1. Mobility Models in Mobile Ad Hoc Networks Chun-Hung Chen 2005 Mar 8 th Dept. of Computer Science and Information Engineering National Taipei University of Technology

2. What is Mobile Network? Why is it called Ad Hoc? Mobile Ad Hoc Networks (MANET) is a network consisting of mobile nodes with wireless connection (Mobile) and without central control (Ad Hoc)  Self-Organized Network Each mobile node communicates with other nodes within its transmitting range Transmission may be interrupted by nodal movement or signal interference

3. It seems that something is watching Sensor Network is recently a hot topic Specified Application in MANET Nodes are equipped some observation devices (GPS, Temperature, Intruder Detection and so on) Nodes may move spontaneously or passively There are more restrictions in Sensor Networks  Power  Transmission Range  Limited Computation Power  Moving Speed (if does)

4. Realistic Mobility Model is better than Proposed Mobility Models Although MANET and Sensor Network are being researched for a while, there do not exist many realistic implementation To implement a real MANET or Sensor Network environment for emulation is difficult  Signal Interference  Boundary We will need to evaluate MANET by simulation To have useful simulation results is to control factors in simulation  Traffic Pattern  Bandwidth  Power Consumption  Signal Power (Transmission Range)  Mobility Pattern  And so on

5. How Many Mobility Model are inspected? Entity Mobility Models  Random Walk Mobility Model  Random Waypoint Mobility Model  Random Direction Mobility Model  A Boundless Simulation Area Mobility Model  Gauss-Markov Mobility Model  A Probability Version of the Random Walk Mobility Model  City Section Mobility Model

6. Group Mobility Models  Exponential Correlated Random Mobility Model  Column Mobility Model  Nomadic Community Mobility Model  Pursue Mobility Model  Reference Point Group Mobility Model

7. Random Walk Parameters:  Speed = [Speed_MIN,Speed_MA X]  Angle = [0,2π]  Traversal Time (t) or Traversal Distance (d)

8. Random Waypoint Parameters  Speed = [Speed_MIN,Speed_MA X]  Destination = [Random_X,Random_Y]  Pause Time >= 0

9. Random Direction Parameters:  Speed = [Speed_MIN,Speed_MA X]  Direction = [0,π] (Initial [0,2π])  Pause Time Go straight with selected direction until bump to the boundary then pause to select another direction

10. Boundless Simulation Area Parameters:  v(t+ △ t) = min{max[v(t)+ △ v,0], V max }  θ(t+ △ t) = θ(t) + △ θ  x(t+ △ t) = x(t) + v(t) * cosθ(t)  y(t+ △ t) = y(t) + v(t) * cosθ(t)  △ v = [-A max * △ t, A max * △ t]  △ θ = [-α* △ t, α* △ t]

11. Gauss-Markov Parameters:  When approach the edge, d value will change to prevent the node stocking at the edge

12. Probability Version of Random Walk

13. City Section

14. Group Mobility Exponential Correlated Random Mobility Model  Column Mobility Model  Given a reference grid, each node has a reference point on the reference grid  Each node can move freely around its reference point (Ex: Random Walk) Nomadic Community Mobility Model  Similar to Column Mobility Model, but all nodes of a group share a reference point Pursue Mobility Model  new_pos = old_pos + acceleration(target-old_pos) + random_vector

15. Reference Point Group Mobility Model  Group movements are based on the path traveled by a logical center for the group  GM: Group Motion Vector  RM: Random Motion Vector  Random motion of individual node is implemented by Random Waypoint without Pause

16. Simulation Parameters Simulation Package: ns-2 50 Mobile Nodes 100m Transmission Range Simulation Time from 0s ~ 2010s  Results is collected from 1010s Routing Protocol: Dynamic Source Routing (DSR) Each mobility model has 10 different runs and show with 95% confidence interval Simulated Model  Random Walk  Random Waypoint  Random Direction  RPGM 100% Intergroup communication 50% Intergroup communication, 50% Intragroup communication

17. What results do different mobility models bring?

18. Observation of Different Mobility Models The performance of an ad hoc network protocol can vary significantly with different mobility models The performance of an ad hoc network protocol can vary significantly when the same mobility model is used with different parameters Data traffic pattern will affect the simulation results Selecting the most suitable mobility model fitting to the proposed protocol

