b 10 10.3% 100 2.47% 1,000 0.73% 10,000 0.22% Grundke & Zincir-Heywood, Dalhousie University: Uniform Continuum Model for Scaling

  16. Routing Traffic • Define routing overhead:  = packet transmissions caused by one link event • Uniformity: data rate = pW (per node) • Assume proactive routing; flat. • If each node broadcasts to (g1)/2, N = (g1)/2. • For R 2r1: = (N/4)1 Grundke & Zincir-Heywood, Dalhousie University: Uniform Continuum Model for Scaling

  17. Ceiling (Routing) pW < b/g ...pW/b < 1/(2N) approx. • Example: If N=100, pW/b< 0.5%.For b~1Mbps and 1000 bits/packet, pW < 5 link events/second • Numerically not serious for modest N. Grundke & Zincir-Heywood, Dalhousie University: Uniform Continuum Model for Scaling

  18. Ceiling (Routing) Routing:  (1/N)Forwarding:  (1/N) N Max pw/b Max pT/b 10 5% 10.3% 100 0.5% 2.47% 1,000 0.05% 0.73% 10,000 0.005% 0.22% Grundke & Zincir-Heywood, Dalhousie University: Uniform Continuum Model for Scaling

  19. Total Traffic: Data + Routing pT + pW<b/g ( + ) pT<b/g ( = pW/pT) • Forwarding traffic dominates:  < / • Routing traffic dominates:  > / Grundke & Zincir-Heywood, Dalhousie University: Uniform Continuum Model for Scaling

  20. Power • Average antenna power per node:kR2(pT + pW) ~ (N) Grundke & Zincir-Heywood, Dalhousie University: Uniform Continuum Model for Scaling

  21. Other Dimensions • See paper! Grundke & Zincir-Heywood, Dalhousie University: Uniform Continuum Model for Scaling

  22. Conclusions • For flat ad-hoc networks: Keep N,R small; use hierarchies • Dimensionless parameters:  = pW/pT = the walk/talk ratio  = forwarding overhead  = routing overhead • In 2D:  is (N/R),  is (N/R2) • / characterizes traffic type • Map simulations into a common space? Grundke & Zincir-Heywood, Dalhousie University: Uniform Continuum Model for Scaling

  23. ? Comments?Questions? www.cs.dal.ca/~grundke/ants/continuumModel.html Grundke & Zincir-Heywood, Dalhousie University: Uniform Continuum Model for Scaling

More Related