a mobility model of theme park visitors ieee trans on mobile computing 2015

A Mobility Model of Theme Park VisitorsG€urkan Solmaz, Student Member, IEEE, Mustafa _Ilhan Akbas,Member, IEEE, and

Damla Turgut,Member, IEEE

Abstract—Realistic human mobility modeling is critical for accurate performance evaluation of mobile wireless networks. Movements

of visitors in theme parks affect the performance of systems which are designed for various purposes including urban sensing and

crowd management. Previously proposed human mobility models are mostly generic while some of them focus on daily movements of

people in urban areas. Theme parks, however, have unique characteristics in terms of very limited use of vehicles, crowd’s social

behavior, and attractions. Human mobility is strongly tied to the locations of attractions and is synchronized with major entertainment

events. Hence, realistic human mobility models must be developed with the specific scenario in mind. In this paper, we present a novel

model for human mobility in theme parks. In our model, the nondeterminism of movement decisions of visitors is combined with

deterministic behavior of attractions in a theme park. The attractions are categorized as rides, restaurants, and live shows. The time

spent at these attractions are computed using queueing-theoretic models. The realism of the model is evaluated through extensive

simulations and compared with the mobility models SLAW, RWP and the GPS traces of theme park visitors. The results show that our

proposed model provides a better match to the real-world data compared to the existing models.

Index Terms—Mobility model, human mobility, wireless network, theme park

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1 INTRODUCTION

RECENT advances inmobile devices enabled the increasedpopularity and usage of mobile applications. Urban

sensing applications, where mostly smart phones are used,and wireless sensor networks (WSNs) with mobile sinks areexamples of these applications. The realistic modeling ofhuman movement has significant importance for the perfor-mance assessment of suchmobile wireless systems.

Human mobility models simulate the movement pat-terns of the mobile users and they form a key component ofthe simulation-based performance evaluation [1]. Earlymobility models relied on some type of variations of theidea of a random walk. Examples of this approach includethe random waypoint (RWP) [2] and Brownian Motion [3]models. These models are only very coarse approximationsof human behavior. One of the most important characteris-tics of human mobility is the combination of regularity andspontaneity in deciding the next destination. This behaviorcan also be defined as making both deterministic and non-deterministic decisions in the same time period. Consider-ing the theme park scenario, visitors usually pre-plan theirvisit. They try to optimize their time on rides while mini-mizing the time to walk from one attraction to another. Nev-ertheless, when they are in the park, they may change theirdecisions spontaneously depending on various factors. Ran-dom mobility models such as RWP do not provide a goodmatch for this behavior.

The current human mobility models can be classified intotwo groups as trace-based [4] and synthetic [5] models. Thetrace-based models generally use GPS traces and Bluetooth

connectivity observations. However, it is difficult to collectreal data and the amount of publicly available data is lim-ited. Therefore, synthetic models, which are defined onmathematical basis, are widely used in simulations. Mostmobility models aim for a generic human movement model-ing. However, different areas exhibit distinct human mobil-ity patterns, such as the areas of different cities [6]. Themobility decisions of people are driven by their goals intheir environments. For instance, walks in a city center aredriven by the need for rapidly reaching to specific destina-tions. In a university campus, walks are constrained inspace by the destination of classrooms, meeting rooms, andcafeterias. At the same time, they are constrained in time bythe schedules of classes and meetings. In an amusementpark, on the other hand, the movement would be deter-mined by the attractions planned to be visited. These exam-ples illustrate the need for the scenario-specific modeling ofhuman mobility.

Theme parks are large crowded areas with unique char-acteristics in terms of movement patterns of visitors, attrac-tions in various locations and walking paths connecting theattractions. In this paper, we present a mobility model oftheme park visitors. The outputs of the model are the syn-thetic movement tracks, pausing locations (waiting points)and pausing times [7]. First, the fractal points are generatedby the model in order to create the pausing locations. Theconcentrated locations of these fractal points are defined asthe meeting locations of visitors or attractions. This methoddecreases the number of waypoints in a map, allowing thesimulation of large numbers of visitors. It also makes themobility model more realistic since real attractions such asrestaurants or rides in the environment can be simulated bytheir individual models. These locations are grouped intofour main attraction types of theme parks: main rides (RD),medium-sized rides (M-RD), live shows (LS), and restau-rants (RT). The waiting times of visitors at these attractionsare modeled using queueing theory. Moreover, we define

� The authors are with the Department of Electrical Engineering and Com-puter Science, University of Central Florida, Orlando, FL 32816.E-mail: {gsolmaz, miakbas, turgut}@eecs.ucf.edu.

