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NETW 707 Modeling and Simulation Amr El Mougy Maggie Mashaly

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NETW 707

Modeling

and

Simulation

Amr El Mougy

Maggie Mashaly

Lecture(7)

Mobility Modeling

- 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

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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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]

- 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

- 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

- 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

- 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