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Mobility of humans and others living beings has been topic of interest from ancient times. Human mobility has aroused interest with advent of new technologies related to mobility. Researchers have tried to find the patterns in human mobility so that the things related to human mobility can be predicted. The paper conducts a literature survey on mobility model and then looks into various types of mobility models proposed. The mobility models have been characterized based on mobility characteristics. The application of various type of models have been discussed in the paper. The most commonly used model are random walk models that have been used for studying movements biological entities such as cells, micro-organisms and animals, disaster recovery planning, containment of infectious disease spread etc. One of the most common applications of mobility models in recent times has been modeling wireless mobile ad hoc networks. Numbers of models have been developed specifically for mobile ad hoc networks. The researchers have developed models for various scenarios encountered in real life to model such as for conferences, surveys, museums, battlefield etc.
Categories and Subject Descriptors
C2.1 [Computer-communication Networks]: Network Architecture and Design; C.4 [Performance of Systems]:
Algorithms, Management, Measurement, Performance, Design, Reliability, Human Factors, Standardization.
Mobility of humans, mobile communication, ad hoc networks, mobility models, mobility applications, Mobility traces, Mobility patterns, Random Walk, Random Waypoint, ad hoc networks, Temporal Dependency, group mobility, spatial dependency, Obstacle mobility, Reference point, Column Mobility, Pursue Mobility, Nomadic Community.
Mobility of humans and other living beings has been a topic of interest for many. Mobility of animals to far-flung places has envisaged the interest of scientific community. The movement of birds to thousands of kilometers across the continents for nesting has left everyone wondering about wonders of nature. Lots of research and numbers of experiments have been conducted to find out the various aspects of animal mobility. Human mobility has aroused interest with the advent of new technologies related to mobility. Researchers have tried to find the patterns in human mobility so that the things related to human mobility can be predicted. Some of the applications where human mobility patterns can be used are spread of infectious diseases, containment of epidemics, infrastructure planning, traffic forecasting, spread of mobile viruses etc.
The interest in human mobility increased with the arrival of mobile technology. In order to design mobile network architectures and scientists look forward to the models so that the human mobility can be predicted and network design may be done as per the predictions. This paper looks into various human mobility models proposed and the research carried out in the field as well as the applications of human mobility models in real life. The paper does a literature review on the subject and then goes into discussing the various models suggested and their usage in real life.
The fundamental research on mobility started by Einstein in 1926 when he put forward a model to characterize "Brownian motion"(random motion of particle suspended in liquid). It was called as Drunkard's Walk due to haphazard walking patterns of drunken person . It was in late 1990 that mobile communication kicked off in big way and for efficient design and management of network the estimation and prediction of user mobility was thought off.
Liu & Paramvir Bahl (1998) developed a hierarchical user mobility model that can be used for prediction of speed of mobiles as well as their future location. The model closely represented the movement pattern of a mobile user and does away the notion of movement being ad hoc in nature. The authors used their model along with Kalman filtering and appropriate pattern matching to develop an accurate location prediction algorithm and called it hierarchical location prediction (HLP). HLP proposed was independent of ATM network's architecture. The HLP operated with two main components: Global prediction that predicted long range movement of mobile and Local prediction that took care of short range movement. In order to get accurate short range results the Local prediction was kept independent of global prediction. The authors used HLP to optimize route establishment and resource reservation in wireless ATM networks .
A Survey of Mobility Models used in the simulations of Ad Hoc Network was conduted by Camp et al. (2002). The authors looked into various types of models including those with group mobility, where mobile movements are dependent on each other as well as entity mobility models where movement of mobile nodes are independent of each other. The research was aimed to provide right choice of models for use in mobile network performance evaluations. The simulation results showed the importance of selecting the mobility model in designing network and demonstrated the drastic change in the performance results of an ad hoc network protocols, when the mobility model was changed .
