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This paper describes the human mobility concept alongside various mobility models and their applications. The effectiveness of each mobility model is highlighted besides capturing some limitations that some models may have. In this paper, mobility models are explained in particular by simulations according to their descriptions in the sources used for the research. Diagrams have been used to illustrate the simulations. Several conclusions are drawn from the mobility models and are highlighted in the last section of the paper.
The movement of humans is a basis on which researchers can build their studies through trailing individuals in real time to analyze their patterns. Human migration data is therefore a crucial tool in the human mobility concept which can be explored using a range of methodologies. In most cases, mobile phone usage provides is used as an effective way of tracking random users over a period of time, revealing that individuals travel short and long distances which may include hundreds of miles. In fact, it can be between countries which may cause influx on the destinations as in the case of tourists. As a result, most countries have resolved into renewing their settlement policies in so as to govern the dramatic change in the patterns of human mobility. The reasons for movement vary from one individual to another, culture to culture or one geographical region to another. In a general view, people may move in order to trade, work or merely for leisure. Adverse conditions may also force people to migrate. Conceptually, diversity in human mobility has made the world a global village (Carr, 2010).
In computer networking, human mobility trends are critically important in a wide range of disciplines. Fundamentally, uncovering human behavior and its features has major benefits to the mobile networking and wireless community particularly if large scale data is available. However, collection of human mobility data is quite challenging for researchers hence requires support from all stakeholders in the networking fraternity. Consequently, different models have been put forward in a bid to contribute to the collection of large scale mobility data that is useful in various aspects of research. For instance, the popularity of social networking has favored the gathering of data on topology information regarding membership in online social networks. Large scale usage of mobile phones also has properties that can be used as a dimension to assess and build findings on human mobility (Mortier, n.d).
The duality of mobile networks is justified by the fact that the network has mobile nodes that are associated with human beings, who are mobile also. Such networks are therefore physical and social. Traces of human mobility have over time been gathered in different environments ranging from busy cities to quiet towns and residences in order to facilitate research on mobile and social networks as well as epidemiology. This research paper aims at examining the different models of human mobility besides looking at their applications.
Human mobility models and applications have been researched widely with different findings being reported by different authors. A range of studies have been done regarding this area and particularly in their implementation in mobile ad hoc wireless networks. Recently dated books, journals and other literary works have been used as sources of material for this research paper. Besides, other relevant materials that are not dated have also been used to enrich the content of this study. Main points that clearly bring out the concept of human mobility and reasons for human movement have been properly documented by Carr (2010). Mortier (n.d) goes ahead to capture the effects of large scale use of mobile phones in research findings on human movement. Human movement encounters uprecedented restricitons as is described by Rhee (n.d). A comprehensive definition of human mobility is given by the book by International Organization for Migration (2008). In another book, Klaus & Gross (2010) provides an outline of different categories of mobility models which are discussed further in this study. D. Lytra (2008), Karagiannis & Le Boudec (n.d) and Rangarajan & Ding (2003) provide a detailed discussion of the Levy walk mobility model while Gowrishankar.S & Basavaraju (2010) brings out areas of applications of the same.
In another web article, Chiang & Shenoy (N.D) cover the main characteristics of random walk mobility model. These are further emphasized by Roy (2010) and Misra (2009). Gavrilova (2006) goes ahead to provide details on the applications of the same model.An account of the random waypoint model is presented by Mohd Saad & Zukarnain (2009) and Schmidt (2011). Unhelkar (2006) gives a comparison of mobily models based on packet delivery efficiency while Hyytiä (2005) captures several drawbacks experienced in the random waypoint mobility model. According to Han (2008), the random direction model is different from the random waypoint model due to its characteristics as captured in the book. Carofiglio (n.d) provides several recommendations on the applications of the random direction model so as to ensure maximum throughput in ad hoc networks. Meghanathan (2010) provides content on the Gauss-Markov mobility model with Borrel (n.d) capturing the useful aspects of the model in routing protocols and networks. Under the group mobility models category, the reference point group mobility model is covered by Frattasi (2010) while its disadvantages are outlined by Battiti (2004). Finally, its applications especially in millitary communications are covered by Jayakumar & Ganapathi (2008).
