NETW 707 Modeling and Simulation Amr El Mougy Maggie Mashaly

1. NETW 707 Modeling and Simulation Amr El Mougy Maggie Mashaly

2. Lecture(7) Mobility Modeling

3. Mobility in Wireless Networks • In mobile networks, users are free to move around • Mobility models are used to describe these movement patterns • Movement patterns depend on the type of network • Trace-based mobility models are always an accurate way for producing movement patterns. However, they are not always available

4. Categorizing Mobility Models

5. Random Models • Nodes move freely • No restrictions in speed, direction, or destination. No correlation with other nodes • Models are simple but may not be realistic

6. Random Waypoint Model • Benchmark mobility model • Simple implementation: • Each node randomly selects a location in the field as its destination • The node travels to its destination at a speed chosen uniformly from 0, • Each node choses its velocity and direction independently of other nodes • Upon reaching the destination, each node pauses for a random pause time • The process is repeated • determine the dynamicity of the topology

7. Random Walk Model • Motivated by the observation that some nodes often move in an unexpected way • As with random waypoint, movement is totally random • The pause time is equal to zero, i.e. • Time intervals are defined, and nodes change their speed and direction at every interval • Every interval, nodes choose a new direction from (0, 2π] and a new speed from 0, • Uniform or Gaussian distributions are typically used • When nodes reach the border, they bounce back with the same or opposite angle • Changes in every time interval are memoryless

8. Random Direction Model • A problem with the random waypoint and random walk models is that they result in non-uniform node distribution • Nodes tend to converge towards the center, diverge away, then converge again, creating density fluctuations • Random direction chooses a direction so that the node will reach the boundary. Then another direction is chosen towards another boundary and the process is repeated • Less fluctuations in node density

9. Limitations of Random Models • Lack of temporal dependence of velocity: sudden stops or movements, increases in speed, are not captured • Lack of spatial dependence of velocity: nodes move independently of other nodes. Not true for example in battlefields • Lack of geographic restrictions on movement: obstacles, streets, freeways are not represented

10. Mobility Models with Temporal Dependency • In reality, mobility may be constrained by physical laws of acceleration, velocity, and rate of change in direction • Thus, current mobility patterns of a node may depend on past patterns • Random models are memoryless and cannot capture such dependency

11. Gauss-Markov Mobility Model • Mobility has a “memory” that is captured by a Gauss-Markov Process • Velocity is defined over the x and ydirections as: • Velocity at time t is given by , and at t-1 it is , • αis called the memory level, is the mean and is the variance • is a Gaussian process with mean 0 and variance

12. Gauss-Markov Mobility Model • When α= 0, the model reduces to random walk, i.e. no memory • When α= 1, the current velocity is the same as the previous one • When α is between 0 and 1, the current velocity partially depend on the previous velocity and partially on the random Gaussian value

13. Smooth Random Mobility • Suggests changing speed and direction incrementally and gradually • Nodes often move in preferred speeds rather than uniform distribution over • Speeds within the preferred set have high probability, while the rest are uniformly distributed • For example, for the preferred set

14. Smooth Random Mobility • Frequency of speed change follows a Poisson process • Upon a speed change event, a new speed is chosen according to the aforementioned probability distribution • The speed is changed to the new one smoothly using uniformly distributed variables from [0, amax], [amin,0] according to: • Thus, the new speed is calculated as

15. Smooth Random Mobility • If a(t) is small then change in speed is gradual and temporal correlation is strong • Change in direction is assumed to be uniform over [0, 2π] • The frequency of direction change follows an exponential distribution • The difference between the old direction and the new one is given by • If the change in direction is too large, it is divided into small slots

16. Mobility Models with Spatial Dependency • In certain situations, the velocities of nodes are correlated in space • Ex: speed of a vehicle is bounded by the vehicle ahead of it, Soldiers on a battlefield move in units • Random and temporal models do not capture this effect

17. Reference Point Group Mobility Model • Each group is composed of a leader and members. The mobility of the group is defined by its leader • The motion of the group leader, and thus the motion trend of the group is defined by the vector • The motion of each member deviates from by some degree • The final motion vector of member i is deviated from using • + • has length uniformly distributed in [0, and angle uniformly distributed in [0, 2π]

18. Pursue Mobility Model • Models situations where several nodes attempt to capture a single node • The target node (being pursued) moves using the random waypoint model • The remaining nodes move using • May be generated by the reference point group mobility model

19. Mobility Models with Geographical Restrictions • Mobility of nodes is bounded by the environment • Used to model movements along freeways, streets, around obstacles, etc. • Nodes move in pseudo-random or predefined pathways

20. Pathway Mobility Model • A predefined map is first created either randomly or based on a real city • The map is a graph where vertices represent buildings and edges represent streets between buildings • The movement of nodes resemble the random waypoint model, but bounded by the map • Nodes choose a destination, travel using a constant speed, pause for and repeat the process

21. Obstacle Mobility Model • Obstacles are modeled as rectangular objects randomly placed in a field • Nodes must change their trajectory upon reaching an obstacle • Wireless signals are assumed to be blocked by the obstacles • Could be used to model conferences, disaster relief or event coverage scenarios