Fuzzy Mobility Analyzer: A Framework forEvaluating Mobility Models in Mobile Ad-Hoc

NetworksMJ. Khaledi

AICTC Research CenterDepartment of computer engineering

Sharif University of Technology, IranEmail: khaledi@ce.sharif.edu

H. R. RabieeAICTC Research Center

Department of computer engineeringSharif University of Technology, Iran

Email: rabiee@sharif.edu

MH. KhalediAICTC Research Center

Department of computer engineeringSharif University of Technology, Iran

Email: m khaledi@ce.sharif.edu

Abstract—Mobility is one of the most challenging issues in mo-bile ad-hoc networks and has a significant impact on performanceof network protocols. Different kinds of mobility models havebeen proposed to represent the movement pattern of mobile nodesin mobile ad-hoc networks. These models attempt to capturevarious mobility characteristics existing in real movement ofmobile nodes. In this paper, a new framework called FuzzyMobility Analyzer has been proposed to evaluate mobility models.At first, our framework categorizes mobility models based ontheir mobility characteristics into five classes; subsequently it usesmobility metrics to capture the mobility and graph connectivitycharacteristics of mobile nodes in each class; finally it specifiesthe similarity degree between mobility classes and real worldmovements of mobile nodes by using the fuzzy set theory.Experimental results on well known mobility models with realworld mobility traces is presented to verify our claims.

I. INTRODUCTION

A mobile ad-hoc network (MANET) is a self organizednetwork that is created and maintained by collections ofwireless mobile nodes without using any infrastructure. Due tothe ease of deployment, many practical applications have beendeveloped for these networks. Mobile classrooms, battlefieldcommunications and disaster relief are some applications ofMANETs [1]. One of the inherent characteristics of thesenetworks is the movement of nodes. This characteristic hasa significant impact on the performance of protocols inMANETs.

In real world scenarios, the movements of mobile nodescapture the following mobility characteristics.

1) Temporal dependency of movement for a mobile nodeduring the time.

2) Spatial dependency of neighboring nodes movements ingroup movements.

3) Existence of obstacles or predefined maps which confinemobile node movements.

4) Existence of social context points where mobile nodesspend a considerable amount of time.

Mobility models were proposed to emulate the movementpattern of mobile nodes in a specific area. Mobility models

determine how nodes change their location, velocity and accel-eration against time. Since mobility patterns play a significantrole on protocol performance, it is desirable for mobility mod-els to emulate the movement pattern of real world scenarios.Otherwise, the observations made and the conclusions drawnfrom the simulation studies may be misleading. Thus, whenevaluating MANET protocols, it is necessary to choose theproper underlying mobility model.

In recent years, a wide variety of mobility models have beenproposed that only consider some of the mobility characteris-tics. In this paper, we propose the Fuzzy Mobility Analyzerfor evaluation of mobility models.

The fuzzy mobility analyzer provides a categorization ofmobility models based on their mobility characteristics whichhas been categorized into five classes. Subsequently, mobilitymetrics are used to capture the characteristics of the mobilityand graph connectivity metrics among mobile nodes. Wepropose new metrics which capture geographic restrictionsand social context points. In addition, we introduce intercontact time which captures graph connectivity characteristicsof mobile nodes. Finally, a novel method is proposed toevaluate mobility models based on the mobility metrics. Tothe best of our knowledge, Fuzzy mobility analyzer is the firstframework for evaluating mobility models.

The rest of this paper is organized as follows. Section IIcategorizes mobility model and briefly describes each mobilityclass. Section III introduces the mobility metrics. SectionIV presents our proposed method. Section V is devoted tosimulation results. Finally, conclusions are presented in sectionVI.

II. MOBILITY MODELS

The mobility models have been categorized based on theirmobility characteristics into five classes: Random Models,Random Variants Models, Group Models, Geographic Modelsand Social Models (Fig. 1).

