Journal of Network and Computer Applications 36 (2013) 1078–1090

Contents lists available at SciVerse ScienceDirect

Journal of Network and Computer Applications

1084-80

http://d

n Corr

E-m

pkhadiv

journal homepage: www.elsevier.com/locate/jnca

Using mobile node speed changes for movement direction change predictionin a realistic category of mobility models

Masoud Zarifneshat n, Pejman Khadivi

Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran

a r t i c l e i n f o

Article history:

Received 19 July 2012

Received in revised form

11 November 2012

Accepted 13 January 2013Available online 8 February 2013

Keywords:

Ad hoc network

Realistic mobility model

Association rule mining

Target tracking

45/$ - see front matter & 2013 Elsevier Ltd. A

x.doi.org/10.1016/j.jnca.2013.01.012

esponding author. Tel.: þ98 910 500 6573.

ail addresses: m.zarifneshat@ec.iut.ac.ir (M. Z

i@ec.iut.ac.ir (P. Khadivi).

a b s t r a c t

In order to evaluate performance of protocols for ad hoc networks, the protocols have to be tested

under realistic conditions. These conditions may include a reasonable transmission range, a limited

buffer size, and realistic movement of mobile users (mobility models). In this paper, we propose a new

and realistic type of random mobility models in which the mobile node has to decelerate to reach the

point of direction change and accelerates with a defined acceleration to reach its intended speed. This

realistic mobility model is proposed based on random mobility models. In reality, mobile objects tend

to change their speed when they are going to change their direction, i.e. decelerate when approaching a

direction change point and accelerate when they start their movement in a new direction. Therefore,

in this paper, we implement this behavior in random mobility models which lack such specification.

In fact, this paper represents our effort to use this accelerated movement to anticipate a probable

direction change of a mobile node with reasonable confidence. The simulation type of this paper is

based on traces produced by a mobility trace generator tool. We use a data mining concept called

association rule mining to find any possible correlations between accelerated movement of mobile

node and the probability that mobile node wants to change its direction. We calculate confidence and

lift parameters for this matter, and simulate this mobility model based on random mobility models.

These simulations show a meaningful correlation between occurrence of an accelerated movement and

event of mobile node’s direction change.

& 2013 Elsevier Ltd. All rights reserved.

1. Introduction

A mobile ad hoc network is designed to link several nodeswithout any infrastructure in a wireless way. Due to productionof small and inexpensive wireless devices, there are severalresearches conducted in the field of mobile ad hoc networks (Baiand Helmy, 2004). For a complete and systematical study of a newmobile ad hoc network protocol, it is essential to simulate andevaluate the new protocol under realistic conditions that reflectsimilar conditions where the protocol is going to be implemented.

The mobility models are designed to describe movementpattern of mobile users including their locations, velocities andaccelerations over time (Bai and Helmy, 2004). Currently, thereare two types of mobility models named as traces and syntheticmodels (Camp et al., 2002). Traces are the exact form of mobilitymodels of real life mobile objects. This means that the tracemobility models are acceleration, speed, and location of a realmobile object recorded to study its movement. This kind of

ll rights reserved.

arifneshat),

mobility models can give accurate information, especially whenthere are a large number of mobile objects and the period that themobile objects are studied in is long enough (Camp et al., 2002).This kind of mobility model is not always available and usable forall ad hoc network simulation environments because for everysimulation a new trace is needed to be generated. Hence, we mayneed another breed of mobility models.

Synthetic mobility models are used in simulation environ-ments especially developed for wireless ad hoc networks (Campet al., 2002). In this kind of mobility models, it is attempted togenerate realistic traces for simulation in ad hoc network simu-lators. In fact, synthetic mobility models use mathematicalequations to produce traces of mobile objects very similar to realtraces produced by real mobile objects (Musolesi and Mascolo,2009). Synthetic mobility models are mainly preferred over tracemobility models and hence, most of the research is done in thisbranch of mobility models (Musolesi and Mascolo, 2009). Thesynthetic mobility models are divided into four main categories.These categories include random models, models with temporaldependencies, models with spatial dependencies, and modelswith geographical restrictions (Bai and Helmy, 2004).

In this paper, we propose modification to random mobilitymodels and Levy walk mobility model (Rhee et al., 2011) in order

M. Zarifneshat, P. Khadivi / Journal of Network and Computer Applications 36 (2013) 1078–1090 1079

to enhance their behavior and change these mobility models intomore realistic ones.

In reality, the mobile object usually does not change itsdirection abruptly without any speed change. Hence, in thispaper, we use this common property in mobile objects to changecurrent random walk and Levy walk models into more realisticones. In our proposed modification, the mobile node deceleratesbefore reaching a direction change point, changes its direction,and then accelerates from zero to its selected speed.

We use this modification to establish a relation between speedvariations of a mobile node and its tendency to change itsdirection. We measure the strength of this relation throughcalculating its confidence and lift parameters. Confidence and liftare proposed to evaluate association rules, determined in datamining. These simulations show that there is a strong correlationbetween accelerated movements of mobile nodes and theirtendency to change direction in proposed mobility models. Thisproperty of our proposed mobility models can be used to predictthe direction change point of a mobile object in applications suchas target tracking in wireless sensor networks.

Moreover, we simulate our mobility models to calculatemetrics that are called mobility metrics. These metrics help toestimate the quality of our proposed models. In order to reach arelation between speed of a node in different mobility models andits tendency to change movement direction, we perform anotherseries of simulations for different mobility models. These resultsshow that in some mobility models there are relations betweenspeed of a node moving with a mobility model moving patternand parameters for direction change tendency.

The rest of this paper is organized as follows. In Section 2, wediscuss about important and recent researches done in order toachieve more realistic mobility models. We also search for worksdedicated to finding relations between different parameters of amobility model and direction change tendency of node. Section 3is dedicated to preliminary issues necessary to understand themechanism of our proposed modification. We also discuss aboutconcepts that are essential to know for realizing parameters wehave simulated. We also represent simulation results we havegained from simulating normal mobility models. We used thesemodels to exert our proposed modification. In Section 4, wepresent our proposed modification to random and Levy walkmobility models. Section 5 is dedicated to the discussion of ourcorrelation analysis importance in the field of target trackingapplication in wireless sensor networks. The simulation resultswill appear in Section 6. Finally, this paper concludes in Section 7.

2. Related work

In this section, we discuss about previous works done so far todesign realistic mobility models. We have two intentions in thissection: first, we review other works done for designing morerealistic mobility models. Second, we review previous works doneto find relations between speed or speed variations and nodetendency to change its direction.

In order to realize more realistic mobility models, Gaikwad andZaveri (2011) have proposed a mobility model to mimic the move-ment of vehicles on roads of a city. They have determined a pointcalled attraction point to which all nodes approach. They alsoconsidered speed variations of vehicles in real life and implementedit in their mobility model. In a similar work, Wei-dong et al. (2010)have devised a mobility model based on actual mobility traces forurban traffic scenarios. Node speed is chosen according to its location.In resident areas, nodes move with lower speeds. However, on roadsnodes move with a proper speed according to density of vehicles onthe road. Mahajan et al. (2006) have proposed two mobility models

based on Manhattan models. In the Stop Sign Model, each intersec-tion has a stop sign and each node should wait on each intersectionfor a defined period. The front node controls the speed of each node.They refined this model, the Traffic Sign Model, by replacing onlywait on intersections by traffic lights on intersections. Hossain andAtiquzzaman (2009) have analyzed the city section model as arealistic model. They have introduced an analytical model to get tosome parameters such as expected epoch length and expected epochtime. Bratanov and Bonek (2003) have proposed a new mobilitymodel that describes vehicle-borne terminals. They have assignedhigh degree of freedom to street patterns and considered terminalmovement to increase the reality. All of these five models areconsidered models with geographic restriction. In these five papers,authors have not investigated the relation between node speed andits tendency to change direction the way we do in this paper.