Manuscript received 11 Feb. 2014; revised 1 Oct. 2014; accepted 30 Jan. 2015.Date of publication 4 Feb. 2015; date of current version 30 Oct. 2015.For information on obtaining reprints of this article, please send e-mail to:[email protected], and reference the Digital Object Identifier below.Digital Object Identifier no. 10.1109/TMC.2015.2400454

2406 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 14, NO. 12, DECEMBER 2015

1536-1233� 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

walking areas of visitors as landmarks in the theme park inorder to separate the walking paths from the roads onwhich transportation vehicles are used.

Let us now consider how such a model is useful for wire-less mobile applications. For instance, a wireless sensor net-work can be deployed in a theme park for finding thefastest way to move from one location to another consider-ing the current density of the crowds in different areas ofthe park ([8], [9]). Such a WSN would rely on the personalmobile devices of the visitors and can be used to offer aninteractive theme park experience. Social networking appli-cations or multi-player games can be offered to the visitorswith the support of a deployed wireless system or in an adhoc working mode. The performance of such a systemwould highly depend on the mobility of the users and mustbe evaluated by simulations before deployment.

Another class of applications would be the theme parkadministration. Theme park administrators must directvisitors efficiently among attractions and balance thenumber of visitors at each attraction. It is desirable to bal-ance the density of the crowd in different areas of thepark due to efficiency of the attractions as well asthe security of the visitors. The administrators can use themobility model to estimate the possible impact of theirdecisions such as the distribution of live entertainers orthe arrangement of the paths for pedestrian traffic. Thepredictive results of the model can be used to decide thelocations of security personnel. The mobility model isalso used as a base for disaster simulations and emer-gency management applications [10].

In this paper, we present a mobility model of theme parkvisitors considering the nondeterministic macro-mobilitydecisions of the visitors as well as the deterministic behav-iors of the attractions. Our model is successful in terms ofrepresenting the social behavior of people to gather inattractions, spending time in queues, and movement deci-sions in terms of the least-action principle of human walks.The outcomes of the proposed model are synthetically gen-erated mobility traces. These mobility traces are comparedto the real-life theme park GPS traces and the traces of twomobility models. The mobility traces of our model have thebest statistical match to the GPS traces amongst the testedsynthetic models in terms of flight length distributions,average number of waiting points, and waiting times.

The rest of the paper is organized as follows. We providea detailed description for our mobility model in Section 2.We evaluate the validity of the model in Section 3, summa-rize the related work in Section 4 and finally conclude inSection 5.

2 HUMAN MOBILITY MODEL

In this section, we present the scenario-specific mobilitymodel for the theme park visitors. Before describing themodel, let us briefly explain the fundamental characteristicsof these entertainment areas. Theme parks are large areaswith one or more “themed” landmarks that consist of attrac-tions. Visitors of a landmark plan to see a subset of theseattractions by walking during their scheduled visit. SLAW[11] model provides an effective strategy in representingsocial contexts of common gathering places of pedestrians

by fractal points and heavy-tail flights on top of these fractalpoints. We extend this idea for a more realistic mobilitymodel and apply queueing models to represent the behav-ior and effects of different types of attractions on mobility oftheme park visitors.

2.1 Modeling a Theme Park

The modeling of a theme park consists of five main phases,which starts with the first phase of fractal points generation,and ends with the theme park model.