The network design in case of mobile ad hoc networks relies on simulations that use realistic movement models for the authenticity of design . As the realistic data on human mobility is not available, the synthetic models of movement pattern are used. For ease of use, simplistic model are used though they may not be real representative of actual movements. Musolesi et al. (2004) indicated that the human movement is strongly dependent on their needs to socialize and their ways to socialize can be mathematically modeled. Working on this theory the authors proposed a mobility model based on social network theory. The model proposed grouping of collections of hosts based on social relationships among the individuals in the group. The grouping carried out is mapped to topography that is dependent on the strength of social ties. The authors, using simulated network, showed that the probability distribution of the average number of neighbors of a host is strongly influenced by the grouping proposed.
The design of efficient network layer and MAC protocols in ad hoc network requires that effect of mobility on the link and route lifetimes is properly represented . Lenders et al. (2006) studied the effect of mobility on the link and route lifetimes by gathering and analyzing data from 20 real users in a test network. In order to separate the line breakage due to reasons other than mobility, authors developed a statistical framework that separated errors related to interference or collision from mobility. Authors found that the distributions of the two popular mobility models, the random reference group and the random waypoint mobility model matched closely with the empirical link lifetime distribution generated by the experiment using the framework developed.
Nordstom et al. (2006) used Bluetooth inquiring devices to analyze human mobility. Authors used traces of measurements provided by using Intel Motes, and the software used in EU Haggle project. Authors modified the software and removed the number of limitations. Authors compared the two traces taken from previous software and the traces taken using modified software. The comparison showed that modification in software allowed more numbers of contacts to be sampled during each Bluetooth scan6].
Most of human mobility related research is aimed at improving the design of mobile ad hoc networks. The Vehicular Ad-hoc Networks (VANETs) design requires a model that can accurately and realistically depict the vehicular movement at microscopic as well as macroscopic levels [7 ]. Most of the models available took into account-limited macro-mobility with limited vehicle movement. The models available did not consider micromobility as well relationship between macro-mobility and micromobility. Harri et al. (2006) reviewed and compared many proposed mobility models for vehicular ad hoc networks. Authors proposed a new realistic vehicular mobility model based on complex motion patterns taking into account the traffic lights, intersections, overtaking and zig zag driving to avoid obstacles and other vehicles coming in the way. Authors demonstrated the effect of new model on the performance of AODV and OLSR and concluded that more realistic models are needed to predict performance of routing protocols in VANETs .
Musolesi & Mascolo (2007) proposed another model based on social network theory. The mobility traces taken from Intel Research Laboratory were used to evaluate their model. The evaluation results indicated that the traces generated by the proposed model characteristically compares closely with the real movements. The characteristic parameters compared were the contacts duration and inter-contacts time. 
Chaintreau et al. (2007) studied the impact of Human Mobility on Opportunistic Forwarding Algorithms, that look for data transfer opportunities, in ad hoc networks. The devices targeted were wireless devices carried by human beings. They conducted experiments using eight distinct data sets and found that the inter contact time distribution can be approximated by power law over the range. The authors observed that this is in variation with the exponential decay implied by other popular models. The authors studied the effect of the new characteristics on one class of forwarding algorithms proposed earlier. The paper makes recommendations for design of opportunistic forwarding algorithms based on this newly observed inter contact time distribution .
Brockmann et al. (2006) used the circulation of bank notes in United States for quantitatively assessing the human mobility pattern. The authors used data for trajectories of 464,670 dollar bills collected at online bill-tracking website www.wheresgeorge.com. Using 1,033,095 reports of dispersal of bank note they calculated geographical displacements and time lag between first and second location of bank notes. They found the bank note dispersal was anomalous in two ways. The travelling distance distribution decreases as a power law and concluded that the trajectories of bank notes follow pattern similar to Levy flights. The authors concluded that human travel behavior is equivalent to continuous time random-walk process where there may be long period between two displacements and there are scale free jumps. The authors indicated that their results can be starting point of new human mobility models that can be used for various purposes such as the spread of human infectious diseases etc .