Statistical studies on human mobility reveal that the tendencies of human movement are likely to result from deliberate intentions by humans when deciding their destinations. They are not mainly caused by geographical limitations such as boundaries, physical roads and other physical features like buildings. On the contrary, these constraints only limit flight lengths hence causing discontinuities in the statistical trends of human mobility (Rhee, n.d). These findings form a basis of different mobility models that follow human movement patterns that may be expected in outdoor human mobile networks and outdoor environments. For instance, the Levy walk mobility pattern is a model that can be used to demonstrate various statistical patterns.
The widespread adoption of mobile phones has happened in an age where migration is characterized by rapid increase in urbanization in many developing countries. International migrants are also on the rise with people from the developing states accounting for a greater part of the population. This migration may be voluntary or otherwise. Through this mobility, people are able to maintain communication with others, thanks to mobile phones, besides creating new networks. Human mobility is therefore defined as the physical movement of individuals from one place to another. It can be over short or long distances and people can move as individuals or in groups, happening either voluntarily or involuntarily within own country or across borders (International Organization for Migration, 2008).
Human mobility models attempt to describe human movements in different scenarios. Categorically, the models are based on the nature of the entity that invokes the movement, particularly the behavior of that entity. An entity mobility model considers the movement of an individual which means that multiple entities are predicted independently. Examples of entity mobility models discussed in this study are the Random Walk, Random Waypoint, Random Direction, Manhattan and the Gauss-Markov models. In contrast, group mobility models predict a number of individual entities as a group which is taken to be moving as a whole. The entities are related to each other in movement. In fact, group mobility models are arguably more realistic that entity mobility models. This is because human beings move in a way that they are not independent from one another. For example, people usually walk around collectively or towards the same direction. Several illustrations of group mobility models are discussed under this study, namely the Nomadic Community, Column, Pursue and Reference Point Group models (Klaus & Gross, 2010).
There are a vast number of mobility models available in this area which limits their exhaustive categorization in this study. Moreover, it is vital to note that these categories are not exclusively isolated from each other which mean that a single model might fit other categories in one way or another. Nevertheless, categorization helps to bring out an outline of mobility models besides creating an intuition of diversity of these models and scenarios. Situations play a critical role in describing mobility models. The character of a situation may be normal or special depending on nature of the surrounding environment. It allows for the analysis of factors that directly influence human mobility and movement of entities.
Entity mobility models
Levy walk mobility pattern
The Levy walk mobility model postulates that the outdoor movement of human beings resembles a form of Levy walk that is common in animals like monkeys and jackals. Studies on this tendency have been performed in thousands of hours using GPS traces on human volunteers. These volunteers are usually obtained from distributed outdoor settings such as colleges, urban areas as well as any other part deemed necessary. According to the model, many statistical findings of human walks observe the power-law, a trait that is similar to Levy walk. However, geographical restrictions make the mobility deviate from ideal Levy walks. They include boundaries, traffic and other obstructions. The resultant feature is a representation of movements with a pattern that resemble the Levy walk. The analysis of a random walk is displays a trajectory consisting of successive random steps. A mathematical formalization of these random steps is used to draw observations of Levy walk.
A Levy walk is characterized by a random series of movement segments which can be deducted from a probability distribution function of the power-law. Large values of length are more common in this distribution than in other distribution models such the Gaussian (D. Lytra, 2008). The Levy walk was mainly used in modeling foraging patterns of animals. The foraging theory revealed that animals search for nutrients and acquire them in way that they maximize the energy intake ratio against the duration of foraging. In fact, Levy walk is found to minimize the mean space travelled and hence the mean energy applied before reaching a target. Much similarity to this theory has been observed in human movement especially the way human beings shop. The longest flight distance denoted as l, is the longest possible path in a straight line without a change in direction or pause and follows the power-law distribution. In effect, the power-law distribution is actually the defining aspect of the Levy walk.
