1. 1 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Algorithms for Radio Networks Winter Term 2005/2006 18 Jan 2006 12th Lecture Christian Schindelhauer schindel@upb.de

2. Algorithms for Radio Networks 2 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Mobility in Wireless Networks (talk to be held at SOFSEM 2005)  Introduction  Wireless Networks in a Nutshelf –Cellular Networks –Mobile Ad Hoc Networks –Sensor Networks  Mobility Patterns –Pedestrian –Marine and Submarine –Earth bound Vehicles –Aerial –Medium Based –Outer Space –Robot Motion –Characterization of Mobility Patterns –Measuring Mobility Patterns  Models of Mobility –Cellular –Random Trip –Group –Particle based –Combined –Non-Recurrent –Worst Case  Discussion –Mobility is Helpful –Mobility Models and Reality

3. Algorithms for Radio Networks 3 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Introduction The history of Mobile Radio (I)  1880s: Discovery of Radio Waves by Heinrich Hertz  1900s: First radio communication on ocean vessels  1910: Radios requried on all ocean vessels

4. Algorithms for Radio Networks 4 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Introduction The history of Mobile Radio (II)  1914: Radiotelephony for railroads  1918: Radio Transceiver even in war air plane  1930s: Radio transceivers for pedestrians: “Walky-Talky”  1940s: Handheld radio transceivers: “Handy-Talky”

5. Algorithms for Radio Networks 5 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Introduction The history of Mobile Radio (III)  1970s Vint Cerfs Stanford Research Institute Van –First mobile packet radio tranceivers ...  2000s Wireless sensor coin sized sensor nodes Mica2dot from California based Crossbow company

6. Algorithms for Radio Networks 6 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Wireless Networks in a Nutshelf Cellular Networks  Static base stations –devide the field into cells  All radio communication is only –between base station and client –between base stations usually hardwired  Mobility: –Movement into our out off a cell –Sometimes cell sizes vary dynamically (depending on the number of clients - UMTS)  Main problems: –Cellular Handoff –Location Service

7. Algorithms for Radio Networks 7 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Wireless Networks in a Nutshelf Mobile Ad Hoc Networks  MANET: –self-configuring network of mobile nodes –Nodes are routers and clients –no static infrastructure –network adapts to changes induced by movement  Positions of clients –in most applications not available –exceptions exist  Problems: –Find a multi-hop route between message source and target –Multicast a message –Uphold the network routing tables

8. Algorithms for Radio Networks 8 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Wireless Networks in a Nutshelf Wireless Sensor Networks  Sensor nodes –spacially distributed –equipped with sensors for temperature, vibration, pressure, sound, motion,...  Base stations –for collecting the information and control –possibly connected by ad- hoc-network  Main problem: –energy consumption nodes are sleeping most of the time –read out the sensor information from the field

9. Algorithms for Radio Networks 9 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Mobility Patterns: Pedestrian  Characteristics: –Slow velocity –Dynamics from obstacles obstructing the signal signal change a matter of meters –Applies for people or animals –Complete use of two- dimensional plane –Chaotic structure –Possible group behavior –Limited energy ressources  Examples –Pedestrians on the street or the mall –Wild life monitoring of animals –Radio devices for pets

10. Algorithms for Radio Networks 10 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Mobility Patterns: Marine and Submarine  Characteristics –Speed is limited due to friction –Two-dimensional motion submarine: nearly three- dimensional –Usually no group mobility except conoys, fleets, regattas, fish swarms  Reception –On the water: nearly optimal –Under the water: horrendous solution: long frequencies or fsound

11. Algorithms for Radio Networks 11 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Mobility Patterns: Earth bound vehicles  Mobility by wheels –Cars, railways, bicycles, motor bikes etc.  Features –More speed than pedestrians –Nearly 1-dimensional mobility because of collisions –Extreme group behavior e.g. passengers in trains  Radio communication –Reflections of environment reduce the signal strengths dramatically even of vehicles aiming at the same direction

