Outdoor Mobility Model | Gauss-Markov

Mobility models simulate the movements of mobile nodes in network. They are for ad-hoc network research. Mobility models can affect performance and behavior of various network protocols. There are different types of mobility models. These depend on whether the movements of mobile nodes are dependent and independent of each other (group and entity mobility models respectively).

Gauss-Markov mobility model is an example of entity mobility model. It was proposed for simulation of personal communication service networks. This model can capture realistic characteristics of outdoor mobility. Such as randomness, correlation, and variation. model uses one tuning parameter to adjust degree of randomness in mobility pattern.

We will discuss Gauss-Markov mobility model in this article. We will also discuss enhanced version of this model. It is called Enhanced Gauss-Markov (EGM) mobility model. This model improves realism and applicability of model for networks of unmanned aerial vehicles (UAVs). We will discuss simulation results and analysis that compare performance of EGM mobility model with other mobility models. Finally, we will discuss with some limitations and future directions.

There are different types of mobility models for indoor and outdoor environments. Indoor models are Random-Walk, Random Way-Point, and Random Direction. On the other hand, outdoor models are Gauss Markov and Probabilistic version of Random-Walk.

Gauss-Markov Mobility Model

The basic idea of Gauss-Markov mobility model is speed and direction of each mobile node at a given time instance. These are calculated based on previous speed and direction, an average value, and random variable from Gaussian distribution. The model assumes that each mobile node has an initial speed and direction.

These can change over time according to the following formulas −

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

$$\mathrm{θ_n=\alpha θ_{n-1}+(1-α) \overline{θ}+\sqrt{(1-α^2)}θ_{rnd}}$$

Where,

• v_n and θ_n are speed and direction of mobile node at time instance,

• n,v_n-1 ,and θ_n-1 , are speed and direction at time instance (n-1),

• v̅ and θ̅ are average speed and direction,

• v_rnd and θ_rnd are random variables from Gaussian distribution with zero mean and unit variance, and

• α is tuning parameter that ranges from 0 to 1.

The tuning parameter α controls degree of randomness in mobility pattern.

• When α is close to 0, mobility pattern is more random and less correlated with previous state.

• When α is close to 1, mobility pattern is more predictable and more correlated with previous state.

Therefore, by varying α, model can adapt to different levels of randomness and correlation in outdoor mobility scenarios.

Advantages

• It can simulate different levels of randomness by adjusting parameter called index of randomness.

• It can model mobility of personal communication services, such as wireless phones.

• It can adapt to different environmental conditions by changing average speed and direction.

Disadvantages

• It does not consider simulation area boundaries and may result in unrealistic movements of nodes outside area.

• It does not account for effects of obstacles, and other factors that may influence mobility patterns.

• It may degrade image details and edges of image.

Enhanced Gauss-Markov Mobility Model

Enhanced Gauss-Markov (EGM) mobility model is modification of Gauss-Markov mobility model. It aims to improve its applicability for networks of UAVs or UAANETs. EGM mobility model introduces additional mechanisms to eliminate and limit sudden stops. It sharps turns within simulation region. It is unrealistic and undesirable for UAVs. EGM mobility model also incorporates altitude and acceleration as additional parameters for each mobile node. These are important factors for UAVs.

EGM mobility model uses same formulas as Gauss-Markov mobility model to calculate speed and direction of each mobile node, but with some modifications. First, model introduces minimum speed threshold, v_min. This prevents mobile nodes from stopping and moving too slowly. If calculated speed is lower than v_min, the model sets the speed to v_min. Second, the model introduces maximum turning angle threshold, θ_max. These prevent the mobile node from making sharp turns. If calculated direction change is greater than θ_max, model sets direction change to θ_max. Third, model introduces reflection mechanism. This prevents mobile node from going out of simulation region. If calculated position is outside simulation region, model reflects direction of mobile node by a certain angle.

The EGM mobility model also calculates altitude and acceleration of each mobile node using similar formulas as speed and direction, but with different parameters. The altitude is calculated as −

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

Where,

• z_n is altitude of mobile node at time instance n,

• z_n-1 is the altitude at time instance (n-1),

• z̅ is the average altitude,

• z_rnd is the random variable from Gaussian distribution with zero mean and unit variance, and

• β is the tuning parameter that ranges from 0 to 1.