2.1.1 Fractal Points

We use the term fractal points based on its usage in theSLAW mobility model. In our model, the fractal points areinitially created in an empty area using the fractional Gauss-ian noise or Brownian Motion generation technique (fGn orfBm), as described by Rhee et al. [12]. A fractal point can beconsidered as a waypoint at the beginning. All fractal pointsand the area, in which these points are generated in, areused to form a landmark as described in the followingphases. It is shown that the use of fractal points and least-action trip planning (LATP) on top of these self-similarpoints satisfy fundamental statistical features of humanwalk [11]. As a human behavior, people are more attractedto visit popular places. This characteristic of human mobil-ity can be expressed using fractal points as explained in thenext subsection. Fig. 1 demonstrates the first phase of themodel in a scenario, where 1,000 fractal points are generatedin an area of 1,000 � 1,000 meters.

2.1.2 Clusters

After generation of the fractal points, we determine theparts of the area with highest density of the points. The goalof this phase is finding the popular areas, where people aremore attracted to gather.

We use a modified version of DBScan [13] algorithm onthe generated fractal points to find the attraction locations.DBScan is a density based clustering algorithm for dis-covering clusters with noise points, which has two inputparameters, epsilon Eps and minimum number of points(neighbors)MinPts.

Fig. 1. Fractal point generation phase of the model.

SOLMAZ ET AL.: A MOBILITY MODEL OF THEME PARK VISITORS 2407

The Eps-neighborhood of a point p, denoted by NEpsðpÞ, isdefined by NEpsðpÞ = fq 2 Djdistðp; qÞ � Epsg, where D isthe database of points. In our DBScan approach, for eachpoint in a cluster, there are at least MinPts neighbors in theEps-neighborhood of that point.

In our model, DBScan algorithm is modified based on therequirements of the scenario. The input parameters includeepsilon, minimum number of neighbors, number of clustersand proportion of noise points among all fractal points. Thenumber of clusters and noise point ratio are used to specifya landmark. For instance, if there are 25 attractions in atheme park, the number of clusters becomes 25. The non-clustered point ratio is used to determine the nondetermin-ism in mobility empirically (e.g., 10 percent) or based on sta-tistical data collected from the visitors of a theme park. Thevalues of the minimum number of neighbors and epsilonare iteratively searched with a heuristic, which alters thevalues of these two parameters according to the results ofthe previous iteration. This heuristic is based on the factthat changing the values of these two parameters directlychanges the resulting number of clusters and the non-clus-tered point ratio. For instance, if epsilon has a larger valueand minimum number of neighbors has a smaller value,DBScan produces less number of clusters, with a smallernon-clustered point ratio.

Let us assume a landmark is required to have 10 clus-ters and the proportion of non-clustered points to beapproximately 0.10. The initial epsilon and minimumnumber of neighbors are set as 30 meters (for dimensionsof 1,000 � 1,000 meters) and eight empirically. After set-ting the initial values, the fractal points are scanned itera-tively to set the new values for epsilon and number ofneighbors parameters. When the expected number ofattractions and the expected approximate proportion ofnon-clustered points are achieved, the clustering of fractalpoints are finalized.

The clustering of the fractal points determines the areaswith highest densities of fractal points. Fig. 2 shows anexample clustering output with over 1,000 fractal points inan area of 1,000 � 1,000 meters. In this example, 15 clustersare generated and marked, whereas 10 percent of the fractalpoints are not included in the clusters.

2.1.3 Attractions and Noise Points

The clusters as the regions with highest number of fractalpoints and non-clustered points are obtained from the pre-vious step. In this phase, the most dense areas found byclustering step are marked as “attractions”.

In our model, attractions are represented by queueingmodels. We decide on the types and the weights of thequeues based on the number of fractal points and the previ-ous work on theme park design [7]. The weight of a queueis defined according to the number of fractal pointsincluded in its corresponding cluster. The central point of aqueue is the average position of all the fractal pointsincluded in its corresponding cluster. Non-clustered fractalpoints are marked as “noise points”. Wanhill [14] definedthe attractions in a theme park by queueing models and thespecified expected percentages are given in Table 1.

