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In the performance evaluation of a protocol for an adhoc network, the protocol should be tested under realistic conditions and realistic movements of the mobile users (i.e., a mobility model). This paper deals with survey of mobility models that are used in the simulations of ad-hoc networks. We describe several mobility models that represent mobile nodes whose movements are independent of each other (i.e., entity mobility models) and several mobility models that represent mobile nodes whose movements are dependent on each other. The goal of this paper is to present a number of mobility models in order to offer researches more informed choices when they are deciding upon a mobility model to use in their performance evaluation. In the later sections we present simulation results that illustrate the importance of choosing a mobility model in the simulation of an ad-hoc network protocol, specifically, we illustrate how the performance of an ad-hoc network protocol changes as a result of changing the mobility model simulated.
Mobility models are needed in the design of strategies for location updating and paging, radio resource management (e.g., dynamic channel allocation schemes), and technical network planning and design (e.g., cell and location area layout and network dimensioning). The purpose of mobility models is to describe typical terminal movement so that the analysis for these purposes can be made.
Thus, the movement pattern of users plays an important role in performance analysis of mobile and wireless networks, especially in third-generation mobile communications, since terminal mobility has a great influence in most UMTS communication aspects involving either performance or traffic generation as a result of handover. Furthermore, due to the increasing requirements on data rates, quality of service, and spectral efficiency, in conjunction with the smaller cell sizes in these networks, the accurate performance evaluation of mobile communication systems will become crucial. Issues such as radio resource management, location management and QoS, as well as traffic handling capacity, are directly affected by mobility.
1.2 Evolution of Mobility Models
A wide variety of studies can be found in literature about mobility modelling, from deterministic to statistical models, which determine the movement of different type of users. Moreover, they can be classified in function of different variables: geographical region, type of service, purpose (e.g. for location updating, for network planning), degree of randomness, and/or level of description (from macroscopic to microscopic models). On the other hand, the proposed modelling techniques also present a wide variety regards to the complexity, from more general models to others that determine the user movement in detail. Our work began by presenting a classification of mobility models that summarizes all this diversity.
2. Introduction to MANETS
In general, a Mobile Ad hoc Network (MANET) is a collection of wireless nodes communicating with each other in the absence of any infrastructure To thoroughly and systematically study a new Mobile Ad hoc Network protocol, it is important to simulate this protocol and evaluate its protocol performance. Protocol simulation has several key parameters, including mobility model and communicating traffic pattern, among others.
The mobility model is designed to describe the movement pattern of mobile users, and how their location, velocity and acceleration change over time. Since mobility patterns may play a significant role in determining the protocol performance, it is desirable for mobility models to emulate the movement pattern of targeted real life applications in a reasonable way. Otherwise, the observations made and the conclusions drawn from the simulation studies may be misleading. Thus, when evaluating MANET protocols, it is necessary to choose the proper underlying mobility model. For example, the nodes in Random Waypoint model behave quite differently as compared to nodes moving in groups . It is not appropriate to evaluate the applications where nodes tend to move together using Random Waypoint model. Therefore, there is a real need for developing a deeper understanding of mobility models and their impact on protocol performance.
3. Mobility models used in simulations
3.1 Random waypoint model (RWM)
It works as follows. All nodes are uniformly distributed around the simulation area at starting time. Each node then choose a random destination and moves there with a speed uniformly distributed over [0,vmax]. Then there is a pause time which could be selected be _to give continuous motion.
3.2 Random direction model (RDM)
This is a more stable model than a random waypoint model. At start the nodes selects a random direction and starts to move along it. Since the area of simulation is confined the node may end up reaching one of the boundaries during the simulation. When a boundary is reached the node pause for a given time and then chooses a new direction to travel. Since the node is on a boundary the selectable angle is 180 degrees
3.3 Modified Random direction model (MRDM)
To give a even more realistic simulation the Random Direction Model was extended with a extra choice for the nodes when their pause time is over. The nodes don't have to travel all the way to the boundary but could stop anywhere along the path
3.4 Column model (CM)
Nodes are only moving along the x-axis. The initial position of node i is (10i,10i)and the node changes the speed v E [0,vmax] at the discrete intervals. This will produce a mobility pattern that is one dimension simpler than the random mobility model since the nodes only move along the x-axis.
3.5 Pursue model (PM)
Another model done in order to try to create group movement. One node in each group is moving according to the random waypoint model The rest of the group is moving towards the target that the .leading. is aiming for. The speed of the pursuing nodes is chosen uniform random in the range [Vpmin, Vpmax]
3.6 Reference Point Group mobility model (RPGM)
Another way to simulate group behaviour in [ where each node belong to a group where every node follow a logical centre reference point. The nodes in a group are usually randomly distributed around the reference point. The different nodes use their own mobility model and is then added to the reference point which drives them in the
direction of the group.