For some mobility models, mobile nodes select waypointsrandomly and independent of their neighbors. This mobilityclass is called a Random model. Random walk [2], Random

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978-1-4244-6398-5/10/$26.00 ©2010 IEEE

Fig. 1. The Categories of Mobility Models in Mobile Ad Hoc Networks

Waypoint [2], Random Direction [2] and Levy walk [3],are important examples of random models. Random variantsmodels are a slight modification of random models. In thisclass, each node selects mobility parameters such as velocityand direction according to their previous movement. Gauss-Markov [2], Smooth random [4] and Semi-Markov Smoothmodel [5] are most important examples of random variantsmodels. There are some situations where mobile nodes movetogether, Group mobility models refer to mobility models thatdescribe the movement pattern in these situations. ReferencePoint Group Mobility model [6], Column [2], Pursue [2]and Nomadic Community [2] are examples of group models.Geographic models are another class of mobility models.These models have been introduced to emulate the movementpattern of mobile nodes where the movement is restricted topredefined paths or obstacles. Manhattan [1], Freeway [1] andObstacle [7] are examples of geographic models. The last classof mobility models is the social model. This class containssocial context points. Social context points are places wheremost of people spend a considerable amount of time on them[8]. Orbit [9], CMM [10] and Slaw [8] are examples of socialmodels.

III. MOBILITY METRICS

In order to evaluate mobility models, in this section, weintroduce mobility metrics which capture the mobility andgraph connectivity characteristics of mobile nodes.

Average Degree of Temporal Dependency. This metric hasbeen proposed to capture the temporal dependency. Degree oftemporal dependency for a mobile node at two time slots t1,t2 is defined as: RD(t1, t2) ∗SR(t1, t2), where RD(t1, t2) =cos(θ), θ is the angle between velocities at t1, t2 time slots;SR(t1, t2) = min(v(t1),v(t2))

max(v(t1),v(t2))is speed ratio at time slots t1, t2.

Average degree of temporal dependency is obtained by takingaverage over temporal dependency of all nodes [1].

Average Degree of Spatial Dependency. This metric hasbeen proposed to capture the spatial dependency. The degreeof spatial dependency between two mobile node i and j isdefined as: RD(i, j) ∗ SR(i, j), where RD(i, j) = cos(θ),θ is the angle between velocity of mobile node i and j;SR(i, j) = min(v(i),v(j))

max(v(i),v(j)) is speed ratio of two mobile nodes

i and j. Average degree of spatial dependency is obtained bytaking average over spatial dependency of all pairs [1].

Average Degree of Freedom. This metric was proposed tocapture geographical restrictions. Degree of freedom at eachpoint is number of directions which mobile nodes can selectfor the next movement. The value of this metric is low whennodes movement is restricted to predefined paths or obstacles.For measuring degree of freedom, the entire simulation areais logically divided into a number of equal grids (length andheight of grids are set according to the simulation area). Fora given grid A, mobile nodes which located in grid A canselect different waypoints located in different grids. Numberof selected grids is referred to the degree of freedom of gridA. Average degree of freedom is obtained by taking averageover degree of freedom of all grids.

Average Social Degree. This metric was proposed to capturesocial context points. For measuring the social degree, theentire simulation area is logically divided into number ofequal grids (length and height of grids are set according tothe simulation area). The social degree of a mobile node isdifference between the total number of grids and the number ofgrids which mobile node was paused on them. It is normalizedby the total number of grids. Average social degree is obtainedby taking average over social degree of all nodes.

Average Link Change Rate. Link change rate is the numberof link appearance and disappearance in unit time. This metricis an indicator of topology change [1].

Average Inter Contact Time. For two mobile nodes i andj, at time t1, inter contact time (i, j) is the length of thelongest time interval [t1, t2] during which nodes are not intransmission range of each other. Moreover, these nodes arein transmission range of each other at (t1 − ε) and (t2 + ε)where ε > 0. Formally,

ICT (i, j, t1) = t2 − t1 (1)

Average inter contact time is average over all pairs. For-mally,

ICT =

∑Tt=0

∑Ni=1

∑Nj=i+1 ICT (i, j, t)P

(2)

Where N , T , P are number of nodes, simulation time andnumber of (i, j, t) with ICT (i, j, t) �= 0 respectively.