Gainaru et al. (2009) have proposed a realistic mobility modelbased on social network theory for movement of humans. This modelgroups the nodes with similar destinations. The groups of nodes withsame destination are placed in their appropriate cell of a grid mapand the simulation runs. In a similar work, Bhandari et al. (2010) havedevised a mobility model for human movement in public areas. Inthis mobility model, there are attraction points which people or nodesare willing to move toward. The randomly distributed nodes insimulation map select most attractive points and start to movetoward them. In another work in the field of human mobility,Papageorgiou et al. (2012) have proposed a mobility model to mimicthe ability of human to move around obstacles. If there is an obstaclein the way to the destination, the node selects a point as itsintermediate destination. This point is the vertex of the obstacle thatis in the direct line of sight to the node and is closest to its finaldestination. This process is repeated until the node reaches thedestination. The authors of these three papers did not consider thespeed variations and turning points since it is not very essential toconsider in the movement of humans.

Ballari et al. (2012) have designed a mobility model for mobilewireless sensor networks in fire prevention applications. This mobi-lity model takes advantage of Bayesian networks and consists of threeparts: a context typology to describe different areas that the sensornetwork monitors, a graph encoding the probabilistic dependenciesamong interesting variables and rules needed for inference of sensorbehavior. Although this method seems to be a more logical but morecomplex algorithm, but there is no sign of any attempt to address theproblem issued in this paper.

Gunasekaran and Nagarajan (2009) have proposed a groupmobility model based on a unified relationship matrix which iden-tifies the community structure more accurately. In this model, nodesare divided to several groups and each node moves toward anattraction point while other nodes of that group keep a small distancefrom it.

Zhao and Wang (2006) have proposed a realistic mobility modelwith smooth motion of nodes. In this mobility model, the mobilenode in each travel starts from immotile state. With a defined rate,it starts to move to reach a speed. It then travels with this constantspeed in a direct line and with a predefined rate it reduces its speedto reach zero speed. This mobility model has some properties. In thismodel, nodes move smoothly. Their average speed is stable and thenode distribution is uniform. This model is the most similar work toour proposed mobility model. In fact, the model modification weproposed is similar to this work, but the authors of this paper havenot analyzed the relation between direction and speed.

Wang et al. (2010) have proposed a mobility model with circularmovements to model the movement of Unmanned Arial Vehicle(UAV). This mobility model is based on semi-random circular move-ment. This paper introduces a very special purpose model with lowdegree of freedom. The problem of speed change in the event ofdirection change cannot be issued in this model.

M. Zarifneshat, P. Khadivi / Journal of Network and Computer Applications 36 (2013) 1078–10901080

Ahmed et al. (2010) have designed a mobility model to realisti-cally implement any obstacles and map. The algorithm in this modelproduces anchors and these anchors form a graph. A shortest pathalgorithm is run on this graph to find best paths for mobile nodesto travel around obstacles. Again in this paper the authors have notmentioned the speed change while turning and the relation betweenthese two.

Lan and Chou (2008) have developed a tool called MOVE whichcan generate mobility models. There are two components in thistool. First, a map editor is integrated to create or import therequired map. Second is the vehicle movement editor, which isresponsible for creating the movement of mobile nodes. Thiscomponent acquires its information from users that can be aroute that the mobile node needs to travel. This model has trafficlight mechanism, driver route choice and overtaking behavior.

Jardosh et al. (2003) have devised a mobility model withobstacle considerations. In fact, this model is one of the primarymodels with such consideration. This model used Voronoi dia-grams to form paths within obstacles.

Khadivi et al. (2005) have proposed a mobility model based onrandom waypoint model for hybrid Wireless Local Area Network(WLAN)/Cellular systems. They have assumed a special place calledHotspot in the simulation area where the mobile node has lowerspeed and longer pause times than other places in the area. Themobile node can go out of a hotspot or go into it with predefinedprobabilities.

As mentioned in this section, none of the introduced worksconsidered the speed change of a mobile object in the event ofdirection change. If it did, the authors of those papers did notinvestigate the relation between mobile node’s speed and ten-dency to change its direction. In the following section, we aregoing to discuss preliminary issues required to understand ourproposed mobility models and their application.

Fig. 1. Average distance traveled in constant direction in the random walk model.

3. Preliminaries

In this section, we study primary subjects needed to understandour proposed modification to random mobility models and Levy walkmobility model. In the first subsection, we discuss about randommobility models and Levy walk mobility model and their propertiesand mechanisms. We also present simulation results we had done onthese mobility models. These simulations are done to achieverelations between the speed and tendency of mobile node to changeits direction. Second subsection is dedicated to introducing metrics.We also discuss about properties of these metrics in this subsection.Finally, the third subsection is about association rule mining and itsparameters to evaluate a rule. In addition, we discuss about how thissubject is related to our proposed modification.

3.1. Random mobility models and Levy walk mobility model

The first mobility model that we are going to discuss in thissubsection is random walk mobility model. Einstein first describedrandom walk mobility model mathematically in 1926 (Campet al., 2002). This mobility model was proposed to mimic themovement of entities in nature. Because these entities move inextremely unpredicted ways, this model which is also namedBrownian motion (Bai and Helmy, 2004) was proposed to copytheir movements (Camp et al., 2002).

In random walk mobility model, a mobile node first chooses itsspeed and angle of direction and then moves with chosen speedon chosen direction (Camp et al., 2002). The direction of move-ment is selected from interval [0, 2p] with a uniform probabilitydistribution (Bai and Helmy, 2004). Speed values are chosen frominterval [minspeed, maxspeed] where minspeed and maxspeed are

model parameters that are set by user. These parameters indicateminimum speed and maximum speed that the mobile node canmove at. The probability distribution of this process is uniform orGaussian (Bai and Helmy, 2004). For a selected speed of v(t) thespeed vector in a 2-D space is (v(t)cos y(t), v(t)sin y(t)) where y isthe angle of speed vector (Bai and Helmy, 2004).

There are two kinds of movement in random walk mobilitymodel: one with constant distance d and the other with constantmovement time t (Camp et al., 2002). After d meters or t seconds anew direction and speed selection is performed. When a mobilenode reaches the borders of simulation field it bounces back tothe field. If the mobile node is moving with direction angle of y(t),the direction angle of the bounce back move is p�y(t), which iscalled border effect (Bai and Helmy, 2004).

Random walk mobility model is considered as a memory lessmodel, which means that the nodes moving with this model retain noknowledge of their past locations or speeds. In this model, currentspeed and direction of mobile node are independent of its previousspeed and direction (Camp et al., 2002). Memory less property of thismodel leads to unrealistic movements of mobile nodes. This causessudden stops and sharp turns (Camp et al., 2002).

If the distance or time step that is set for a mobile node issmall, then the random walk model is changed to a random

roaming mobility model and node movements are restricted to asmall portion of simulation field (Camp et al., 2002). In that case,the steps (time or distance) are not long enough and a mobilenode cannot move widely in the simulation field.