The lack of tools for monitoring the times based location of humans has limited the ability to form basic laws that govern human movement . In order to track human movement Gonzalez et al. (2008) studied the movement trajectory of 100,000 mobile phone users for a period of 6 months. The authors compared the trajectory of the mobile user with those predicted by random walk and Levy flight models. They found that each individual's motion is characterized by a time independent travel distance and there was significant probability of individual returning to a few highly frequented locations. This is in contrast to the random trajectories of human movement predicted by random walk and Levy flight models. The authors found that humans follow simple reproducible patterns in spite of diversity of their travel history. 
Hui & Crowcroft (2008) took up study of mobility for the purpose of designing efficient algorithm for data dissemination among mobile users. They collected human mobility trace for a university town as well as from a a busy metropolitan city for three years for this study. They used two metrics, node centrality and community structures by analyzing the human mobility traces, to design efficient forwarding algorithms that provided better delivery cost and delivery ratio for mobile networks. The algorithms suggested were designed to select next hop for relaying packet using the patterns observed in encounters between nodes and social relation ship between the node owners. The relationship took into account how often the two people met and duration of their stay together. Their experiment showed that the use of this information can significantly improve forwarding efficiency of the system over the best traditional algorithms used for this function. 
Mun et al. (2008) noticed that while using the traces of human mobility the devices used were using GPS that allowed exact location of the mobile user to be recorded. They indicated that such type of accurate recording is not required for such work and the privacy risk that accurate GPS based recording poses can be avoided if the same data can be collected using coarsely generated location. The authors explored the feasibility of using signal strength and visibility of GSM cell towers and WiFi beacons for generating mobile profiles as this data is available on users mobile handset. The advantage of this techniques is that the continuous sampling of GPS data that drains the battery life can be avoided and the phones even without GPS facility can be used for the purpose. The authors indicated that most of the earlier works used indoor data or large coverage data of GSM users and did not take into account smaller cells such as WiFi. The authors profiled the unconstrained mobility of the mobile using Nokia N95 handset and the cellular service provider T-Mobile. The data was collected by writing application using Python. The cell phone was used to collect data on cell tower ID, Wi FI beacons available and GPS location every two seconds. The data was collected from four differently populated areas from the U.S. cities and most popular places were visited by the participants in these locations. The data gathered covered 12.5 hours with 59% of data pertaining to stationary state, 21% driving and 20% walking. The authors demonstrated that their mobility classification approach achieved an accuracy of 88% and concluded that their approach was worthy of further research .
La & Michiardi (2008) indicated that logistic constrains restricted the availability of real life data of human mobility due to limitations in duration of experiments, numbers of participants, technology used etc. Due to these reasons proper data on user's mobility was not available and spatial analysis of user's mobility was difficult to achieve. The authors studied the mobility of users in SecondLife, a online virtual reality space where people can connect to interact, do business and play games. The authors chose to use this innovative platform that can be scaled up for large number of participants, it is not bound by limitations described above and required no logistic organization. The authors used a custom made software named crawler that connects to SecondLife and collects information related to location of all users online. The authors found that their results qualitatively fit to real life data. The methodology used by the authors can be used to carry out large experiments at a very low cost and the data generated can be used for trace-driven simulations of many applications such as information diffusion in wireless networks or the study of epidemics .
Balcan et al. (2009) analyzed the transmission of one of the most dangerous new influenza A(H1N) strain based on human mobility. The H1N1 influenza strain was confirmed in 142 countries and affected large number of people. The authors undertook the research to estimate the spread of virus and to assess the effect of seasons on the spread. They used meta population model integrating transportation and mobility data worldwide. The model utilized data on 3,362 subpopulations in 220 different countries as well as individual mobility across the countries. The data on the chronology of the 2009 H1N1 virus was used to assess the spread of disease. The studies showed the potential of H1N1 virus spreading in the months of October/November in the Northern hemisphere. Thus, to control spread of virus large scale vaccination could be organized just before these months .