The Levy flight describes a walk that tends towards a stable distribution after many steps taken from the origin. It is argued that the inter-contact time of human walks resemble a tendency to the power-law only up to sometime. After this time, it decays exponential (Karagiannis & Le Boudec, n.d). An important fact is that inter-contact time distribution shows dichotomy and can best fit the truncated power law. The reason for this is that the power law distribution of inter-contact time is actually generated short flights and is truncated as result of long jumps. The flight duration is not necessarily a defining factor of the Levy walk since the starting and end points are the main aspects of concern. For this reason, all points traversed along a path by an individual need to be included in a mobility study. Research by mathematicians and physicist on Levy flights and walks have proven that the mean squared displacement of the flights is infinite while Levy walk is a function of time (Rangarajan & Ding, 2003).
In network mobility, human movement is a critical aspect that must be given primary concern. The Levy walk model represents the features of human movements at node level. For instance, the routing performance of DTN (Delay Tolerant Networks) is greatly related to the inter-contact time distribution and time duration between successive contacts of similar mobile nodes. The inter-contact time has a power-law resemblance up to sometime after which it decays exponentially. The truncated distributions are used in quantifying the opportunistic routing performance of delay tolerant networks. The Levy walk mobility model is also used commonly in biology in analyzing animal foraging patterns. In computing and routing protocols, simulation of the Levy walk mobility model is used to demonstrate behavioral adaptability of the protocols using the mobility models (Gowrishankar.S & Basavaraju, 2010).
Random trip/walk mobility model
Random walk mobility model is based on the argument that entities naturally move around in unpredictable ways. According to this model, an entity moves from one location to another by through a randomly chosen direction and speed. The direction and speed in this context are limited to certain ranges that are defined beforehand. The speed ranges from a chosen minimum to an arbitrary maximum while direction may vary from 0 to 2Ï€. It is important to note that every movement is limited to an interval of time that is constant. The direction and speed for subsequent movements are calculated after every movement. Moreover, movement may not only be limited to a constant interval of time but also to constant distance.
Fig 1: Illustration of the random walk mobility model.
The diagram illustrates the motion pattern of a mobile node in a two dimensional random walk mobility model against time. Most random walk mobility models are strategically designed for dynamic location area or derivation of dwell time. In fact some surveys report that the average percentage of occurrence of personal and social trips ranges from a minimum of seventy five percent and are centered on one's home ground or office premises. These non-commuting trips by humans are can be focused on and modeled as random walks so as to derive the rate of location update and dwell time (Chiang & Shenoy, N.D). Random walk is a mobility pattern that is known to be memory-less. This characteristic makes it capable of generating unrealistic movements especially unexpected stops and sharp turns. However, while this may be a drawback, the distributions of mobility parameters in this model are a function of time. For this reason, they eventually evolve towards a stable and steady state. In a computer simulation, consistent results are obtained when the parameters have achieved the stable state of distributions. The steady state of the observed mobility parameters depend on the sampling time of the parameters. For instance, two stable states may be used in network mobility simulation. They are the mobile link and continuous-time steady-state distributions (Roy, 2010).
Mobile link steady state distributions are the parameters of the mobility model when sampling is done between transition and the time after steady state. On the other hand, continuous steady state distribution is achieved when sampling is done at any unit time instant after the mobility model has reached steady state. Ideally, each node in a random walk chooses direction randomly which is distributed through [0,2Ï€] and a random speed distributed uniformly through [speedmin, speedmax]. This happens for a given period of time over a distance before the choice is repeated. In fact, this model is often compared to Brownian motion since it bears a resemblance to particle movement in a fluid (Misra, 2009). An equivalent view of random walk model is that the world is split into cells such as squares and a node may jump at each step to any of its random neighboring cells. This however, can happen only up to several steps away. Similar movement can also be observed on a sphere. Nevertheless, the random walk model is unrealistic in most cases but in the long term, the nodes tend to keep close to their origin hence limiting their overall mobility.