We have conducted simulations on random models and Levywalk model in order to find relations between node speedvariations and the tendency of node to change its direction.In this subsection, the results of these simulations are presented.By using two parameters which we defined, we tried to find arelation with speed of mobile nodes. The first parameter isaverage time spent in constant direction. This parameter showsthe average time a mobile node spends in constant direction andthat it does not change its direction over that period. The otherparameter defined in these simulations is average distancetraveled in constant direction. This parameter indicates theaverage distance a node travels with no direction change. Bythese simulations, we determined mentioned parameters as afunction of node speed.

Fig. 1 shows the average distance parameter as a function ofnode speed. The walk time of this simulation is 30 s.

As shown in Fig. 1 the average distance that a mobile nodetravels with a constant direction increases with increase of nodespeed. Therefore, we can approximate this distance according tothe current speed of the node. By doing calculations, we can findthe expected location in which the mobile node intends to changeits direction. Since the values in Fig. 1 are gained by repeating thesimulations, these values can be treated as expected transition

Fig. 3. Average time spent in constant direction in the random direction model.

M. Zarifneshat, P. Khadivi / Journal of Network and Computer Applications 36 (2013) 1078–1090 1081

length. It is not determined that the calculations will give theexact coordinates of transition end point.

Another mobility model, which falls in random mobilitymodels group, is random waypoint mobility model. This modelis extensively used in simulation of ad hoc networks. Randomwaypoint model is a stochastic model in which, nodes constantlychoose next destination (waypoint) and move toward them(Aschenbruck et al., 2008).

In random waypoint mobility model, there are pause timesbetween changes in speed and direction (Camp et al., 2002). Theprocess of this model is as follows. The mobile node stays incurrent location for a period (pause time) and when this timeexpires, it chooses a location in the simulation field randomly(Johnson and Maltz, 1996). Then with a random speed chosenfrom the interval [minspeed, maxspeed], the mobile node movestoward that location with that speed (Camp et al., 2002). Thisprocess continues until the simulation time is over. Selection ofspeed and location of each node is independent of other nodes(Bai and Helmy, 2004). Random waypoint model is similar torandom walk model if the pause time is zero (Camp et al., 2002).Bettstetter et al. (2004) have investigated the random waypointmodel statistically. They investigated movement duration and cellchange rate to find out about the degree of mobility.

In the situation that pause time is long and maxspeed is small, thetopology of ad hoc network is approximately stable (Bai and Helmy,2004). The maxspeed and pause time are two important parametersto create various kinds of scenarios. If node’s speed is uniformlydistributed on [minspeed, maxspeed] and pause time is equal to zero, itis inferred that the nodal speed is 0.5maxspeed (Bai and Helmy, 2004).Since the relative speed of nodes is important for link break orformation determination other than node’s absolute speed, averagenode speed is not a good metric for representing nodal speed. A goodmetric can be relative speed of nodes that can measure level of nodalspeed (Bai and Helmy, 2004).

In the random waypoint mobility model, the nodes aredistributed randomly in the simulation field at the beginning ofthe simulation. This will cause instability in average node neigh-bors (Camp et al., 2002). This defect can be resolved by too longsimulation times. The transition length is defined as the distancea node travels between two waypoints. It is proved that theaverage of transition length over all nodes is equal to the averageof transition length of a single node (Bai and Helmy, 2004).

Fig. 2 shows average time (transition time) in which the mobilenode moves in constant direction in the random waypoint model. Themaximum pause time of this simulation is equal to 10 s.

Fig. 2 shows that average time spent in constant direction isreduced exponentially with increase of node speed. It can be inferredfrom the curve that 86% of higher portion of average time interval isequivalent to 25% of lower portion of node speed interval.

The last random mobility model we discuss is random direction

mobility model. Random direction model was devised to overcome

Fig. 2. Average time spent in constant direction in the random waypoint model.

the problem of neighbor count variations caused by random way-point model (Camp et al., 2002). This problem is the clustering ofmobile nodes in the center of simulation field. In random directionmodel mobile nodes choose a random direction in which they travel.Then, the mobile node travels to the boundary of simulation field onthat direction angle. When the node reaches the boundary it pausesfor a random pause time and then again it chooses another directionangle from 01 to 1801 to travel (Royer et al., 2001).

A modification to the random direction mobility model isproposed (Royer et al., 2001). In this modification the mobile nodedoes not have to travel to the boundary of simulation field topause its movement. Instead, it chooses a direction angle and alocation on that chosen direction. On that location, the mobilenode pauses before changing its direction.

Fig. 3 shows the average time spent in constant direction inthe random direction mobility model versus node speed. Max-imum pause time in this simulation is 10 s.

As shown in Fig. 3, the average time spent in constantdirection or transition time for mobile node moving with therandom direction mobility model decreases with increase of nodespeed. Like the curve shown in Fig. 2, this figure implies thatabout 86% of reduction in average time values has happened in25% of node speed interval.

As the last mobility model discussed in this subsection weintroduce the Levy walk mobility model. The original type of Levywalk model is adopted from the random walk mobility model.This model is devised by treating the random walk model withinfinite spatial and temporal moments of the memory Shlesingeret al. (1982). A step in the Levy walk model consists of fourcomponents. These components are flight length, direction, flighttime and pause time (Rhee et al., 2011). Flight is the longestdistance the mobile node can travel without changing its direc-tion or pausing. The node selects flight length and pause time byProbability Distribution Functions (PDF) which have Levy distri-butions with coefficients a and b, respectively. The direction angledistribution is close to normal and flight time and length arehighly correlated (Rhee et al., 2008).

In the process of Levy walk model, in each step, the four valuesmentioned are generated and if the values of flight length and pausetime are negative the respective step is discarded and another step isproduced (Rhee et al., 2008). Using this process, two differentcategories of Levy walk models can be produced. When a and b are2 then the model becomes Brownian motion (Rhee et al., 2008). Fig. 4shows sample trajectories of three mobility models: Brownianmotion, levy walk and random waypoint.

3.2. Mobility metrics

In this paper we have used mobility metrics to compare differentmobility models. In mobility metrics, the metric evaluates parameters

Fig. 4. Sample trajectories of (a) Brownian motion, (b) Levy walk, and (c) Random waypoint (Rhee et al., 2011).

M. Zarifneshat, P. Khadivi / Journal of Network and Computer Applications 36 (2013) 1078–10901082

related to mobility. These metrics are average distance, relative speed,repetitive behavior, spatial dependency, and temporal dependency. Inthis paper, we only use relative speed and repetitive behavior metrics.Therefore we discuss about these mobility metrics.

The first mobility metric that we introduce is relative speed.This metric is measured for a pair of mobile nodes in thesimulation field (Johansson et al., 1999). This absolute relativespeed is averaged over simulation time. This parameter is deter-mined as follows (Johansson et al., 1999):

Mx,y ¼1

T

Z9vðx,y,tÞ9dt ð1Þ

In Eq. (1), T is the simulation time and v(x,y,t) is the relativespeed between nodes x and y in time t.

In order to reach a total metric measure the parametercalculated in (1) is averaged over all node pairs as shown in thefollowing equation (Johansson et al., 1999):

M¼1

9x,y9

Xx,y

Mx,y ð2Þ

In Eq. (2), 9x,y9 is the number of pairs of nodes and Mx,y is theaverage relative speed between nodes x and y. This metric measuresthe relative speed between all pairs of mobile nodes. Hence, for twonodes that are still or moving with the same speed in parallel therelative speed measure is the same equal zero (Johansson et al.,1999). This metric is a good indicator for inter node link formationand disconnection. The number of link changes increases with theincrease of relative speed (Johansson et al., 1999).