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Fig. 2. The Proposed Method

IV. THE PROPOSED METHOD

Our proposed method is based on the fuzzy set theory. Givena set of patterns {p1, p2, ..., pn}, a fuzzy c partition of thesepatterns specifies the degree of membership of each pattern ineach class. It is represented by c×n Matrix U , where uik fori = 1, ..., c and k = 1, .., n is the degree of membership of pk

in class i. The following property must be true for U to be afuzzy c partition [11].

c∑i=1

uik = 1, 1 ≤ k ≤ n

n∑k=1

uik > 0, 1 ≤ i ≤ c

uik ∈ [0, 1], 1 ≤ i ≤ c, 1 ≤ k ≤ n

We used fuzzy set theory to assign mobility class mem-bership to mobility traces which have been collected fromreal environments. Mobility class membership determines inwhat degree the real world mobility traces are similar to eachmobility class.

Our proposed method is operated in two phases: trainingphase and test phase ( Fig. 2).

The inputs of training phase are known mobility tracesof which the user of the fuzzy mobility analyzer alreadyknows the mobility class. The known mobility traces havebeen generated by mobility simulators. In the first stage, themobility metric selection module, selects appropriate mobilitymetrics for representing the input mobility traces. Then, eachmobility trace is viewed as a d dimensional mobility met-rics vector. Next, the mobility class membership assignmentmodule assigns the mobility class membership to the knownmobility traces according to the k-nearest neighbors rule.The k-nearest neighbors to each known mobility trace arefound, and then membership in each mobility class is assignedaccording to the following equation:

uj(p) ={

0.51 + (nj/K) × 0.49, if j = i(nj/K) × 0.49, if j �= i

(3)

Where uj(x) is the mobility class membership of knownsample x (assuming x belongs to class i) in mobility class jand nj is the number of nearest neighbors which belong tothe jth class.

In the test phase, some selected unknown mobility traceswhich have been collected from real world mobility scenarios

would be analyzed. The main goal of this phase is to determinethe mobility class membership of an unknown mobility tracein each mobility class. Mobility class membership correspondsto the degree of similarity between real mobility traces andmobility classes. In the first stage, the preprocessing moduleremoves environment noise from unknown mobility traces.Then, the mobility metric measurement module measuresmobility metrics which were selected in the training phase.Next, each unknown mobility trace is represented with ad dimensional mobility metrics vector. Finally, the fuzzyclassification module assigns the mobility class membershipto the unknown mobility traces.

For fuzzy classification module, the fuzzy K-Nearest Neigh-bors (F-K-NN) method has been used [11]. In this method, knearest neighbors to each unknown mobility trace are found.Then, the mobility class membership in each class is assignedaccording to the following equation.

ui(p) =

∑Kj=1 uij(1/ ‖ p − pj ‖2/(m−1))∑K

j=1(1/ ‖ p − pj ‖2/(m−1))(4)

Where uij is the mobility class membership of the jth mo-bility metrics vector in the ith mobility class. The variable mdetermines the weight of distance in calculating membership.In the results presented in section V, we used m = 2. In Fig.3, a pseudo-code for F-K-NN is shown.

For distance metric, normalized Euclidean distance has beenused. Given two d dimensional mobility metrics vectors x, y,the normalized Euclidean distance is defined as:

D(x, y) = (d∑

i=1

| xi − yi |2σ2

i

)1/2 (5)

Where σ2i is variance of the ith dimension.

Using this method, the degree of similarity between realmobility traces and mobility classes would be specified basedon the selected mobility metrics.

V. SIMULATION RESULTS

In this section, we present results obtained from evaluatingwell known mobility traces.

For training phase, we chose mobility traces which havebeen generated by mobility simulators. We used our previouslydeveloped mobility simulator called MobiSim [12] to generatemobility traces. MobiSim is an open source java based simu-lator which can generate mobility traces for various mobility

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2010 proceedings.