Mobile devices being attached to or controlled by human beings make simulation of human mobility of great importance for designing mobile networks . The human mobility related studies have led to the discovery of many statistical patterns of human mobility such as , pause-times and inter-contact times, truncated power-law distributions of flights, heterogeneously defined areas of individual mobility, and fractal way-points. However, none of the proposed models are able to capture all the features given above. Lee et al. (2009) proposed a new model called Self-similar Least Action Walk (SLAW), which can take care of all the above features while producing synthetic walk traces. The model was developed using GPS traces of human walks undertaken by 101 volunteers in five different outdoor sites. Total of 226 traces were collected daily. The traces gathering was done among the people with common interests such as tourists and student in a campus. The influence of the mobility pattern on network protocol's performance was studied using DTN routing for various models including SLAW. The results of studies showed that SLAW was able to bring out unique performance features of five DTN protocols. The number of input parameters required by SLAW were very few, the number of walkers, size of the walk-about area and the Hurst value, making it simple to work with. The real walk traces are also not needed by SLAW for generating synthetic traces. The applications of SLAW can be traffic forecasting, accurate urban planning, mobile network design or virus spread analysis or anything where emulation of human mobility is required .
Musolesi and Cecilia (2009) conducted a comprehensive survey of current mobility models available. The models discussed by the authors include synthetic and trace-based models, analytical models, mobility models based on social networks. They observed that most of the models available are for specific places or environment and the generalization of traces using these models will not be correct. The authors summarized the research challenges by specifying various issues that need to be looked into. The problem of generality require extraction of mobility traces from heterogeneous environments. The authors propose the concept of connectivity models, which can be complementary to existing mobility models. The connectivity models deal with the mobile's connectivity as it moves. The connectivity plays important role in jobs such bandwidth provisioning solutions and designing of delay tolerant networks. The integration of mobility model and connectivity model is another area of research proposed by the authors for effective characterization of human mobility. The authors also advocate the study of the influence of the obstacles in path on human connectivity and mobility patterns. Apart from these more tools are required for testing of mobility modeling and Standardization of the Trace Formats is required so that the data can be exchanged easily among researchers .
Large number of applications require predictions of human mobility for proper system/infrastructure design. However, the prediction of human mobility are dependent on the degree to which human behavior is predictable. Song et al. (2010) tried to explore the limits of predictability in human mobility. Mobile phone carrier are able to record the most accurate and detailed information about their users that consists of wide range and segment of population. The authors used record of billing for a period of three month of 50,000 mobile phone users out of more than 10 million users. The criterion for selection of users was that they should have average call frequency of â‰¥ 0.5 per hour and should have visited more than two locations during period of observation. The degree of predictability was captured using entropy. The authors assigned three entropy measure for capturing individual's mobility pattern. These are, random entropy that captures degree of predictability of user's location, the temporal-uncorrelated entropy that captuires heterogeneity of visitation pattern and the actual entropy that depend on the order of visits and time spent at each location during visits. The measurements of entropy of individual users trajectory by the authors showed that the user mobility is 93% predictable across the whole user base. Another important observation was the similarity in predictability across the population .
HUMAN MOBILITY MODELS
The mobility models have been used to maximum extent in mobile ad hoc network simulations. The specific mobility characteristics of models may be used to categorize them into several classes as follows::
Random Mobility Models
Random Walk Model
Random Waypoint Mobility Model
Random Direction Mobility Model
Mobility Models with Temporal dependency
Gauss-Markov Mobility Model
Smooth random mobility models
Boundless Simulation Area Mobility Model
Mobility Models with Spatial dependency
Reference point group model
Column Mobility Model
Pursue Mobility Model
Nomadic Community Mobility Model
Mobility Models with graphical restrictions
Pathway mobility model
Obstacle mobility model
We shall describe each model in detail in following paras:
Random Mobility Models
Random Walk Model
Einstein was the first one to describe Random Walk Mobility Model in 1926 while studying the Brownian motion. The Random Walk Mobility was developed for profiling the erratic movement of many entities in nature. The movement in this model assumes that the next point of movement is random in direction as well as speed. The direction and speed of movements are selected from predefined ranges. Every movement in this model is assumes a constant distance movement or constant time movement. At the end of this movement new speed and direction is calculated. When the node moves to the boundary of the simulation model it bounces off the boundary at an angle depending on the angle of incidence to the boundary. 