Repetitive behavior is the next mobility metric that is sur-veyed. It is highly probable that a realistic movement has arepetitive behavior (Theoleyre et al., 2007). This metric is basedon the fact that for real daily mobility scenarios the mobile nodetends to repeat a movement in its total movement pattern. Forinstance a person goes out to work in the morning and comeshome at night. This is a pattern that is repeated during theworking days of the week. Therefore, it is a real world scenarioin which a mobile node repeats a moving pattern for a consider-able portion of its entire movement.

In order to evaluate the repetitive behavior of mobility models,repetitive behavior metric is proposed in (Theoleyre et al., 2007). Inthis metric, an average time ratio is calculated. This time ratio is theduration that mobile node is inside the transmission range of itsinitial point divided by total simulation time (Theoleyre et al., 2007).

3.3. Association rule mining

In this subsection, we discuss one of the most commonconcepts and algorithms of data mining. In this paper we useassociation rule mining to measure the strength of correlationbetween two parameters: accelerated movement of mobile nodeand its movement direction change.

The association rule mining is originally proposed for shoppingbasket mining. The aim of this mining method is to discover theitems which are most common in a shopping basket of costumers.These patterns allow the authorities of say a supermarket toanalyze their costumers and find out their buying patterns toreorder their shelves to increase profit.

An association rule is the concurrence of two events shown in aproper technical way. These rules are generated by frequent itemsets(Jiawei Han and Kamber, 2006). An itemset is called frequent if itssupport is equal to or greater than a predefined minimum support ormin_support. Support of an itemset is the probability of occurrenceof items in that itemset together. That is measured by dividing thenumber of transactions containing the items of itemset by the totalnumber of transactions (Jiawei Han and Kamber, 2006). A frequentitemset is used to generate association rules.

An association rule consists of two parts: antecedent andconsequent (Jiawei Han and Kamber, 2006). Association rule isin the form of A) B in which A and B are two itemsets (JiaweiHan and Kamber, 2006). Itemset A is antecedent and itemset B isconsequent. This rule says itemset or event A happens and withthat knowledge itemset or event B will happen.

In order to produce all possible association rules, all combina-tions of frequent itemset members are generated and then, fromthese rules, strong ones are selected as strong and frequentpatterns (Jiawei Han and Kamber, 2006). An association rule isstrong if its confidence is equal to or greater than a predefinedminimum confidence or min_confidence. The confidence of anassociation rule is a conditional probability, defined as theprobability of event B, knowing that event A had happened. Inother words, this probability answers the question of how manytransactions that contain itemset A also contain itemset B.

If we formulate the support and confidence parameters thenthe formulas are as follows.

supportðAÞ ¼ PðAÞ ð3Þ

Eq. (3) shows the probability of occurring of the itemset orevent of A.

supportðA) BÞ ¼ PðA \ BÞ ð4Þ

Eq. (4) shows the support of an association rule that is theprobability of occurrence of A and B together.

conf idenceðA) BÞ ¼ PðB9AÞ ¼PðA \ BÞ

PðAÞ¼

supportðA) BÞ

supportðBÞð5Þ

In Eqs. (4) and (5), PðA \ BÞ is the probability of simultaneousoccurrence of two events A and B. According to Eqs. (3)–(5), therules that are frequent and strong are chosen as association rules.

We discussed about support and confidence as interestingnessmeasures to select interesting association rules. Nevertheless,these two measures may not reflect true interestingness ofa rule and may mislead us. Therefore, lift is proposed as another

M. Zarifneshat, P. Khadivi / Journal of Network and Computer Applications 36 (2013) 1078–1090 1083

measure to evaluate the correlation of two events (Jiawei Hanand Kamber, 2006). In this measure, the correlation is calculatedbased on independent event probability. In statistics, two eventsare said to be independent if the probability of their simultaneousoccurrence is equal to the product of the probability of individualevents (Jiawei Han and Kamber, 2006). This relation is formulizedin Eq. (6).

PðA \ BÞ ¼ PðAÞ � PðBÞ ð6Þ

Lift of two events is equal to the probability of simultaneousoccurrence of two events divided by the product of probabilitiesof each event. If we divide both sides of Eq. (6) by the right side ofthis equation we have lift parameter on the left side and value of1 on the right side.

lift¼PðA \ BÞ

PðAÞ � PðBÞ¼

PðB9AÞPðBÞ

¼conf idenceðA) BÞ

supportðBÞð7Þ

Eq. (7) tells us that if two events are independent their associatedlift is equal to 1 (Jiawei Han and Kamber, 2006). If lift of two events isless that 1 we say they are negatively correlated and if the lift oftwo events is greater than 1 we say these two events are positivelycorrelated (Jiawei Han and Kamber, 2006). Negative correlation oftwo events means that with increase in probability of one event theprobability of the other event is decreased. On the other hand,positive correlation of two events means that with increase inprobability of one event the probability of the other event is increasedtoo (Jiawei Han and Kamber, 2006).

We used the interestingness measures used in association rulemining to validate an association rule we proposed in this paper.

4. Proposed mobility models

In this section, we introduce a new approach to modifyrandom mobility models and the Levy walk mobility model. Thisapproach generates more realistic equivalences of these mobilitymodels.

In the original version of these mobility models, the mobile nodehas an abrupt movement. That is, mobile nodes do not comply withlaws of physics and change their speed from zero to a selected valueabruptly (with no real world acceleration). Although this idea ofsmooth moving mobile nodes is not a new idea and there are worksdone in this field (Bai and Helmy, 2004; Zhao and Wang, 2006).In real situations, mobile objects do not change their direction withsudden moves. Therefore, in these works for smooth mobility models,in addition to smooth change of mobile node speed, the authorssuggested smooth change of movement direction of mobile nodes.The application of our proposed mobility models compared to thesemodels is in the way we use the correlation between the speedvariations of mobile node and its direction change. We use thiscorrelation to be able to predict the node direction change.

The main contribution of this paper is applying the smoothspeed change to the random mobility model and Levy walk modeland seeking a relation between speed variations and mobile nodetendency to change its direction. We also have simulated metricsdescribed in Section 3.2 on our proposed mobility models.

As mentioned before, our proposed modification to the men-tioned mobility models is to make mobile nodes change theirspeed smoothly. That is mobile nodes should change their speedgradually to reach their desired speed. In real life situations,mobile objects change their speed with acceleration. In thestandard form of mentioned mobility models, the mobile nodechanges its speed abruptly, which is unrealistic.

In real situations, the required force to change the speed of anobject is equal to the product of its mass and the acceleration itneeds to change its speed from its initial value to final value in a

specific time interval (Young and Freedman, 2011). Therefore, inreal life we should use force to move objects and change theirspeed so acceleration and mass of the object are non-zero values.

In standard forms of mentioned mobility models, mobilenodes select a speed and a direction and move in that directionor toward a selected point. Each movement in which the mobilenode does not change its direction is called a transition. Betweentransitions, the mobile node moves with a constant speed until itgets to the selected destination. When the mobile node arrives atits destination, it stops completely and then changes its directionand then, abruptly changes its speed from zero to the selectedvalue and starts a new transition.

In our proposed mobility model, we added an acceleratedmovement at the beginning and ending of a transition. In somecases, the mobile node would like to change its speed or stop andstart moving without changing its direction. We changed allabrupt variations in speed into smooth accelerated movementsas real life scenarios may reveal.

When a mobile object changes its speed, it is said that theobject has an accelerated movement. If the object changes itsspeed with a constant rate, as an example reduces its speed withthe rate of 4 m/s in each second or increases that with the rate of2 m/s in each second, it is said that the object has a constantacceleration. When the object reduces its speed it is said that ithas a negative acceleration, while, any increase in the speed isequal to having positive acceleration. If the rate of speed changeis not constant and it changes over time, it is said that the movingobject is having accelerated movement with variable acceleration.In this paper, we have only simulated the constant accelerationfor mobile nodes.