19. Considerations when Applying Each Mobility Model Random Walk  Small input parameter: Stable and static networks  Large input parameter: Similar to Random Waypoint Random Waypoint  Scenarios such as conference or museum Random Direction  Unrealistic model  Pause time before reaching the edge  Similar to Random Walk Boundless Simulation  Although moving without boundary, the radio propagation and neighboring condition are unrealistic Gauss-Markov  Most realistic mobility model Probabilistic Random Walk  Choosing appropriate parameters to fit real world is difficult City Section  For some protocol designed for city walk

20. Exponential Correlated Random Mobility Model  Theoretically describe all other mobility models, but selecting appropriate parameter is impossible Column, Nomadic Community, Pursue Mobility Models  Above three mobility models can be modeled by RPGM with different parameters RPGM Model  Generic method for group mobility  Assigned an entity mobility model to handle groups and individual node

21. Random Waypoint Considered Harmful Yoon has published a paper indicating that network average speed of RWP will decay to zero in simulation  Setting the minimum speed larger than zero Besides speed decaying, the nodes with RWP tend to cross the center of the area

22. If you can ’ t move quickly, please don ’ t go too far

23. If you are close to the wall, don ’ t be afraid

24. Fixed Lower Speed, Varied Shorter Distance

25. Varied Lower Speed, Fixed Shorter Distance

26. Ripple Mobility Model with LSSD

27. Ripple Mobility Model with LSSD and Shorter Radius

28. How does the speed distribute during the simulation

29. That ’ s the Answer

30. Spatial Distribution Comparisons Cumulate the nodal appearance in the square of 100mx100m (Moving area is 1000mx1000m)

31. Conclusions The defects in RWP are explored by some research and solutions are also proposed  Decaying Average Speed  Unfair Moving Pattern Most proposed solutions target to one of the defects but not both To generate different moving pattern within the same speed range is a reasonable requirement but it has not been brought up

32. Reference Tracy Camp, Jeff Boleng, and Vanessa Davies, “A Survey of Mobility Models for Ad Hoc Network Research”, Wireless Communication and Mobile Computing (WCMC) 2002 Guolong Lin, Guevara Noubir, and Rajmohan Raharaman, “Mobility Models for Ad Hoc Network Simulation”, INFOCOM 2004

33. First Model X 1, X 2,…, X n as non-overlapping time periods  During each time periods X i, the node travels with some random speed V i for some random distance D i {X i } is a renewal process This model is applied on the homogeneous metric space X i =D i /V i X i+1 =D i+1 /V i+1

34. Analytical Results of First Model

35. Residual distance γ t is represented the remaining distance in time period X i contains t  X i = (t 0, t 1 )  Residual waiting time β t is represented the remaining time in time period X i contains t

36. Second Model The initial Speed and Distance are derived from the stable state of First Model  The movement state of a node at time t  ∞ is characterized by V t, γ t, β t  For X 0, D 0 is selected according to F γ (z) V 0 is selected according to F V (z) The remaining periods are chosen as the same as the first model

37. Analytical Observation Second model has the following distribution  If the following formula is satisfied,  Speed distribution is uniformly distributed within [V min, V max ]

38. Simulation Results in Boundless Area (R max =1000m, (0,20)) Original:  Distance D is picked from  Speed V is picked uniformly from [V min, V max ] Modified:  D 0 is picked from  V o is picked uniformly from [V min, V max ]  D i is picked from  V i is picked from

39. Speed Distribution Comparison between Modified and Original in Boundless Area

40. Simulation Results in Bounded Area (1500mx1500m, (0,20)) Original:  Destination is picked uniformly within the simulation region  Speed is picked uniformly from (V min, V max ) Modified  Destination is picked uniformly within the simulation region  First Speed is picked uniformly from (V min, V max )  Following Speed is picked according to

41. Speed Distribution Comparison between Modified and Original in Bounded Area

42. Extended Version of First and Second Model Pause Time Z is considered in the extended model Z is independent of D, V (hence X) It generates the following time sequence  X 1, Z 1, X 2, Z 2, X 3, Z 3,…, X n, Z n,…  The sequence is not renewal process If pair of X and Z is considered, then {Y i } is renewal process  Y 1 (X 1 +Z 1 ), Y 2 (X 2 +Z 2 ), Y 3 (X 3 +Z 3 ),…, Y n (X n +Z n ),…

43. Discussions and Conclusions Renewal theory is useful to analyze and solve the problem of speed decay in the RWP model Derive target speed steady state distribution from the formula to simulate the different impact on routing protocol Do not need to discard the initial simulation data to achieve steady state How is the nodal distribution? RWP in Bounded Area is not derived from analytical work