Many variants such as 1-D, 2-D, 3-D, and d-D of Random Walk Mobility Model have been developed. It was shown by Polya in 1921 that the walk in case of 1 or 2-D models always comes back to the origin. This ensured that this mobility model could be used safely in cases where movement of the entities revolves around the starting point of the entity. For example, most of the time everyone returns to their house at the end of the day irrespective of their movement during the day.
As earth's surface is modeled using 2 dimensional representation, the corresponding 2-Dimentional Random Walk Mobility Model gains importance while tracking movement of anything on earth's surface. The Random Walk Mobility Model does not take into account the previous history of movements such as speed or direction while deciding on next step or we can say it provides a memory less pattern. This property of the model can lead to some unrealistic movements such as sudden turns and sudden stops. 
Random Waypoint Model
Unlike random walk model, the Random Waypoint Mobility Model includes the pause time whenever there is change in speed and/or direction. The start of movement in Random Waypoint Mobility Model is with pause i.e. staying at starting point for a period. After the pause time, the movement destination is selected randomly with uniform speed distribution between minimum and maximum speed. On arrival at next destination, the movement is again paused before starting for next destination. In case of continuously moving nodes, the pause time may be nil. This model is also one of the most used models for mobility especially in mobile ad hoc networks.
Some of the common issues with Random Waypoint Mobility Model are that it provide elementary zig-zag pattern which may not be natural. The second problem in its use is the improper selection of velocity distribution.
Random Direction Mobility Model
The Random Waypoint Mobility Model does not cater to the clustering of node in some part of the area. In order to overcome this Random Direction Mobility Model was created. In Random Direction Mobility Model, the initial movement is similar to that of Random Waypoint Mobility Model but as soon as the boundary of mobility area is reached, the movement is paused and then goes in another angular direction (between 0 to 180 degrees) and proceeds as earlier. As the node is already on the boundary, the direction is limited and node do not cross the boundary. Due to this reason, the average hop count for data packets using this model is much higher than the other mobility models including Random Waypoint Mobility Model. The network partitions for Random Direction Mobility Model are also are higher than other mobility models. The model simulates microcell of a larger area  
Another model called Modified Random Direction Mobility Model, where the nodes need not travel to boundary before stopping to change direction. In this, a random direction is selected and node moves in that direction and stops before changing new random direction. The modifications allowed production of movement similar to that produced by the Random Walk Mobility Model with pause times.  
The Random Direction Mobility Model provides unrealistic simple traffic flows and user sojourn densities. Gloss et el. (2005) proposed a more realistic Random Direction Mobility Model that used location dependent parameterization of the random direction mobility model. This new model proposed by the authors allowed creation of very flexible inhomogeneous mobility scenarios and showed that model proposed by them can model arbitrary mobility patterns that are less complex to implement. 
Limitations of Random Models
The Random Walk/Way point models provide the movement simulation in simple manner. This has led to their wider acceptance for analysis. However, in number of case they may not represent realistic scenarios including geographic restriction, temporal dependency and spatial dependency as shown below :
Geographic Restrictions of Movement
The nodes are allowed to move freely within the area. However, in reality the movement cannot be restricted. Especially in case of urban areas, the mobile's movement is bounded by buildings, vegetation, roads etc.