We changed all speeds in appropriate places based on fixedaccelerations. We defined two acceleration values that are enteredby the user: a negative acceleration and a positive acceleration.According to definitions of negative and positive accelerations, mobilenodes that are starting their movement in a transition will havepositive acceleration and those which are ending their movement in atransition will have negative acceleration.

The general process of moving the mobile nodes for thestudied mobility models is as follows. First, the mobile nodeselects its speed, direction, and location of transition ending. Sincewe are modifying a number of existing mobility models, for eachmodel, we use the same approach of the respective model forselection of speed, direction, and transition ending. Then the nodecalculates to see if it has enough distance to the end of transitionto accelerate and decelerate completely according to positive andnegative accelerations the user has entered.

If the mobile node has enough distance to accelerate with thepositive acceleration from zero to the selected speed, and decele-rate with negative acceleration to reach zero in a transitions, thenode starts its movement in current transition. Otherwise, themobile node should lower the selected speed to make enoughdistance to accelerate and decelerate completely with positiveand negative acceleration values.

When the required distance to accelerate and decelerate withpredefined values is lower than the total distance of a transition,then, the mobile node moves with the selected speed in thedirection of transition until it arrives at an appropriate location tostart its deceleration.

As we mentioned before, quantities like time and distance arecontinuous. Nevertheless, in a computer simulation we cannotshow all the values of a continuous quantity. Therefore, we showa sample of these values. That is why we defined the time tickconcept. In our simulations, time tick is a unit of time insimulator. Time is a continuous quantity; nevertheless in acomputer, we should have a discrete quantity to deal with. Infact, a time tick is a sample of overall state of a mobile node that

Fig. 5. Three segments of transition.

Fig. 6. X and y projections of s vector.

M. Zarifneshat, P. Khadivi / Journal of Network and Computer Applications 36 (2013) 1078–10901084

is updated in every second. This information is stored in a tracefile as the output of our mobility model to be used in othersimulations of ad hoc networks. However, the calculations ofdistance and time of a mobile node should be done based oncontinuous aspect of quantities. In our simulations, we have donecalculations of time and distance in a continuous way andreported the speed and location of the mobile node in eachsample time (time tick).

In our proposed mobility models, all the calculations are donebased on transitions. The speed of mobile node in start and endinglocations of each transition is equal to zero. The locations of eachmobile node at the start and ending points of each transition arecalculated in each model according to the algorithm of the respectivemodel. We divided a transition to three segments. The first segment isthe distance that the mobile node travels from zero speed to reachthe selected speed of current transition. The acceleration of thissegment is equal to positive acceleration entered by the user. Thesecond segment is the distance in which the mobile node travels withconstant speed of current transition. The third segment is the distancethat the mobile node travels from current transition speed to reachzero speed at the end of transition.

The positive and negative accelerations are constant values.If the sum of lengths of segments one and three is equal to orgreater than transition length then the length of the secondsegment is zero. Therefore, the transition consists of segmentsone and three. In situations where even with deleting of segmenttwo there is not enough distance for segments one and two wereduce the selected speed of current transition to make enoughroom for these two segments. Therefore, we always have seg-ments one and three in one transition but according to positiveand negative accelerations we may have segment two or not.Fig. 5 shows the segments of a transition.

In Fig. 5, P0–P3 are locations of starting and ending points ofsegments. V0–V3 are speed values of the mobile node in thesepoints. V0 and V3 are speed values of mobile node in starting andending points of a transition, which are equal to zero. V1 and V2are speed values of mobile node in current transition that ischosen by the mobility model algorithm. The coordination ofpoints P0 and P3 is known because they are starting and endingpoints of the transition. In our proposed mobility models, wecalculate the coordination of points P1 and P2 by particle motionequations in classical mechanics.

If the segment two is with zero length then the coordinationsof P1 and P2 are the same. Since in each segment, we know thespeed of mobile node in starting and ending points, we use thetime independent equation, which needs the primary and sec-ondary velocities, and the acceleration in which the mobile objectis moving. Eq. (8) shows this formula.

d¼v2

1�v20

2að8Þ

In Eq. (8), d is the displacement of mobile object in meter (m),a is the acceleration of mobile object in meter per square second(m/s2), v0 is the primary velocity of mobile object in metersper second (m/s) and v1 is the secondary velocity of mobile object.

We use (8) to calculate the coordination of P1 and P2. Since thesimulation field is a 2D plain we have two components of x and yfor each point. In mobility models that we have studied there is amovement direction parameter, which is used to determine the

movement direction of a mobile node. We treat the displacementparameter as a vector where its length is equal to d and itsdirection is equal to the direction parameter introduced in themobility model. Therefore, for calculation of P1 we need P0 and

add d!

to P0. As mentioned before we add reflection of d!

on the

x-axis to x component of P0 and add reflection of d!

on the y-axisto y component of P0. We use P1 to calculate P2 in the same way.Fig. 6 shows the calculation of x and y projections.

In Fig. 6, y is the angle that vector d!

has with the x-axis. The

length of the projection of vector d!

on the x-axis is d.cos y and its

reflection on the y-axis is d.sin y as shown in Fig. 5.To sample the node movement trajectory in each second and

insert each sample in the respective trace file another motionequation is needed. Eq. (9) is the velocity as a function of time andacceleration.

v¼ atþv0 ð9Þ

In (9), v is the velocity we need to calculate, a is theacceleration, t is the time and v0 is the initial velocity. Forcalculating the speed of a mobile node in each second, t is alwaysequal to one and v0 is equal to speed of node in the previoussecond and if in the previous second the mobile node is in thestart point of transition this value is equal to zero. In order tocalculate location of the mobile node in each sample, we use thevalue that is obtained from (9) and use it as secondary velocity inEq. (8) to acquire the displacement in one-second time interval ofa mobile node. The initial velocity needed in (8) is the velocitythat is acquired in previous one-second time interval by (9). Thisprocess is repeated for segment 3 of transition. For sampling themobile node moving in segment 2, we use (10) that is displace-ment of mobile object with constant speed.

d¼ vtþd0 ð10Þ

In (10), d is the mobile object displacement, v is the velocity ofmobile object, t is the time and d0 is the initial displacement ofobject. In segment two of transition speed of mobile node used inEq. (10), t is equal to one, and d0 is equal to location of the mobilenode in previous one-second time interval.

So far, we discussed about general process of our proposedmodification and its mechanism to change the speed of mobile nodein a transition. Now we study each mobility model separately in thesense of algorithm modification due to our proposed modification.

We present the general process of all mobility models westudied in this paper and introduced in Section 3.1 in theflowchart of Fig. 7.

In the flowchart of Fig. 7, the general process of discussedmobility models in Section 3.1 with our proposed modification isdepicted. First, the algorithm selects the required parametersrelated to dynamic of the mobile node in each mobility model.In other words, the first step is a general form of the discussedmobility models. The parameters selected in this step are

Fig. 7. General process of modified mobility models.

Fig. 8. Flowchart of modification and sampling process.

M. Zarifneshat, P. Khadivi / Journal of Network and Computer Applications 36 (2013) 1078–1090 1085

direction, speed, transition length, etc. In step two, the end pointof the current transition is calculated. This point with startingpoint forms the transition line that is important for us to obtainthe segments of the transition.

