Outdoor Mobility Model | Gauss-Markov

Mobility models simulate the movements of mobile nodes in wireless networks and are essential for ad-hoc network research. They significantly affect the performance and behavior of various network protocols. Mobility models are classified into two main categories: entity mobility models (where nodes move independently) and group mobility models (where node movements are correlated).

The Gauss-Markov mobility model is an entity mobility model originally proposed for simulating personal communication service networks. This model captures realistic characteristics of outdoor mobility such as randomness, correlation, and variation in movement patterns. It uses a single tuning parameter to adjust the degree of randomness, making it flexible for different mobility scenarios.

Gauss-Markov Mobility Model

The Gauss-Markov mobility model calculates the speed and direction of each mobile node at a given time instance based on the previous speed and direction, an average value, and a random variable from a Gaussian distribution. The model uses the following mathematical formulations:

$$\mathrm{v_n=\alpha v_{n-1}+(1-\alpha) \overline{v}+\sqrt{(1-\alpha^2)}v_{rnd}}$$

$$\mathrm{\theta_n=\alpha \theta_{n-1}+(1-\alpha) \overline{\theta}+\sqrt{(1-\alpha^2)}\theta_{rnd}}$$

Where:

• v_n and ?_n are speed and direction of mobile node at time instance n

• v_n-1 and ?_n-1 are speed and direction at time instance (n-1)

• v? and ?? are average speed and direction

• v_rnd and ?_rnd are random variables from Gaussian distribution with zero mean and unit variance

• ? is the tuning parameter that ranges from 0 to 1

The tuning parameter ? controls the degree of randomness in the mobility pattern. When ? is close to 0, the mobility pattern becomes more random and less correlated with the previous state. When ? is close to 1, the mobility pattern becomes more predictable and highly correlated with the previous state.

Advantages

• Simulates different levels of randomness by adjusting the randomness index parameter

• Models mobility for personal communication services effectively

• Adapts to different environmental conditions by changing average speed and direction

Disadvantages

• Does not consider simulation area boundaries, potentially causing unrealistic movements outside the area

• Does not account for obstacles and environmental factors that influence mobility patterns

• May result in abrupt stops and sharp directional changes

Enhanced Gauss-Markov Mobility Model

The Enhanced Gauss-Markov (EGM) mobility model is a modification designed specifically for Unmanned Aerial Vehicle Ad-hoc Networks (UAANETs). It addresses the limitations of the original model by introducing additional mechanisms and parameters.

Key enhancements include:

• Minimum speed threshold (v_min) Prevents nodes from stopping or moving too slowly

• Maximum turning angle (?_max) Prevents sharp turns that are unrealistic for UAVs

• Reflection mechanism Keeps nodes within simulation boundaries

• Altitude and acceleration parameters Important factors for three-dimensional UAV movement

The altitude calculation follows:

$$\mathrm{z_n=\beta z_{n-1}+(1-\beta) \overline{z}+\sqrt{(1-\beta^2)}z_{rnd}}$$

The acceleration calculation is:

$$\mathrm{a_n=\gamma a_{n-1}+(1-\gamma) \overline{a}+\sqrt{(1-\gamma^2)}a_{rnd}}$$

Where ? and ? are tuning parameters for altitude and acceleration correlation, respectively.

Comparison of Models

Performance Analysis

Simulation studies using NS-2 simulator have shown that the EGM model outperforms other mobility models for UAANET applications. Key performance improvements include:

• Higher average speed and lower pause time, reflecting continuous UAV movement

• Smoother directional changes with lower average turning angles

• Better connectivity with higher node degree and lower path loss

• Improved network performance with lower end-to-end delay and higher packet delivery ratio

Conclusion

The Gauss-Markov mobility model provides a foundation for simulating realistic outdoor mobility with adjustable randomness levels. The Enhanced Gauss-Markov model significantly improves upon this foundation by incorporating UAV-specific constraints and three-dimensional movement parameters, making it highly suitable for modern aerial network simulations.