Temporal Dependency of Velocity
In the random models, the velocity of the movement is independent of previous movement and is purely a random process. This leads to situations such as sudden stoppage or sudden acceleration or sharp turns etc. In real life, the velocity of vehicles will vary and they will accelerate slowly rather than abruptly shown in models. Similarly, the change of direction is always smooth.
Spatial Dependency of Velocity
The Random Walk/Way point models provide movement of each node independent on other nodes. However, this type of movement may not be true especially in case of scenarios such as conducted tours where movement is led by a leader, making movements of nodes correlated.
In order to overcome these limitations number of other mobility models have been proposed and are described in following paras.
Mobility Models with Temporal Dependency
The mobility of a node is always limited in terms of rate of change of direction, acceleration and velocity due to physical laws and other constrains. In order to simulate realistic mobility environment the velocity of the node is correlated to its previous velocity in some ways. This is called Temporal Dependency of velocity. 
Gauss-Markov Mobility Model
The Gauss-Markov Mobility Model was designed for the situations where using one parameter the level of randomness can be changed. At the start of the movement a direction and speed is assigned to the mobile node. The speed and directions are changed at fixed intervals. However, the change depends on the last speed and direction as per following equations :
Where, sn and dn are the new speed and direction of the node at time interval n. ¡ is the tuning parameter that is varied to change the randomness and 0 â‰¤ ¡€ â‰¤ 1; and are constants representing the mean value of direction and speed as n ® ¥; and sxn-1 and dxn-1 are random variables from a Gaussian distribution. By changing Î± to 0 value totally random values are obtained while making Î± to 1 gives linear motion. Keeping values of Î± between 0 to 1 provides intermediate levels of randomness .
To prevent node remaining at the edge of the grid for a long period, the nodes are made to move away when they are close to the boundary by modifying the variable for mean direction. The Gauss-Markov Mobility Model can be used to avoid sharp turns or sudden stops seen in the Random Walk Mobility Model. This is done by using previous direction and velocity to influence the direction and velocity in next step.
The Gauss-Markov Mobility Model has been used for simulation of PCS (Personal communication system) as well as for ad hoc network simulations. 
Boundless Simulation Area Mobility Model
In the Boundless Simulation Area Mobility Model the current direction of movement and speed are related to previous direction of movement and speed. The handling of boundary of a simulation area is also different in Boundless Simulation Area Mobility Model. In this model, once the nodes reach one side of the boundary of simulation area they continue their travel and may reappear on opposite side. This creates a torus shaped area that allows unobstructed travel to a node. 
Smooth Random Mobility Model
In the Smooth Random Mobility Model, the velocity of the node is related to previous velocity. In this model the direction and speed of the movement is changed smoothly and incrementally. Thus, there are no sudden acceleration or sharp turns. The model assumes that frequency of speed change is a Poisson process. The degree of temporal dependency is determined by maximum allowable direction change in each time slot and acceleration speed. 
Mobility Models with Spatial dependency or Group Mobility
In random models, the movement, location and speed of each node is independent of other nodes in the area. However, in real scenarios there is certain amount of dependency between the nodes in an area e.g. the speed of vehicle in a freeway is dependent on the vehicle ahead of it to avoid collision. In case of collaboration environment, the movement of members is dependent on team leader's movement. This requires that in certain situations, the mobility of node is dependent on other nodes in the space and this is termed as Spatial Dependency of velocity. These types of models are also called group mobility models.  
Reference Point Group Mobility Model
The Reference Point Group Mobility (RPGM) was proposed by Hong et el. (1999) and describes the random motion of nodes in a group and random motion of an individual within that group . In RPGM the movement of the group is dependent on the group leader or logical center of the group. Thus, group center governs the movement including direction and velocity of its group members. The Reference Point Group Mobility model can be used to emulate various types of mobility scenarios by defining predefined paths for group leader and pother parameters. Hong et el. (1999) created following three mobility scenarios using RPGM .