Fig. 3. The pseudo-code for F-K-NN

models. Due to the variety of mobility models, we just selectedsome widely used mobility models as representatives of theirmobility classes. We generated Random walk (RW), RandomWaypoint (RWP), Random Direction (RD) and Levy walk asrepresentatives of random models, Gauss-Markov from ran-dom variants models, Reference Point Group Model (RPGM)from group models, Manhattan from geographic models andSlaw from social models.

In all models, 20 nodes move in the area of 500m×500mfor a period of 10000 sec. The transmission range is assumedto be equal to 250m. For all models except Levy walk andSlaw, speed varies from 5 to 15 m/s. In Slaw and Levy walk,pause time and path length have levy distribution [3] andvelocities are chosen according to the path length at each step.We chose one as a coefficient of pause time distribution inthese models. For Levy walk, we chose the coefficient of pathlength distribution from 1 to 1.5.

In the training phase, 20 known mobility traces have beenselected from each of RW, RWP, RD, Levy walk, Gauss-Markov, RPGM, Manhattan and SLAW models. Then, theselected mobility metrics are extracted for each known mo-bility trace. Next, mobility class memberships of the knownmobility trace in random, random variants, group, geographicand social mobility classes are calculated.

For the test phase, we chose unknown mobility traces whichhave been collected from real environments. The first data setcontains mobility traces of taxicabs in San Francisco, USA. Itcontains the GPS coordinates of approximately 500 taxis over30 days in San Francisco Bay Area, USA. The average timeinterval between two records is less than 60 seconds [13]. Weused linear interpolation to find positions at every 60 seconds.The second data set includes mobility traces of humans in fivesites. These are two university campuses (NCSU and KAIST),New York City, Disney World (Orlando), and North Carolinastate fair. The GPS receivers record the current positions atevery 10 seconds into a daily track log. The data set containspositions at every 30 seconds by taking average over threesamples [3]. The third data set contains a number of traces ofBluetooth sighting by groups of users carrying small devices

(iMotes) for a number of days. Three iMote-based experimentswere used. The first gathered data from eight researchersand interns working at Intel Research lab in Cambridge. Thesecond obtained data from twelve doctoral students and facultycomprising a research group at the University of CambridgeComputer Lab. The third experiment was conducted during theIEEE INFOCOM 2005 conference in Miami where 41 iMoteswere carried by attendees for 3 to 4 days[14].

In the test phase, each of the input mobility metric is ex-tracted from the unknown mobility traces. Then, the unknownmobility trace is represented with a vector of mobility metrics.Next, F-K-NN is used to assign mobility class membershipinto unknown mobility traces.

Tables I to IV show the simulation results with differentinput mobility metrics and several real world scenarios. Inthese tables each row refers to the test trace and each columnrefers to the assigned mobility class membership. For example,the value of ith row and jth column indicates the mobilityclass membership of the ith trace in the jth class. Wehave tested this method with different values for K. All thefollowing results were obtained by using 5 for K.

Tables I and II show the mobility class membership of cabtracker traces in each mobility class. In Table I, average degreeof freedom and average spatial dependency have been selectedas mobility metrics. As shown in Table I, cab tracker traceshave the highest mobility degree in the geographic class.

The RW, RWP, RD, Levy walk, Gauss-Markov, Manhattanand Slaw models, have the lowest average degree of spatialdependency. In RW, RWP, RD, Levy walk, Gauss-Markov andSlaw, movement of each node is independent of its neighbors.Therefore, the degree of spatial dependency is low. In Manhat-tan, a node’s movement is influenced by nodes behind it in thesame lane. This implies that the Manhattan has a high spatialdependency. But due to lanes with opposite directions in thismodel, the positive degree of spatial dependency cancels withthe negative degree of spatial dependency of a node with itsneighbors in the opposite direction. As a result, Manhattanlike random models have low values of spatial dependency.In RPGM the leaders of each group determine the movementpattern of group members. Therefore, RPGM has the highestdegree of spatial dependency.