In wireless and ad hoc networks, mobility is ensured in order to form dynamic temporary networks without the need for centralized administration. The establishment of connection between mobile nodes requires good routing protocols as the mobile node changes topology every now and then. The movement of the nodes is an important characteristic that makes the random walk model useful as it affects the performance of the network protocol. This mobile node pattern with a random movement is well depicted in the random walk mobility model. The random walk is most appropriate for pedestrian movements since this is where mobility is restrained to limited geographical coverage particularly within residential and office buildings (Gavrilova, 2006).
Random waypoint model
The Random Waypoint Mobility Model is comparable to the random walk model. However, it includes pause times that occur between changes in direction and speed. If pause time is zero, random way point model is similar to random walk model. A mobile node starts at one location where it stays for a certain period of time. This is actually the pause time. After the expiry of pause time, the mobile node chooses a different destination randomly alongside a new speed which ranges from nil to the stipulated maximum [0,speedmax]. Subsequently, it travels towards the new destination at the chosen speed. When it arrives at the destination, it takes a break (pause time) before starting the procedure again. This is continuously repeated as long as the mobile node is range of connectivity (Mohd Saad & Zukarnain, 2009).
In this model, a number of uniformly distributed fixed points are used as targets and are referred to as waypoints. Nodes move from one waypoint to another in segments that represent straight lines. The waypoints are chosen in such a way that information can be retrieved by the mobile nodes from anywhere in the domain as they move along their designated paths at predefined speeds (Schmidt, 2011). A comparison of mobility models reveals that the random way point model has the highest delivery ratio of packets in wireless networks besides having the lowest end-to-end delay and hop count (Unhelkar, 2006).
Fig 2: Random waypoint model diagram
Source: Klaus & Gross
Common problems have been observed with this model however. For instance, zigzag trajectories in the model make the paths followed by mobile nodes to appear unnatural. Moreover, any practical mechanism needs to be robust and provide reasonable performance alongside multiple moving patterns particularly similar to random waypoint model. In addition, the velocity distribution of the random waypoint model presents a common problem in simulation studies. Its velocity distributions range from zero to maximum which create situations of stationary states where each node stops moving (Hyytiä, 2005).
The random waypoint model bears a number of parameters that can easily be adjusted to match certain scenarios. Its versatility makes it useful in modeling networks and algorithms especially mobile users in wireless networks. It is applied in the location of arbitrary packets in a multi-hop network. Therefore it can be used in the study of the effects of mobility in the performance of cellular networks. The fact that users behave independently in a system is used to determine total handover rates into a cell as well as the mean number of handovers during a call. The relationship between mobility factor and maximum speed of a node may also be analyzed in this mobility model. Therefore, simulation evaluations of ad hoc routing protocols can be performed more efficiently with the random way point mobility model.
Random direction model
This model is sometimes used interchangeably with the random waypoint model. It aims at overcoming density waves in the number of neighbors produced by the random waypoint model. A density wave occurs when nodes cluster in one part of a simulation area particularly the central area in the case of the random waypoint model. This clustering makes nodes to appear as if they are converging, dispersing and then converging again. The random direction model is therefore implemented to alleviate this behavior. Additionally, it promotes a partially constant number of neighbors throughout a simulation. In the model, mobile nodes randomly choose a direction of travel, just as in the random walk mobility model. The node then moves to the border of the simulation area following a specific direction. Upon reaching the boundary, it pauses for some specified time before choosing another regular direction between 0 and 2Ï€ and the process continues. It can be said that this is a model that allows mobile nodes to travel to the edge of a simulation area before changing speed and direction (Han, 2008). This is the characteristic that differentiates this model from the random waypoint model.
Figure 3: Diagram of random direction mobility model
Source: Klaus & Gross
The straight lines in the diagram show the paths followed by the moving nodes towards the edges of the simulation before changing direction. Different approaches are used in implementing the random direction model. For instance, the rate of users leaving the simulation area can be set to be equal to the rate of users entering the area. As much as this approach may have merits and demerits, it leads to uniform user distributions in steady state. A major advantage of the random direction strategy is the resultant uniform stationary distribution that is achieved in a simulation. Nevertheless, the drawback is that it is also unrealistic as it experiences sudden changes in speed and direction.