In-Place Mobility Model: In this, the complete field is bifurcated into number of regions with each region adjacent to another. Each group exclusively occupies the region. This situation is equivalent to battlefield.
Overlap Mobility Model: in this model, there are number of groups and they move in same field in an overlapping manner. Each group may have different purpose and characteristics than other groups in the area. This situation emulates the disaster relief work.
Convention Mobility Model: This model emulates the conference environment. The entire area is divided into number of regions and some groups can move in a similar pattern between regions.
Hong et el. (1999) applied RPGM to routing and clustering in ad hoc wireless network. They observed that various protocols are affected differently for different mobility patterns. 
The Reference Point Group Mobility can be used in scenarios of disaster recovery where teams move in co-ordination with others. Thus in case of an avalanche rescue the human members of the team estimate the location of survivors and then dogs are led to that direction and they move around in a random paths in the area guided by their human counterparts. 
Column Mobility Model
The Column Mobility Model emulates a set of nodes that move a in a column (around a given line) in a certain direction e.g. soldiers in a row moving forward. A little change in model emulates the people walking in a single file or in a line one behind another. While implementing this model the initial grid is defined. The nodes then randomly move around this reference grid via an entity mobility model. Any movement of node beyond the boundary of the simulation area is prevented by flipping the movement direction by 180 degrees, as soon as it reaches the boundary, making it travel back toward the center or reference. 
Pursue Mobility Model
The aim of Pursue Mobility Model is to simulate the tracking of a target. The target moves as per Random Waypoint model. For example, police trying to catch an escaped criminal. The criminal can move in any direction and with any speed, he deems fit to escape from police.
Nomadic Community Mobility Model
The Nomadic Mobility Model emulates the movement of a group or community of nodes from one place to another. Within the group, the individual nodes have their own personal spaces where their movement is random. Thus, in this model each individual node moves around a reference point using a random mobility model such as Random Walk Mobility Model. As the reference, point moves or changes its location the nodes in the community or node also move and then continue their movement around the reference point in random fashion. The extent of movement of individual node around the reference point is defined can be defined to limit the distance of movement from the reference point.
This type of model emulates scenarios such as a group of students visiting an art museum. The students will go from say one room to another together but within the room individual student will watch and move around as per his interest.
Mobility Models with Graphical Restrictions
The random models allow the node to move freely in the area. However, in real life scenarios the movement is restricted by the environment. For example, the movement of a person while walking is restricted by buildings or other obstacles and movement of vehicles are restricted to freeways or roads only. Thus, the movement is in predefined fashion in a given area.
Pathway mobility model
The geographic constraints encountered by mobile node can be integrated into the mobility model by restricting the node's movement along the pathways defined in the map. The map may be predefined in the model area and can be the actual map of the city or the place to be covered. Tian et al. (2002) used the graph based mobility model for a city and evaluated the performance of Destination Sequenced Distance Vector (DSDV), Ad-hoc On demand Distance Vector (AODV) and Dynamic Source Routing (DSR) network routing protocols with random walk based model. The nodes were placed randomly around the edges of the map and the destination of each node was chosen randomly. The node took the shortest path to destination using pathways defined. The node paused on reaching destination before starting for new destination. The simulation results by the authors showed that the spatial constrains strongly effect the performance of ad hoc routing protocols. 
Obstacle mobility model
In the real life, the movement of nodes is not without obstacles. The obstacles are there within a building as well as outside areas. In order to see the effects of these obstacles these need to be integrated into the mobility model to get better picture during simulation. Johansson et al. (1999) used this model to depict the real life scenarios. The authors use three different scenarios for the model. They tested Destination Sequenced Distance Vector, Ad-hoc On demand Distance Vector and Dynamic Source Routing for all the following three mobility scenarios. 
Conference: This is characterized by low mobility. The study took conference with 50 people out of which some remained static and about 10% of the people moved with low mobility. The simulation results indicated that AODV and DSR performed well where as DSVD was able to deliver only 75.6% of packets. This showed that quick adaptation is required by ad-hoc routing protocol to topology changes even for routes that live long. 