Each attraction has a corresponding queue according toits particular properties. M=D=n queue has a constant ser-vice time, whereas M=M=1 and M=M=n queues have ser-vice times according to exponential distribution. Thenumber of service channels n corresponds to the amount ofvisitors served per service time. In our model, M=D=nqueue model is used for the main rides and the medium-sized rides since they have similar queue behaviors.M=M=1 queue model is used for restaurants and M=M=nqueue model is employed for live shows since restaurantsand live shows have exponential service rates, while mainrides and medium-sized rides have constant service rates.

The waiting points for the visitors in a landmark aredefined by the locations of the attractions or the noisepoints. The attractions are clusters of fractals, whereas thenoise points are non-clustered fractals. Both can be consid-ered as the locations where the visitors spend a certainamount of time. For example, a point where a visitor stopsfor a while to take pictures can be considered as a noisepoint in the scenario.

2.1.4 Landmarks

Landmarks are generated as a result of the previous steps,including the generation of fractal points, density-based iter-ative clustering, generation of queues according to theirweights, queue types, and service rates. In this phase, weform landmarks by the inclusion of visitors, which aremobileelements of a landmark. A specified number of visitors aredistributed to attractions and noise points randomly. Therandom distribution is achieved according to the weights ofattractions, and theweights of the noise points are set to 1.

A landmark is a place where there are multiple staticqueues, static noise points and mobile visitors. Each land-mark has two dimensions specifying its size. Fig. 3 showsa landmark model with initial placement of 20 visitors

Fig. 2. Clusters generated by DBScan over 1,000 fractal points.

TABLE 1Attraction Percentages

Attraction Queue model Percentage

Main rides (RD) M/D/n 17%Medium-size rides (M-RD) M/D/n 56%Restaurants (RT) M/M/1 17%Live shows (LS) M/M/n 10%


(mobile nodes), queues, and noise points in an area of1,000 � 1,000 meters. In this figure, central points of thequeues are represented by squares. The noise points and ini-tially located mobile nodes are shown by small dots andcircles respectively. Each queue is presented with its attrac-tion type: main rides (RD), medium-sized rides (M-RD),live shows (LS), and restaurants (RT).

The proposed landmark model is used to model walkingareas of the visitors such as the Magic Kingdom park (land-mark) in the Disney World theme park by assigning thenumber of queues and the proportion of noise pointsaccordingly. The landmark model separates walking areasof visitors from the areas where the vehicles are used fortransportation. This differentiation is important for the real-istic mobility modeling of visitors in large theme parks,where walking between various landmarks is not possibledue to the long distances.

2.1.5 Theme Park Map

For modeling the theme park, we use a graph theoreticalapproach. The theme park map is modeled as a graph con-sisting of vertices and weighted non-directional edges. Eachvertex in the graph represents a landmark. If there is a roadbetween two landmarks, an edge is added with a weightcorresponding to the transportation time.

Theme parks are usually large areas with transporta-tion services among the main locations of attractions suchas buses, trains and cars. Most of the theme parks arelocated in non-uniform 2D areas, which brings a chal-lenge to simulate a theme park with a model assuming auniform 2D area. By separating landmarks as vertices in atheme park graph model and adding weighted non-direc-tional edges between the landmarks, we generalize themodel of human mobility in a landmark to the human

mobility in the whole theme park. The mobility modelincludes the landmarks and the edges between them fortransportation of visitors. We do not assume that a themepark is a uniform 2D area, since it includes geographicalobstacles such as areas without pavements for pedes-trians and paths or roads used for transportation. Thesecharacteristics enable our mobility model to be more real-istic compared to the existing models.

Fig. 4 illustrates the phases of our model in a step-by-stepfashion. These phases start with the generation of fractalpoints, density-based clustering and continues with the gen-eration of attractions and the noise points. Attractions, noisepoints and visitors all together form a landmark as shownin the fourth phase. In the last phase, multiple landmarksand roads are modeled with a graph.