The third step checks if the calculated transition end point islocated in the simulation field. If the end point is not in thesimulation field then a correction step assigns related coordinatesinside the simulation field. In the fourth step, our proposedmodification is applied to the transition which has been gener-ated by the discussed mobility models. Since this step is the mainpart of our proposed modification, a more detailed review of thisstep is presented in the flowchart of Fig. 8. In step five, we check ifthe simulation is over, and if the answer is positive, the algorithmends, otherwise the whole process repeats. In Fig. 8, the process ofstep four in the flowchart of Fig. 7 is depicted.

In the flowchart of Fig. 8, the process of modification beginswith calculation of points P1 and P2 of segments of currenttransition by Eq. (8). Upon determination of P1 and P2, we canform three segments of transition and use Eqs. (8)–(10) to samplethe state of the mobile node to a trace file. Each sample contains

the sampling time, node coordination in that sampling timein which x and y values are determined, mobile node speed andmobile node direction.

5. Discussion of correlation importance

In this section, we discuss the importance of the proposedmobility models. As mentioned before, we proposed an associa-tion rule between the speed variation and the tendency of mobilenode to change its direction.

In target tracking application of wireless sensor networksit is attempted to track an object in a field monitored by severalsensor nodes. The speed of the target may vary and the networkshould be able to track a target with different speeds withminimum probability of losing it.

In order to improve the proficiency of a tracking algorithm in caseof high speed targets, Alaybeyoglu et al. (2010) have proposed analgorithm in which there are several clusters formed in the path ofthe target to capture it. This decreases the probability of losing a fastmoving target. They used the algorithm to predict the target’s nextlocation based on its previous locations. Based on the next location oftarget the algorithm forms several clusters along the predicted pathto avoid a target which travels with high speed.

In an ideal situation, the algorithm should be able to predictthe locations of target direction change to have the best perfor-mance. In this way, the probability that the algorithm loses thetarget is low. Since the target does not change its direction unlessit is between two direction change locations, the network doesnot lose the target. In this situation, we propose that networkshould only form clusters on the locations of target directionchange. By doing so, the sensor nodes in between the twodirection change locations can be turned off to conserve energy.Moreover, if we know the probable location in which the target isgoing to change its direction, the network can form larger clusters

M. Zarifneshat, P. Khadivi / Journal of Network and Computer Applications 36 (2013) 1078–10901086

based on the target speed to determine the target’s new move-ment direction in the case of abrupt direction change.

Our proposed idea is mainly based on changing granularity oftracking according to target speed. If the target moves with ourproposed mobility model, its speed variations can be used topredict a probable direction change. This prediction helps thenetwork to form clusters in appropriate locations to avoid targetloss. When the target shows speed variations the network realizesthat it is about to change its direction with high probability andtherefore, forms clusters around that location.

As we discussed in Section 3.3, an association rule is in the form ofA) B in which A and B are two itemsets or in a more general waytwo events. For correlation analysis in this paper, we assumed thataccelerated movement of a mobile node and direction change eventof the node form an association rule. Therefore, we have a ruledefined and we are not going to mine any rules. Instead, we usecorrelation and validity parameters to first validate the proposed ruleand second verify the correlation between events on two sides.

We define two events for the association rules. The first eventis the accelerated movement of the mobile node and the secondone is the change in the direction of node. If we show the firstevent with A and the second event with D then the proposedassociation rule is A) D. This rule means that occurring acceler-ated movement of a mobile node is followed by its directionchange. We use confidence and lift to analyze the validity andcorrelation between two events on both sides of this rule. Theseparameters are introduced before in Section 3.

The confidence parameter tells us that in what percentage ofthe time that mobile node has accelerated movement, the mobilenode changes its direction. In fact, confidence is a conditionalprobability where its sampling space is the percentage of time themobile node has accelerated movement. If we have a transactionalpoint of view, the confidence of the proposed rule is the percentage oftransactions with accelerated movement that also have directionchange. This parameter gives us information about the strength of anassociation rule that means the more the confidence of an associationrule, the stronger the association rule becomes. In some cases, theconfidence parameter may not be a reliable parameter to determinethe strength and correlation of two sides of an association rule. Hence,we use the lift parameter, which is based on independence theoremin statistics. This parameter checks if the event of accelerated move-ment of mobile node is correlated with direction change of that node.If the value of lift is greater than 1, the correlation is positive and anyincrease in the probability of accelerated movement increases theprobability of direction change. The farther the lift is from 1 the morethe increase becomes. If lift is less than 1, the correlation is negativeand the increase in probability of one side of rule decreasesprobability of the other. With lift parameter, we can differentiatebetween positive and negative correlations. The confidence para-meter is not capable of such distinction.

The ultimate goal of our analysis is to find a strong andmeaningful relation between speed variations and tendency ofmobile node to change its direction. We select the speed varia-tions as antecedent because in application of target tracking inwireless sensor networks the speed of target is a parameter that iseasy to perceive and is a good measure to anticipate the move-ment behaviors of a mobile target.

Our idea needs to be refined and validated in order to beapplied in wireless sensor networks. Therefore, it is an open topicfor future researches.

6. Simulation results

In this section, we discuss about the simulation environmentsand parameters. Then, we analyze the simulation results of our

proposed modification to random mobility models and the Levywalk mobility model.

In this paper, we have categorized our simulations into twogroups. The first group is simulations for correlation analysis ofour proposed association rule. This group contains the simulationruns for confidence and lift of proposed association rule. Thesesimulations are run for our proposed modification applied tostudied mobility models to understand how much two sides ofthe proposed association rule are correlated. They also measurethe validity of our proposed association rule.

The second group of simulations is simulating the metrics ofmobility models. In this group of simulations, we treated ourproposed modification to studied mobility models as a new classof mobility models. Therefore, we validate our new class ofmobility models with simulating metrics on modified and normaltypes of studied mobility models. The metrics that are simulatedin this paper are discussed in Section 3. The normal traces ofstudied mobility models are generated by Mobisim V. 2.0 software(Mousavi et al., 2007). This simulator is exclusively designed forsimulating ad hoc mobility models and running some metrics forthese models. It also contains some learning algorithms andclassifications to classify different mobility model traces.

There are 100 repeats for each value of parameter. In eachrepeat, we simulated mobility model for 200,000 ss. The simula-tion field length and width are not variable and are equal to500,000 m. Except for simulations where field dimension is thex-axis of diagram, the values are changed from 500 to 10,000 mwith 500 m increment. We have chosen 500,000 for field dimen-sions to eliminate the effect of border in the simulation field. Thesimulations are run with 10 nodes in the field.

6.1. Validation and correlation analysis of proposed association rule

In this subsection, we present the simulation results ofvalidation and correlation analysis of our proposed associationrule. These results contain confidence and lift of mobility modelsthat are generated due to application of our proposed modifica-tion to the studied mobility models. The simulations in thissubsection are run with 20 values for different parameters.

The first mobility model that is modified and the simulationsare presented is the Levy walk mobility model. Table 1 shows theparameters for simulating the Levy walk mobility model.

The confidence proposed association rule in the modifiedversion of this mobility model is at least 99.8% according to oursimulations. Nevertheless, the confidence parameter does notform a regular curve with dimension of simulation field. There-fore as our simulations show the confidence of association rule inthe modified Levy walk model is very high so the conditionalprobability of direction change of mobile node knowing that themovement is accelerated is 0.998 in this model. Fig. 9 shows thelift parameter as a function of dimension of simulation field.