In routing protocols, route stability is a requirement for quality of service for mobile users. Various metrics have been considered for selecting source destination and routing path of a mobile node. The selection of high throughput routes is considered, focusing on route stability which is an aspect of critical importance. The concept of random direction model is used in estimating the available path duration hence avoiding disruption of service that may result from route failure. Route failure is avoided by an alternative path before the one being used currently breaks (Carofiglio, n.d).
Therefore, maximization of throughput and reduction of traffic latency are essential in ensuring reliable source-destination connections over time. To that effect, a route is mainly selected according to the knowledge of nodes motion and the probability of availability of future paths. When the random direction model is applied in this manner, it determines system capability and ensures support for user communication and network reliability. Thus, route stability based on quality of service is perceived by network users. Hence, the importance of random mobility models is stressed in their usefulness in the analytical approach of studying the behavior of network routes.
Gauss-Markov mobility model
This model uses a single tuning parameter to vary the degree of randomness in the mobility pattern. The next location of a node is determined and generated by the preceding location and velocity. In a nutshell, a mobile node is initially assigned a velocity and a direction. An update of direction and speed is applied to it constantly at fixed time intervals. The Gauss-Markov mobility model differs from the other models in that subsequent node movements are dependent on previous movements. The degree of this dependence is adapted by a distinct parameter denoted as Î±. This parameter varies between values of 0 and 1 (0â‰¤Î±â‰¤1). If for instance the parameter is equal to zero, it means that the new movement does not depend the preceding movements, a result that is similar to the random walk model. On the other hand, if the parameter is within the range specified earlier, then it means that intermediate levels of randomness are achieved. Finally, if Î± is equal to negative unity, then the entity is said to be moving in a linear mode.
Figure 4: Diagram of Gauss-Markov model
Source: Klaus & Gross
The above figure illustrates the travelling pattern of a mobile node using the Gauss-Markov model which begins in the center of the simulation. In the Gauss-Markov model, the frequency of link change in a network increases exponentially with the increase in the mobility of a node. The result is a relatively lower throughput especially in the commonly used multicast protocols (Meghanathan, 2010). The average speed can be specified for a mobile node in this model. In simulation, collisions with the simulation boundary are avoided by adapting the direction of a node when it approaches the boundary. When the entity reaches a certain distance towards the boundary, it is forced away from it in another direction. The current direction is modified to move automatically away from the boundary as a basis of calculation for the next step. Hence, the entity is prevented from dwelling near a boundary for prolonged periods. The expiry of the predefined time interval allows for calculation of a new direction and speed according to the current location, velocity and direction.
The Gauss-Markov mobility model does not exhibit the sharp stops and turns experienced in the previously discussed mobility models. This is because it adapts the direction and velocity updates based on the current parameters. Depending on the set parameters, it allows for modeling along a spectrum in many applications particularly random walk and fluid flow. In other words, the model captures the velocity correlation of a mobile node in time. In fact, it represents a broad array of mobility patterns particularly the constant fluid flow model and the random walk model.
By now, a known fact is that mobility is a predominant factor that influences outcome of network protocols and simulations. Since there are no traces of user mobility on large scale, mobility models are used in the research of such work. These models are made akin to reality in the best way possible by considering the prevalent characteristics. The behavior in human mobility presents a scale-free usefulness to various aspects important in networks and communications.
The Gauss-Markov mobility model finds its application in such scenarios where humans tend to aggregate. Such places as markets, stores and shopping centers and people move from one interesting place to another. This model conceptualizes people as tending to judge the interest of a certain place depending on the interests of other people in that same place. This means they follow trends while mimicking their colleagues (Borrel, n.d). This is indeed the useful aspect employed in the Gauss-Markov model in the simulation of network routing and protocols.