In Manhattan, the movement of mobile nodes is restrictedto a predefined map. As a result, Manhattan has the lowestaverage degree of freedom. After Manhattan, Levy walk andSlaw have the lowest value. In these models, the lengths offlights which are lines between two consecutive waypoints,have a truncated power-law distribution. This causes most ofthe selected flight lengths fall into a limited range. Truncatedflights imply geographic restrictions. Therefore, Levy walk andSlaw have low value for average degree of freedom. Since,in RW, RWP, RD, Gauss-Markov and RPGM models, mobilenodes move freely and without any restrictions, these modelshave high value for average degree of freedom.

In cab tracker traces the movement of each taxi is in-dependent of its neighbors. Therefore the degree of spatialdependency is low. Since the movements of taxis are restricted

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to the streets, these traces have low average degree of freedom.Therefore, geographic mobility class (Manhattan) has the mostsimilarity to cab tracker traces where the average degree ofspatial dependency and the average degree of freedom havebeen selected as mobility metrics (Table I).

In Table II, average degree of temporal dependency andaverage degree of spatial dependency have been selected asmobility metrics. As shown in Table II, cab tracker traceshave the highest mobility degree in random and social mobilityclasses.

The RW, RWP, RD and RPGM models, have the lowestaverage degree of temporal dependency. Because in thesemodels the movement pattern of each node is independent ofits previous movement. Manhattan and Gauss-Markov havemedium values. In Manhattan, the velocity of a node istemporarily dependent on its previous velocity. But suddenstops due to pauses in the intersection of streets lead toreduction of temporal dependency. In Gauss-Markov, frequentchanges of velocity and direction of mobile nodes at each timereduce the temporal dependency. Therefore, Manhattan andGauss-Markov have medium values. Levy walk and Slaw havethe highest value for temporal dependency. In these modelsa velocity is selected according to the flight length. Sinceflight length has a truncated power-law distribution in Slawand Levy walk, most of the flights lengths have short length.Therefore, Slaw and Levy walk have the highest value oftemporal dependency.

The taxi movement contains three consecutive phases. Inthe first phase, the taxi smoothly increases its speed to reach adesirable speed. After that, the taxi moves smoothly accordingto the desirable speed. In this phase, the taxi speed smoothlyfluctuates around the desirable speed. In the third phase, itreduces its speed to zero before a full stop. This pattern ofmovement causes a high degree of temporal dependency incab tracker traces. So, the cab tracker traces have the high-est mobility degree in random(Levy walk) and social(Slaw)mobility models where spatial and temporal dependency havebeen selected as mobility metrics (Table II).

Table III shows the mobility class memberships of humanmobility traces in each mobility class. In Table III, averagesocial degree and average degree of temporal dependency havebeen selected as mobility metrics. As shown in Table III,human mobility traces have the highest mobility degree inrandom and social mobility classes.

Since the movement pattern of mobile nodes in Slaw isconfined to 3 to 5 regions, this model has the highest averagesocial degree. After Slaw, Levy walk, RD and Manhattan havethe highest values. In RD, the mobile node pauses and changesits direction when it reaches to the simulation boundary.This implies that the simulation boundaries are social contextpoints. In Manhattan, the mobile node pauses and changes itsdirection when it reaches the intersection of streets. Therefore,mobile nodes in Manhattan move in some specific regions.RW, RWP, Gauss-Markov and RGPM have the lowest valuefor social degree. This is due to the fact that in these modelsthere aren’t any social context points.

The human mobility traces have high social degree due toexistence of social context points. Since the current velocityis independent on the previous velocity, these traces have highaverage degree of temporal dependency. Therefore, humanmobility traces have the highest mobility class membershipin Levy walk and Slaw where the average social degree andthe average degree of temporal dependency have been selectedas mobility metrics (Table III).

Table IV shows the mobility class membership of iMote-based mobility traces in each mobility class. In Table IV,average link change rate and average inter contact time havebeen selected as mobility metrics. As shown in Table IV,iMote-based mobility traces have the highest mobility degreein social mobility class.