The acceleration is calculated as −

$$\mathrm{\alpha_n=\gamma \alpha_{n-1}+(1-\gamma) \overline{\alpha}+\sqrt{(1-\gamma^2)}\alpha_{rnd}}$$

Where,

• α_n is the acceleration of mobile node at time instance n,

• α_n-1 is the acceleration at time instance (n-1),

• α̅ is the average acceleration,

• α_rnd is the random variable from Gaussian distribution with zero mean and unit variance, and

• γ is the tuning parameter that ranges from 0 to 1.

The EGM mobility model can be compared and contrasted with Gauss-Markov mobility model in terms of complexity, flexibility, and applicability.

• The EGM mobility model is more complex than the Gauss-Markov mobility model, as it involves more parameters and mechanisms to simulate realistic movements of UAVs.

• The EGM mobility model is also more flexible than Gauss-Markov mobility model, as it can adjust to different levels of randomness and correlation for speed, direction, altitude, and acceleration separately.

• The EGM mobility model is more applicable than the Gauss-Markov mobility model for UAANETs, as it can capture important features of UAVs such as minimum speed, maximum turning angle, altitude, acceleration, and reflection.

In this model, there is no area specifically designed for simulation. But, imagine that model goes beyond defined area and reaches its limits. In such cases, average speed and average direction values are replaced by average values. To calculate mean value, we can use protractor. By combining two moons, we can cover complete 360 degree.

The model takes into account limitations of where it is currently located. For example, if it's closer to 225-degree range. This includes that range in average calculation and ensures complete coverage. The major factors to consider are randomness index, average speed. Random variable of Gaussian distribution.

This approach is easy and straightforward to understand. However, it can result in loss of image detail and edge sharpness.

Simulation Results and Analysis

To evaluate the performance of EGM mobility model and compare it with other mobility models, i.e., Random Waypoint, Random Direction, and Gauss-Markov. Some simulation experiments were conducted using NS-2 simulator. Simulation setup and scenarios were based on realistic parameters and assumptions for UAANETs. The simulation results were measured in terms of various metrics. For example average speed, average pause time, average turning angle, average node degree, average path loss, average end-to-end delay, and average packet delivery ratio.

The simulation results showed that EGM mobility model had significant advantages. It has advantages over mobility models in terms of realism and performance for UAANETs.

• It had higher average speed and lower average pause time than other models. It reflected continuous and fast movements of UAVs.

• It had lower average turning angle than other models. It reflected smooth and gradual changes of direction of UAVs.

• It had higher average node degree than other models. It reflected high connectivity and density of UAVs.

• It had lower average path loss than other models. It reflected high quality of communication links among UAVs.

• It had lower average end-to-end delay and higher average packet delivery ratio than other models. It reflected high efficiency and reliability of data transmission among UAVs.

The simulation results and analysis demonstrated. This EGM mobility model was realistic and suitable for UAANET.

Conclusion

Mobility models are used for simulating how things move in networks. The Gauss-Markov model is used to simulate outdoor movement. It has realistic features. But it also has problems, i.e., ignoring boundaries and obstacles. To solve these problems for unmanned aerial vehicle networks. Enhanced Gauss-Markov model was introduced. It has extra features to prevent sudden stops and sharp turns. It considers altitude and acceleration. It is more realistic for UAVs.

Comparing the Enhanced Gauss-Markov model with the regular Gauss-Markov model. Enhanced model is more complex and flexible. It can adjust randomness and correlation separately. It is for speed, direction, altitude, and acceleration. In simulations, the Enhanced model performed better than other models. It is better in terms of speed, pause time, turning angle, connectivity, communication quality, delay, and packet delivery. But, the enhanced model still has limitations. It does not account for specific areas. So nodes can move unrealistically outside the defined region. It may also lose some image details. In conclusion, Enhanced Gauss-Markov model is an improvement over traditional models. It accurately represents UAV movements. It improves performance for UAV networks.