3.7 Individual Simulated Behavioral model (ISB)
This is another new and different idea how to do more accurate and better simulations. They use a theory about an individually simulated behavioral model where all objects has their own properties. They verified their idea with DSR and proved that it generates reproducible and .realistic. mobility patterns.
4. Brief Description of Mobility Models
We provide a categorization for various mobility models into several classes based on their specific mobility characteristics in FIG 1-1
Figure 1-1. The categories of mobility models in Mobile Ad hoc Network
For some mobility models, the movement of a mobile node is likely to be affected by its movement history. We refer to this type of mobility model as mobility model with temporal dependency. In some mobility scenarios, the mobile nodes tend to travel in a correlated manner. We refer to such models as mobility models with spatial dependency. Another class is the mobility model with geographic restriction, where the movement of nodes is bounded by streets, freeways or obstacles.
In random-based mobility models, the mobile nodes move randomly and freely without restrictions. To be more specific, the destination, speed and direction are all chosen randomly and independently of other nodes. This kind of model has been used in many simulation studies.
4.1 The Random Waypoint Model
The Random Waypoint Model was first proposed by Johnson and Maltz. Soon, it became a 'benchmark' mobility model to evaluate the MANET routing protocols, because of its simplicity and wide availability. To generate the node trace of the Random Waypoint model the setdest tool from the CMU Monarch group may be used. This tool is included in the widely used network simulator ns-2
Figure 1-2. Example of node movement in the Random Waypoint Model
In the network simulator (ns-2) distribution, the implementation of this mobility model is as follows: as the simulation starts, each mobile node randomly selects one location in the simulation field as the destination. It then travels towards this destination with constant velocity chosen uniformly and randomly from [0,Vmax], where the parameter Vmax is the maximum allowable velocity for every mobile node. The velocity and direction of a node are chosen independently of other nodes. Upon reaching the destination, the node stops for a duration defined by the 'pause time' parameter Tpause . If Tpause=0, this leads to continuous mobility. After this duration, it again chooses another random destination in the simulation field and moves towards it. The whole process is repeated again and again until the simulation ends. As an example, the movement trace of a node is shown in Fig.1-2.
In the Random Waypoint model, Vmax and Tpause are the two key parameters that determine the mobility behavior of nodes. If the Vmax is small and the pause time Tpause is long, the topology of Ad Hoc network becomes relatively stable. On the other hand, if the node moves fast (i.e.,Vmax is large) and the pause time Tpause is small, the topology is dynamic.. Varying these two parameters, especially the Vmax parameter, the Random Waypoint model can generate various mobility scenarios with different levels of nodal speed. Therefore, it seems necessary to quantify the nodal speed.
Intuitively, one such notion is average node speed. If we could assume that the pause time Tpause=0, considering that Vmax is uniformly and randomly chosen from [0, Vmax], we can easily find that the average nodal speed is 0.5 Vmax 2. However, in general, the pause time parameter should not be ignored. In addition, it is the relative speed of two nodes that determines whether the link between them breaks or forms, rather than their individual speeds. Thus, average node speed seems not to be the appropriate metric to represent the notion of nodal speed.
The Random Waypoint model has several variations. In the following subsections, we will discuss one of them, the Random Walk model.
4.2 Random Walk Model
The Random Walk model was originally proposed to emulate the unpredictable movement of particles in physics. It is also referred to as the Brownian Motion. Because some mobile nodes are believed to move in an unexpected way, Random Walk mobility model is proposed to mimic their movement behavior . The Random Walk model has similarities with the Random Waypoint model because the node movement has strong randomness in both models. We can think the Random Walk model as the specific Random Waypoint model with zero pause time.
However, in the Random Walk model, the nodes change their speed and direction at each time interval. For every new interval t, each node randomly and uniformly chooses its new direction θ(t) from (0,π2]. In similar way, the new speed follows a uniform distribution or a Gaussian distribution from [0, Vmax]. Therefore, during time interval t, the node moves with the velocity vector (v(t)cosθ(t), v(t)sinθ(t))). If the node moves according to the above rules and reaches the boundary of simulation field, the leaving node is bounced back to the simulation field with the angle of θ(t) or π-θ(t), respectively. This effect is called border effect .
The Random Walk model is a memory less mobility process where the information about the previous status is not used for the future decision. That is to say, the current velocity is independent with its previous velocity and the future velocity is also independent with its current velocity.