Lack of similarity between movement directions of neigh-boring nodes in RW, RWP, RD and Gauss-Markov causeslinks between neighboring nodes to change frequently. As aresult, these models have the highest link change rate andthe lowest inter contact time. Manhattan and RPGM havemedium values for link change rate and inter contact time.In RPGM most of the time, nodes are close to each other andthe link between each neighbor node would not be changed. InManhattan, mobile nodes must consider the safety distance sothe neighbor nodes have similar velocities and directions andthe link between two neighbors node would not be changed.Since in Slaw and Levy walk models the velocity differencebetween neighboring nodes have the lowest value, Slaw andLevy walk have the lowest link change rate and the highestinter contact time.

The iMote-based mobility traces have the lowest link changerate and the highest inter contact time. Therefore, iMote-basedmobility traces have the highest mobility degree in Slaw wherethe average link change rate and the average inter contact timehave been selected as mobility metrics (Table IV).

In summary, we can conclude the following points:1) Although in Levy walk each node selects mobility

parameters such as pause time and path length randomly,this model is not similar to other random models suchas RW, RWP and RD.

2) The Levy walk and Slaw models have the same mo-bility metrics. Because these models were proposed toemulate human walk and both of them have the samedistributions for pause time and flight length. Also inboth models the velocity is selected according to theflight length.

3) Real world mobility traces have temporal dependency,geographic restrictions and social context points.

4) Each mobility class captures some mobility characteris-tics of real world mobility traces.

5) Based on geographic restrictions, Manhattan is mostsimilar to the real world mobility traces.

6) Based on temporal dependency, Levy walk and Slaw aremost similar to the real world mobility traces.

7) Based on graph connectivity metrics, Levy walk andSlaw is most similar to the real world mobility traces.

8) Manhattan can emulate the movement pattern of mobile

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2010 proceedings.

TABLE IMOBILITY CLASS MEMBERSHIP WITH AVERAGE DEGREE OF FREEDOM

AND AVERAGE DEGREE OF SPATIAL DEPENDENCY IN CAB TRACKER

TRACES

Test Random Random Group Geographic SocialPatterns Models Variants Models Models Models

ModelsCab 0 0 0 1 0

tracker#1Cab 0 0 0 1 0

tracker#2Cab 0 0 0 1 0

tracker#3Cab 0 0 0 1 0

tracker#4Cab 0 0 0 1 0

tracker#5

TABLE IIMOBILITY CLASS MEMBERSHIP WITH AVERAGE DEGREE OF TEMPORAL

DEPENDENCY AND AVERAGE DEGREE OF SPATIAL DEPENDENCY IN CAB

TRACKER TRACES

Test Random Random Group Geographic SocialPatterns Models Variants Models Models Models

ModelsCab 0.49 0 0 0 0.51

tracker#1Cab 0.17 0 0 0 0.83

tracker#2Cab 0.72 0 0 0 0.28

tracker#3Cab 0.8 0 0 0 0.2

tracker#4Cab 0.07 0 0 0 0.93

tracker#5

nodes in streets, if temporal dependency is added to thismodel.

VI. CONCLUSION

In this paper, we introduced a new method for evaluating themobility models based on mobility metrics. Moreover, we in-troduce some new mobility metrics. The proposed frameworkuses fuzzy set theory to assign mobility class membership intoreal world mobility traces. The mobility class membership canspecify to what degree the real world mobility trace belongsto each mobility classes or mobility models. We tested thisframework using some of well known mobility models. Theresults illustrated the effectiveness of the proposed framework.

ACKNOWLEDGMENT

The authors would like to thank members of Sharif DigitalMedia Lab (DML) for their invaluable cooperation.

This work was supported by Sharif Advanced Informationand Communication Technology Center (AICTC).

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TABLE IIIMOBILITY CLASS MEMBERSHIP WITH AVERAGE DEGREE OF TEMPORAL

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This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2010 proceedings.