12. Algorithms for Radio Networks 12 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Mobility Patterns: Aerial Mobility  Examples: –Flying patterns of migratory birds –Air planes  Characteristics –High speeds –Long distance travel problem: signal fading –No group mobility except bird swarms –Movement two-dimensional except air combat  Application –Collision avoidance –Air traffic control –Bird tracking

13. Algorithms for Radio Networks 13 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Mobility Patterns: Medium Based  Examples: –Dropwindsondes in tornadoes –Drifting buoyes  Chararcteristics of mobility –determined by the medium –can be often modelled by Navier-Stokes-equations –Medium can be 1,2,3- dimensional –Group mobility may occur is unwanted, because no information –Location information is always available this is the main purpose

14. Algorithms for Radio Networks 14 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Mobility Patterns: Outer Space  Characterization –Acceleration is the main restriction –Fuel is limited –Space vehicles drift through space most of the time –Non-circular orbits possible –Mobility in two-planet system is chaotic –Sometimes group behavior is desired, yet never been implemented  Radio communication –Perfect signal transmission –Energy resource usually no problem (solar paddles)

15. Algorithms for Radio Networks 15 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Mobility Patterns: Robot Motion

16. Algorithms for Radio Networks 16 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Mobility Patterns: Characterization  Group behavior –Can be exploited for radio communication  Limitations –Speed –Acceleration  Dimensions –1, 1 1/2, 2, 2 1/2, 3  Predictability –Simulation model –Completely erratic –Described by random process –Deterministic (selfish) behavior

17. Algorithms for Radio Networks 17 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Mobility Patterns: Measuring Mobility

18. Algorithms for Radio Networks 18 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Models of Mobility Cellular Mobility: Random Walk

19. Algorithms for Radio Networks 19 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Models of Mobility Cellular Mobility: Trace Based

20. Algorithms for Radio Networks 20 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Models of Mobility Cellular Mobility: Fluid Flow

21. Algorithms for Radio Networks 21 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Models of Mobility Random Trip Mobility  Random Walk  Random Waypoint  Random Direction  Boundless Simulation Area  Gauss-Markov  Probabilistiic Version of the Random Walk Moblity  City Section Mobility Model

22. Algorithms for Radio Networks 22 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Models of Mobility: Group-Mobility Models  Exponential Correlated Random  Column Mobility  Nomadic Community Mobility  Pursue Mobility  Reference Point Group

23. Algorithms for Radio Networks 23 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Models of Mobility: Particle Based Mobility  Helbing

24. Algorithms for Radio Networks 24 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Models of Mobility: Combined Mobility Models 

25. Algorithms for Radio Networks 25 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Models of Mobility: Combined Mobility Models  Non-Recurrent Models

26. Algorithms for Radio Networks 26 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Models of Mobility: Worst-Cased Mobility Models  Pedestrian  Vehicular

27. Algorithms for Radio Networks 27 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Modeling Worst Case Mobility V:Pedestrian Model ↔ Maximum velocity ≤ v max A:Vehicular Model ↔ Maximum accelaration ≤ a max

28. Algorithms for Radio Networks 28 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer The Mobile Ad Hoc Network  As a start: synchronous round model In every round of duration Δ 1.Determine positions (speed vectors) of possible comm. partners 2.Establish (stable) communication links 3.Update routing information 4.Do the job, i.e. packet delivery, live video streams, telephone,…

29. Algorithms for Radio Networks 29 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer The Mobility Model  Velocity bounded (pedestrian) mobility model for all i  {1,…,n}  Acceleration bounded (vehicular) mobility model for all i  {1,…,n}  Technical assumptions: –polynomial distances and speeds –complete knowledge of position

30. Algorithms for Radio Networks 30 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Crowds  Crowdedness of node set –natural lower bound on network parameters (like diversity) 1.Pedestrian (v) model: Maximum number of nodes that can collide with a given node in time span [0,Δ] 2.Vehicular (a) model: Maximum number of nodes that may move to node u meeting it with zero relative speed in time span [0,Δ]  crowd(S) := max u  S crowd(u)