4.3 Limitations of the Random Waypoint Model and other Random Models
The Random Waypoint model and its variants are designed to mimic the movement of mobile nodes in a simplified way. Because of its simplicity of implementation and analysis, they are widely accepted. However, they may not adequately capture certain mobility characteristics of some realistic scenarios, including temporal dependency, spatial dependency and geographic restriction:
1. Temporal Dependency of Velocity: In Random Waypoint and other random models, the velocity of mobile node is a memoryless random process, i.e., the velocity at current epoch is independent of the previous epoch. Thus, some extreme mobility behavior, such as sudden stop, sudden acceleration and sharp turn, may frequently occur in the trace generated by the Random Waypoint model. However, in many real life scenarios, the speed of vehicles and pedestrians will accelerate incrementally. In addition, the direction change is also smooth.
2. Spatial Dependency of Velocity: In Random Waypoint and other random models, the mobile node is considered as an entity that moves independently of other nodes. This kind of mobility model is classified as entity mobility model in Ref.. However, in some scenarios including battlefield communication and museum touring, the movement pattern of a mobile node may be influenced by certain specific 'leader' node in its neighborhood. Hence, the mobility of various nodes is indeed correlated.
3. Geographic Restrictions of Movement: In Random Waypoint and other random models, the mobile nodes can move freely within simulation field without any restrictions. However, in many realistic cases, especially for the applications used in urban areas, the movement of a mobile node may be bounded by obstacles, buildings, streets or freeways.
5. MOBILITY MODELS WITH TEMPORAL DEPENDENCY
Mobility of a node may be constrained and limited by the physical laws of acceleration, velocity and rate of change of direction. Hence, the current velocity of a mobile node may depend on its previous velocity. Thus the velocities of single node at different time slots are 'correlated'. We call this mobility characteristic the Temporal Dependency of velocity.
However, the memory less nature of Random Walk model, Random Waypoint model and other variants render them inadequate to capture this temporal dependency behavior. As a result, various mobility models considering temporal dependency are proposed. In Section 5.1, Gauss-Markov Mobility Model is described in detail.
5.1 Gauss-Markov Mobility Model
The Gauss-Markov Mobility Model was first introduced by Liang and Haas and widely utilized. In this model, the velocity of mobile node is assumed to be correlated over time and modeled as a Gauss-Markov stochastic process. In a two-dimensional simulation field, the Gauss-Markov stochastic process can be represented by the following equations:
Where and are the velocity vector at time t and time t-1 respectively, is the uncorrelated random Gaussian process with mean 0 and variance and are the vectors that represent the memory, level, asymptotic mean and asymptotic standard deviation, respectively.
For the sake of simplicity, we may write the general form (Eq.1) in a two - dimensional field as follows:
When the node is going to travel beyond the boundaries of the simulation field, the direction of movement is forced to flip 180 degree. This way, the nodes remain away from the boundary of simulation field.
Based on these equations, we observe that the velocity of mobile node at time slot t is dependent on the velocity at time slot t-1. Therefore, the Gauss-Markov model is a temporally dependent mobility model whereas the degree of dependency is determined by the memory level parameter α . α is a parameter to reflect the randomness of Gauss-Markov process. By tuning this parameter, Liang and Haas state that this model is capable of duplicating different kinds of mobility behaviors in various scenarios5:
1. If the Gauss-Markov Model is memoryless, i.e., α = 0 . The Eq.1 is
where the velocity of mobile node at timeslot t is only determined by the fixed drift velocity and the Gaussian random . Obviously, the model described in Eq.2 is the Random Walk model.
If the Gauss-Markov Model has strong memory, i.e., α = 1 . The Eq.1 is
that the temporal dependency is an important mobility characteristic that should be captured. Where the velocity of mobile node at time slot t is exactly same as its previous velocity. In the nomenclature of vehicular traffic theory, this model is called as fluid flow model.
If the Gauss-Markov Model has some memory, i.e., . The velocity at current time slot is dependent on both its velocity at time t-1 and a new Gaussian random variable . The degree of randomness is adjusted by the memory level parameter α . As α increases, the current velocity is more likely to be influenced by its previous velocity. Otherwise, it will be mainly affected by the Gaussian random variable.
In the Gauss-Markov model, the temporal dependency plays a key role in determining the mobility behavior.
6. Comparision between Random waypoint and Gauss morkav model
Fig: Number of nodes versus Route Request Packets
Fig: Number of nodes versus control packets
Fig: Number of nodes versus sum of collisions
Fig: Terrain dimensions versus Throughput