Group mobility models
Reference point group mobility model
In the reference point group mobility model, otherwise known as RPGM model, the movement of a group of entities is represented as well as that of individual entities within the group. In actual sense, a foundation for the derivation of other models is provided by this model. It is conveniently assumed that a group of entities moves in accordance with a specified mobility model with predefined parameters while individual entities in the group move in accordance to another mobility model having a different set of parameters (Frattasi, 2010). RPGM presents a common framework for group mobility; hence it can be used in simulation of various mobility models.
The concept of group center, referred to as the reference point, is defined as a virtual point moving along a set of waypoints in group motion. The members of the group encounter random deviations from the group motion. Each node in a group follows a logical reference center which acts as the group leader and determines the motion and behavior of the group. The member nodes are then distributed randomly around this logical point. As the reference points of individual nodes move from time t to t+1, their current locations are updated in accordance to the reference center. Once they are updated and their reference points calculated, they are joined to a random vector of motion which represents the random movement of every node about its reference point. Varying scenarios and mobility applications may be represented or created by this model such as meeting room and static isolated groups.
However, a major disadvantage of the RPGM model is that node movement in a group is limited to a relatively low velocity motion (Battiti, 2004). Moreover, so many open parameters are left out by the model such that a range of choices has to be made in specifying a complete simulation setup. Additionally, physical locations of the nodes are instantaneous. For this reason, deriving the movement characteristics of the nodes in the group becomes difficult.
The RPGM model finds various applications in communication especially for its applicability in other models as well. It can be used to generate topologies in ad hoc networks that have node mobility based on group motion. It supposes the concept of an omniscient observer, a characteristic that enables the maintenance of complete information on the mobility of groups as well as that of member nodes. RPGM represents mobile nodes using their physical coordinates. Group mobility can be used in military communication particularly in the battlefield. For instance, individual soldiers may move collectively in a group. In another illustration, in cases of disaster relief, rescue crews operate in groups while working cooperatively (Jayakumar & Ganapathi, 2008).
In the movement of soldiers, the movement of the group leader may be denoted by time t and a velocity vector v. These parameters not only define the movement of the leader but also determine the general movement of the group as a whole. Every soldier in the group deviates from the velocity vector of the group leader by a certain degree. This vector may be chosen in a random manner depending on the predefined paths. If the predefined paths are selected appropriately, the RPGM model may be used to emulate a wide range of human mobility behaviors. These are useful in the cases mentioned earlier, that is, battlefield communication and disaster relief scenarios.
Other group mobility models include the column mobility model in which a number of nodes form a line and move forward in a uniform direction. The Nomadic Community Mobility model involves a set of nodes moving collectively from one location to the other. Finally, pursue mobility model entails a set of entities that follow a given target in a simulation area. Many other mobility models exist in various theoretical frameworks as well as simulation environments, analysis settings and models.
A larger number of mobility models than discussed in this study are used in the simulation of wireless networks and in other areas of communication with regards to human mobility. This study has covered several classes of mobility models which have been described in details including their areas of application. In fact, the importance of choosing the appropriate model for a specific research case has been clearly shown. Mobility models significantly affect simulation results. A model in use is required to be complex enough so as to provide results that represent real case scenarios in a simple way. In addition, it should be easy to implement besides providing fast performances in simulation. The most accurate mobility patterns are achieved through putting together traces of real cases of moving entities. Such traces may then be used to verify the mobility results to approximate synthetic mobility models in relation to real user movement and behavior.
In this study, an analysis has been achieved on mobility patterns and the effects they have on routing performance of MANETs (Mobile ad hoc networks) in a systematic manner. It can be concluded that mobility patterns influence the performance of various routing protocols. Clearly, connectivity, performance and mobility are interrelated. Thus, it would be prudent to conclude that protocols may vary relatively with the type of mobility model used. Certain protocols produce better throughputs under certain models while they may perform poorly in other mobility models. Moreover, it can be argued that human mobility is specific to time, location as well as the individuals themselves. Therefore, trajectories that ensure employ these properties have to be considered when simulating different mobility algorithms and models that can potentially be implemented in real human exposure scenarios.