Fig. 9 shows that the lift parameter of proposed associationrule in the modified Levy walk mobility model is very high.Therefore, accelerated movement of mobile node and its move-ment direction change events are highly and positively correlated.The lift value is reduced in an exponential manner with increaseof dimensions of simulation field. As the dimensions of thesimulation field grow the probability of direction changes,reduces and the number of times in which the mobile nodechanges its direction after an accelerated movement reduces. Thespeed diagram for the Levy walk model does not show a regularcurve. This is shown in Fig. 10.

The next mobility model that we discuss is the modifiedrandom direction mobility model. The simulation parameters ofthis model are shown in Table 2.

Fig. 10. Lift as a function of node speed in the modified Levy walk model.

Table 2Simulation parameters of the random direction mobility model.

Variables Pause time (s) Speed (m/s)

Value 10 10–200

Fig. 11. Lift as a function of dimension of simulation field in the modified random

direction model.

M. Zarifneshat, P. Khadivi / Journal of Network and Computer Applications 36 (2013) 1078–1090 1087

The confidence for random direction mobility model is 100%.That is, all the times there is an accelerated movement when themobile node changes its direction. Fig. 11 shows lift parameter asa function of dimension of simulation field.

As Fig. 11 shows that the lift value increases with the increasein dimensions of simulation field. Unlike the modified Levy walkmodel, increase in simulation field width and length increases thecorrelation between accelerated movement of mobile node anddirection change events. Fig. 12 shows lift parameter as a functionof node speed in modified random direction.

According to Fig. 12, the lift value decreases exponentiallywith increase of mobile node speed in simulation area. As shownin Fig. 12 the lift value is high, indicating strong correlationbetween two studied events in our proposed association rule. Liftvalue decreases as the node speed increases mainly because ofinstability of network in high speed of mobile nodes.

The third mobility model where its simulation results arepresented is modified random walk. Fig. 13 shows confidenceparameter as a function of dimension of simulation field.

As Fig. 13 shows confidence parameter reduces as the fielddimensions increase. Nevertheless, the general value of confi-dence is so high that the minimum is more than 99.84%. Fig. 14shows the lift parameter as a function of field dimensions.

The lift values shown in Fig. 14 are not very high but they arestill above 1 hence the correlation between two sides of theproposed association rule in the modified random walk mobilitymodel is positive.

The last mobility model is modified random waypoint. Theconfidence parameter in this mobility model is at least 99.2%,which indicates a meaningful validity of the proposed associationrule. Fig. 15 shows the lift parameter as a function of fielddimensions.

As Fig. 15 presents lift values are more than 1 and theminimum is 10. Lift values also increase with increase in dimen-sions of simulation field. Fig. 16 shows the lift values as a functionof mobile node speed.

Fig. 16 shows that lift in modified random waypoint model ismuch more than 1, thus the positive correlation is too strong.Nevertheless, with increase of node speed, lift will exponentiallydecrease.

Table 1Simulation parameters of the Levy walk mobility model.

Variables Alpha Beta Flightscale Flight

(m)

Pause

(s)

Speed

(m/s)

Pausescale

Values 1 1 10 5–200 3–10 10–50 1

Fig. 9. Lift as a function of dimensions of simulation field in the modified Levy

walk model.

6.2. Mobility metrics simulations

In this subsection, we present the simulation results formetrics we discussed in Section 3.2. In these simulations, wetreat our proposed modified mobility models as a new class ofmobility models and compare them with their normal equiva-lences by simulating different mobility metrics. The simulationsin this subsection are run with 10 values for different parameters.

Fig. 17 shows a comparison between relative speed evaluationof normal and modified Levy walk mobility models.

As it is shown in Fig. 17, the curve is not very regular but showsthat the relative speed of nodes moving with modified version of theLevy walk mobility model is smaller than their normal equivalence.As mentioned in Section 3 if relative speed between two nodes is lowthen the probability of link disconnection between those two nodesdecreases. Fig. 18 shows the repetitive behavior evaluation as afunction of flight distance model.

As shown in Fig. 18, the time that a mobile node has repetitivebehavior in the modified Levy walk mobility model is more than inthe normal Levy walk model. More time having repetitive behaviorwill lead to more predictable mobile node movement. Fig. 19 showsrelative speed metric for random direction mobility model.

As shown in Fig. 19, in the random direction model, themodified version has lower relative speed than the normal one.As mentioned before, this property leads to decreased linkdisconnection probability. Fig. 20 shows repetitive behaviormetric for the random direction model.

Fig. 12. Lift as a function of node speed in the modified random direction model.

Fig. 13. Confidence as a function of dimension of simulation field in the modified

random walk model.

Fig. 14. Lift as a function of field dimensions in the modified random walk model.

Fig. 15. Lift as a function of field dimensions in the modified random

waypoint model.

Fig. 16. Lift as a function of node speed in the modified random waypoint model.

Fig. 17. Relative speed as function of field dimensions in the Levy walk models.

M. Zarifneshat, P. Khadivi / Journal of Network and Computer Applications 36 (2013) 1078–10901088

As Fig. 20 shows, mobile nodes in our proposed modifiedrandom direction model show more repetitive behavior than itsnormal version.

Fig. 21 shows the repetitive behavior evaluation for therandom walk mobility model.

As Fig. 21 represents the repetitive behavior in the modifiedrandom walk is much more than in its normal version. Fig. 22shows the relative speed evaluation of modified and normalrandom walk mobility models as a function of field dimensions.

Fig. 22 shows that the relative speed in the modified randomwalk mobility model is lower than in the normal random walkmodel. This suggests that the link error probability is lower whenthe nodes are moving with the modified random walk mobilitymodel. Fig. 23 shows the relative speed metric for the randomwaypoint model.

Fig. 23 suggests that the nodes in the modified randomwaypoint model have lower relative speed but for higher fielddimensions this gap closes. Fig. 24 shows the repetitive behaviormetric for the random waypoint model.

As Fig. 24 represents, there is a meaningful difference betweenrepetitive behavior time of modified and normal random way-point models. Nodes moving with modified model tend to spendmore time repeating their movements.

As shown in this section, the lift of different models for fielddimensions is always more than 1; hence the correlation betweenaccelerated movement and direction change is positive. Thesimulations show the same results for the nodes speed. Inrepetitive behavior metric our proposed models show more timeduration for any values of parameters. In the other hand forrelative speed, they show less speed.

7. Conclusion

In this paper, we proposed a modification to the class ofrandom mobility models and the Levy walk mobility model inorder to have more realistic mobility models. The modification isto have accelerated movement instead of sudden speed change.We also proposed an association rule for the relation between

Fig. 18. Repetitive behavior as a function of flight distance in the Levy walk

models.

Fig. 19. Relative speed as a function of field dimensions in random direction

models.

Fig. 20. Repetitive behavior as a function of field dimensions in random direction

models.

Fig. 21. Repetitive behavior as a function of field dimensions in random walk

models.

Fig. 22. Relative speed as a function of field dimension in random walk models.

Fig. 23. Relative speed as a function of field dimensions in random waypoint

models.

Fig. 24. Repetitive behavior as a function of field dimensions in random waypoint

models.

M. Zarifneshat, P. Khadivi / Journal of Network and Computer Applications 36 (2013) 1078–1090 1089

accelerated movement and direction change of mobile node.Through the simulations and by using confidence and lift mea-sures, we showed that the variation in the speed of mobile node isa reliable indicator to change in its direction.

The other group of simulations done in this paper is thesimulations of relative speed and repetitive behavior of nodesin the original mobility models and their new version when ourproposed modification was applied. These simulations show thatin the modified mobility models, the relative speeds betweenmobile nodes are less than their normal equivalences. Therepetitive behavior metric simulations show that the time inwhich the mobile nodes have repetitive behavior is longer inmodified version of mobility models than in normal ones.