Event Coverage: This is characterized by high mobility. In this scenario group of highly mobile vehicles or people who change their positions frequently were considered. This scenario depicts the group of reporters covering an event such as sporting event. This scenario tested the ability of the protocols to respond to fluctuating traffic and fast topology changes. The results showed that performance of all the three protocols gave high throughput. However, performance of AODV and DSR was better than DSVD. 
Disaster Relief : This scenarios is characterized by some slow moving nodes and some fast moving nodes such as vehicles. The simulation used three groups that communication-using node available on vehicles. The simulation results showed that the performance of DSVD was the lowest though the average delay was low. This shows the inability of DSVD to adapt to fast route changes. 
APPLICATIONS OF MOBILITY MODELS
There are many applications where Mobility model are used. However, most of the applications use random walk model. The mobility modeling is very important in mobile ad hoc network and the maximum use of mobility models is in this field. Numbers of models have been developed specifically for mobile wireless ad hic network. Some of the applications are given below:
Random walk models in biology
The random walk model is one of the simplest and most used models for modeling the movement of biological entities such as cells, micro-organisms and animals. Codling et.el (2008) used this model to study the movement, dispersal and population redistribution of micro-organisms and animals . They discussed the use of their model for demonstrating the blood vessel growth caused by cell migration.
The Random Walk Motion Model for Share Prices
The use of random walk model for share prices in options trading has found to be very useful . This model has also been used for estimating the paid loss development to indicate the magnitude of deviations from estimated losses in financial system . The model has also been used for estimating consumption by a consumer.
Mobility Models for Wireless Ad Hoc Networks
Ad hoc networks is one of the most researched networks now due to their ability to work without any fixed network infrastructure or centralized administration. In the continuously changing environment, the mobile ah-hoc network needs good routing protocol to maintain connectivity between the nodes. Most of developments in mobility models are related to wireless ad hoc networks and have been discussed along with the description of models. Some of the places where these models have been used are given in following paras.
The Random Waypoint Mobility is most used in mobile ad hoc network design and estimations. This model simulates the real movement of human beings or vehicles who are carriers of mobile devices. It takes into account the starting time and pause between each movement which may be due to signal or turns while moving in a vehicle.
Lassila et el. (2005) studied the connectivity properties of mobile ad hoc network using Random Waypoint Mobility Model. They used the model for estimation of the mean durations of the connectivity periods and the probability of network being connected. They found that the model gave fairly accurate estimation for the probability of connectivity. They also showed that mobility creates a positive effect on connectivity for sparse networks and negative effect in case of dense network. 
The model has been used in cellular network for characterizing the key performance measures such as mean sojourn time and mean handover rate from the point of view of an arbitrary cell as well as for measurement of mean handover rate in the network .
The mobility of node plays an important role in performance of routing protocol used. Saad & Zukarnain (2009) studied the performance of Ad hoc On-demand Distance Vector (AODV) using three most popular mobility models; Random Walk Mobility Model, Random Waypoint Mobility Model and Direction Mobility Model. The authors used discrete-event simulator OMNeT++ for simulation of mobility as well as OSI layers used in wireless simulation. They found that performance of the routing protocol depends on the performance metrics used. The authors found that Random Waypoint Model to be the best performing model for both sets of metrics used. The Random Waypoint Model gave highest throughput whereas the in case of Random Direction as well as the Random Walk Model, the throughput drops drastically over a period. 
Royer et el. (2001) used Random Waypoint model for simulations studies on mobile ad hoc networks. The use of this mobility model showed that the average number of nodes seen by a node periodically decreases and increases and the frequency of the change depends on the speed of the node. The destination selected by the node should be in simulation area and this leads to a situation where the nodes will tend to travel in the direction that has most choice of destinations. This makes nodes travel through the middle of the area and leads to node converging to center of area and then disperse and so on.