31. Algorithms for Radio Networks 31 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Taming Mobility in the Link Layer  General Concept –Increase transmission distance –to guarrantee a certain life span Δ for each link –Apply the mobility model (i.e. a max or v max is known) Start position End position Transmission distance

32. Algorithms for Radio Networks 32 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Transmission Range of Pedestrian Communication  Pedestrian model / Velocity bounded model end Walking range start end Sa- tisfies triangle inequality

33. Algorithms for Radio Networks 33 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Transmission Range of Vehicular Communication  Vehicular mobility model / Acceleration bounded model end start end Sa- tisfies triangle inequality

34. Algorithms for Radio Networks 34 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Mobile Radio Interferences An edge g interferes with edge e in the 1.Pedestrian (v) model 2.Vehicular (a) model No interference Interference g g e e e e g e g p q q p

35. Algorithms for Radio Networks 35 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Mobile Results (I) Theorem In both mobility models we observe for all connected graphs G: Lemma In both mobility models α  {v,a} every mobile spanner is also a mobile power spanner, i.e. for some ß≥1 for all u,w  S there exists a path (u=p 0,p 1,…,p k =w) in G such that:

36. Algorithms for Radio Networks 36 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Load, Congestion and Spanners  Interference number of the network G: –Int(G) := max e  E(G) |Int(e)|  Load and path system –Set of all message paths defines path system P –ℓ(e) := # number of packets sent over edge e according to P  Congestion of an edge (with respect to a path system P ) –Congestion of a network G:  Mobile spanner –A network is a mobile spanner, if for all u,w exists a path (u=p 0,p 1,…,p k =w) such that for α  {v,a}:

37. Algorithms for Radio Networks 37 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Mobile Results (II) Theorem Given a mobile spanner G for any of our mobility models then –for every path system P in a complete network C –there exists a path system P‘ in G such that Theorem The Hierarchical Grid Graph constitutes a mobile spanner with at most O(crowd(V) + log n) interferences (for both mobility models). The Hierarchical Grid Graph can be built up in O(crowd(V) + log n) parallel steps using radio communication

38. Algorithms for Radio Networks 38 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer The Hierarchical Grid Graph (pedestrians)  Start with grid of box size Δ v max  For O(log n) rounds do –Determine a cluster head per box –Build up star-connections from all nodes to their cluster heads –Erase all non cluster heads –Connect neighbored cluster heads –Increase box size by factor 2  od

39. Algorithms for Radio Networks 39 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer The Hierarchical Grid Graph (vehicular)  Algorithm: –Consider coordinates (x(s i ),y(s i ),x(s‘ i ),y(s‘ i )) –Start with four-dimensional grid with rectangular boxes of size (6Δ²a max, 6Δ²a max,2Δv max,2Δv max ) –Use the same algorithm as before x vxvx t=0 x vxvx t= Δ x vxvx t=2 Δ

40. Algorithms for Radio Networks 40 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Stable Basic Networks under Worst Case Mobility Corollary There exist distributed algorithms that construct a mobile network G for velocity bounded and acceleration bounded model with the following properties: 1.G allows routing approximating the optimal congestion by O(log² n) 2.Energy-optimal routing can be approximated by a factor of O(1) 3.G approximates the minimal interference number by O(log n) 4.The degree is O(crowd(S)+ log n) 5.The diameter is O(log n)  Still no routing can satisfy small congestion and energy at the same time!

41. Algorithms for Radio Networks 41 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Discussion: Mobility is Helpful

42. Algorithms for Radio Networks 42 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Discussion: Mobility Models and Reality

43. 43 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Thanks for your attention! End of 12th lecture Next lecture:We 25 Jan 2006, 4pm, F1.110 Next exercise class: Th 19 Jan 2006, 1.15 pm, F2.211 or Tu 24 Jan 2006, 1.15 pm, F1.110 Next mini examMo 13 Feb 2006, 2pm, FU.511