References

Ahmed Sabbir, Karmakar C, Kamruzzaman Joarder. An environment-aware mobi-lity model for wireless ad hoc network. Computer Networks June 2010;54(9):1470–89.

Alaybeyoglu Aysegul, Erciyes Kayhan, Kantarci Aylin, Dagdeviren Orhan. Trackingfast moving targets in wireless sensor networks. IETE Technical Review2010;27(1):46–53.

M. Zarifneshat, P. Khadivi / Journal of Network and Computer Applications 36 (2013) 1078–10901090

Aschenbruck Nils, Gerhards-Padilla Elmar, Martini Peter. A survey on mobilitymodels for performance analysis in tactical mobile networks. Journal Tele-communication and Information Technology 2008;2:54–61 [no. 2/2008].

Fan Bai, Ahmed Helmy. A survey of mobility models in wireless ad hoc networks.In: Wireless ad hoc and sensor networks. Kluwer Academic Publishers; 2004.p. 1–29 [chapter 1].

Ballari Daniela, Wachowicz Monica, Bregt K, Manso-Callejo Miguel. A mobilityconstraint model to infer sensor behaviour in forest fire risk monitoring.Computers, Environment and Urban Systems 2012;36(1):81–95.

Bettstetter Christian, Hartenstein Hannes, Perez-Costa Xavier. Stochastic proper-ties of the random waypoint mobility model. Wireless Networks 2004;10(5):555–67.

Bhandari Shiddhartha Raj, Lee Gyu Myoung, Crespi Noel. Mobility model for user’srealistic behavior in mobile ad hoc network. In: Proceedings of the eighthannual communication networks and services research conference (CNSR2010). Montreal; 2010. p. 102–7.

Bratanov PI, Bonek E. Mobility model of vehicle-borne terminals in urban cellularsystems. IEEE Transactions on Vehicular Technology 2003;52(4):947–52.

Camp Tracy, Boleng Jeff, Davies Vanessa. A survey of mobility models for ad hocnetwork research. Wireless Communications and Mobile Computing2002;2(5):483–502.

Gaikwad, S, Zaveri, Mukesh. A novel mobility model for realistic behavior invehicular ad hoc network. In: Proceedings of the IEEE 11th internationalconference on computer and information technology (CIT). Pafos; 2011.p. 597–602.

Gainaru Ana, Dobre Ciprian, Cristea Valentin. A realistic mobility model based onsocial networks for the simulation of VANETs. In: Proceedings of the 69th IEEEvehicular technology conference. Barcelona; 2009. p. 1–5.

Gunasekaran S, Nagarajan N. An improved realistic group mobility model forMANET based on unified relationship matrix. In: Proceedings of the IEEEinternational advance computing conference (IACC 2009). Patiala; 2009.p. 1270–4.

Hossain MS, Atiquzzaman M. Stochastic properties and application of city sectionmobility model. In: Proceedings of the IEEE global telecommunicationsconference (GLOBECOM 2009). Honolulu, HI; 2009. p. 1–6.

Jardosh Amit, Belding-Royer Elizabeth, Almeroth C, Suri Subhash. Towardsrealistic mobility models for mobile ad hoc networks. In: Proceedings of the9th annual international conference on mobile computing and networking(MobiCom ‘03). San Diego; 2003. p. 217–29.

Jiawei Han, Kamber Micheline. In: Stephan Asma, editor. Data mining: conceptsand techniques. 2nd ed. San Francisco, CA, United States of America: MorganKaufmann Publishers; 2006.

Johansson Per, Larsson Tony, Hedman Nicklas, Mielczarek Bartosz, DegermarkMikael. Scenario-based performance analysis of routing protocols for mobilead-hoc networks. In: Proceedings of the 5th annual ACM/IEEE internationalconference on mobile computing and networking (MobiCom ‘99). Seattle;1999. p. 195–206.

Johnson B, Maltz A. Dynamic source routing in ad hoc wireless networks. In:Tomasz Imielinski, Korth Hank, editors. Mobile computing. Boston, UnitedStates of America: Kluwer Academic Publishers; 1996 p. 153–81.

Khadivi Pejman, Samavi Shadrokh, Saidi Hossein, Todd D. Hotspot randomwaypoint a new mobility model for hybrid WLANCellular systems. In:Proceedings of the 13th iranian conference on electrical engineering (ICEE’05).Zanjan, Iran; 2005. p. 502–7.

Lan Kun-Chan, Chou Chien-Ming. Realistic mobility models for vehicular ad hocnetwork (VANET) simulations. In: Proceedings of the 8th international con-ference on ITS telecommunications (ITST 2008). Phuket; 2008. p. 362–6.

Mahajan Atulya, Potnis Niranjan, Gopalan Kartik, Wang –I. Evaluation of mobilitymodels for vehicular ad-hoc network simulations. In: Proceedings of the IEEEinternational workshop on next generation wireless networks (WoNGeN2006). Bangalore; 2006. p. 1–13.

Mousavi SM, Rabiee HR, Moshref, M, Dabirmoghaddam A. MobiSim a frameworkfor simulation of mobility models in mobile ad-hoc networks. In: Proceedingsof the third IEEE international conference on wireless and mobile computing,networking and communications (WiMOB 2007). White Plains, NY; 2007. p.82–9.

Musolesi, Mirco, Mascolo, Cecilia. Mobility models for systems evaluation. Mid-dleware for network eccentric and mobile applications; 2009. p. 43–62.

Papageorgiou Christos, Birkos Konstantinos, Dagiuklas Tasos, Kotsopoulos Stavros.Modeling human mobility in obstacle-constrained ad hoc networks. Ad hocnetworks, vol. 10; 2012 p. 421–34.

Royer M, Melliar-Smith Michael, Moser E. An analysis of the optimum nodedensity for ad hoc mobile networks. In: Proceedings of the IEEE internationalconference on communications (ICC 2001). Helsinki; 2001. p. 857–61.

Rhee Injong, Shin Minsu, Hong Seongik, Lee Kyunghan, Chong Song. On the Levy-walk nature of human mobility: do humans walk like monkeys? In: Proceed-ings of the 27th Conference on Computer Communications (IEEE INFOCOM2008). Phoenix, AZ; 2008. p. 924–32.

Rhee Injong, Shin Minsu, Hong Seongik, Lee Kyunghan, Chong Song. On the Levy-walk nature of human mobility. IEEE/ACM Transactions on Networking2011;19(3):630–43.

Shlesinger F, Klafter Joseph, Wong YM. Random walks with infinite spatial andtemporal moments. Journal of Statistical Physics 1982;27(3):499–512.

Wang Wei, Guan Xiaohong, Wang Beizhan, Wang Yaping. A novel mobility modelbased on semi-random circular movement in mobile ad hoc networks.Information Science 2010;180(3):399–413.

Wei-dong, Yang, Li-min, Sun, Ji-zhao, Liu. A realistic mobility model for urbantraffic scenario in vehicular delay tolerant network. In: Proceedings of the IETinternational conference on wireless sensor network (IET-WSN). Beijing; 2010.p. 84–8.

Young D, Freedman A. University physics with modern physics. 13th ed. UnitedStates of America: Addison-Wesley; 2011.

Zhao Ming, Wang Wenye. Design and Applications of a smooth mobility model formobile ad hoc networks. In: Proceedings of the IEEE military communicationsconference ( MILCOM 2006). Washington, DC; 2006. p. 1–7.