2.2 Visitor Model

In the model, the visitors are represented by mobile nodes.We define the states of the mobile nodes in a landmarkas “initial”, “inQueue”, “moving”, “inNoisePoint” and“removed”. At the beginning of the simulation, all mobilenodes are in “initial” state. A mobile node changes its stateto “inQueue” when it starts waiting in a queue. The statechanges to “inNoisePoint” when the node starts waiting ina noise point. There are two different states of waiting inorder to differentiate waiting in a noise point or in a queue.When a mobile node starts changing its location to arrive toa new destination, which may be an attraction or a noisepoint in the landmark, it is in the “moving” state. The stateof a mobile node is “removed” when the hangout time ofthe node passes. Fig. 5 shows the five states of visitors andthe state transitions.

Initially, each visitor decides on the amount of time tostay in the particular landmark, which is defined as thehangout time. Hangout times of the visitors are generatedby using the exponential distribution. Then, each visitor

Fig. 3. A landmark model including attractions, noise points and initiallydistributed mobile nodes.

Fig. 5. States of a visitor.

Fig. 4. The phases of modeling a theme park.


selects a subset from the set of all attractions at the land-mark to visit. The size of the subset (the number of queuesto visit) selected by a visitor is proportional to the corre-sponding hangout time of that visitor. If the visitor is not in“inQueue” state when the hangout time ends, the visitorleaves the landmark. In other words, the visitor arrives atan exit point of the landmark. If the visitor is waiting in aqueue, (in “inQueue” state), the visitor continues to wait inthe queue and leaves the landmark after being serviced. Weassume every visitor has a constant speed. After attractionsubset decision, the visitors move according to the leastaction principle among the selected attractions and noisepoints. The visitor marks an attraction or a noise point asvisited and does not visit these points later. This principle isalso used to explain how people make their walking trailsin public parks.

The next destinations of visitors are decided by usingAlgorithm 1, which is a modified version of Least ActionTrip Planning [11] algorithm. In LATP, a visitor tries to min-imize the Euclidean distance traveled from a waiting pointto a new waiting point (destination). The waiting points areeither the attractions or the noise points in the landmark.This strategy is different than Dijkstra’s Shortest Path sinceit does not always cause the new destination to be the near-est waiting point, where every unvisited point has a proba-bility to be the next destination. The parameter a is used todetermine this probability. The algorithm is modified tomatch the requirements of our mobility model. InAlgorithm 1, A is the set of attractions which are planned tobe visited by the visitor, whileN is the set of all noise points.W represents the set of attraction weights, while cp is thecurrent position of the visitor. Pr is the set of probabilities ofthe next destination points of the visitor. Waiting points arenot identical and have varied weight values, while theweight of a noise point is always 1 and the weight of aqueue (attraction) is set as the number of fractal pointsincluded in its corresponding cluster. The probabilities ofthe queues with larger weight values, such as main rides,are higher for selection as the new destination points. Inother words, visitors are more attracted to gather in queueswith larger weight values. For the calculation of Euclideandistances (dðcp; aÞ for attractions and dðcp; nÞ for noisepoints), we use the exact positions of the noise points in thelandmark and the positions of the central points of queues.

Algorithm 1.Algorithm for deciding the next destination

1: for each n inN do2: PrðnÞ :¼ ð 1

dðcp;nÞÞa3: end for4: for each a in A do5: PrðaÞ :¼ ð 1

dðcp;aÞÞa6: PrðaÞ :¼ PrðaÞ �WðaÞ7: end for8: Select a point p according to probabilities Pr from the set

A [N9: if p 2 N then10: return Position of the noise point p11: else12: return Position of a random sit-point in the queue p13: end if

At each iteration of the simulation, we check the queuesto find the number of visitors serviced and the states of allvisitors for possible changes. For instance, if a visitor is ser-viced by an attraction, the state of the visitor must changefrom “inQueue” to “moving”.

When an attraction is selected, the visitor goes to a ran-dom sit-point inside the clustered area as the new destina-tion position. Waiting time of a visitor in a queue dependson the number of visitors already waiting in the queueahead of that visitor, service rate and the number of visitorsper service of the attraction. When a visitor goes to a noisepoint, the waiting time of the visitor is generated using thetruncated Pareto distribution.

Most theme park visitors travel in groups such as fami-lies. While this model is based on individual mobility deci-sions, group mobility characteristics of the proposedapproach or the social behaviors of the groups formed as aresult of the attractions can be analyzed to improve themobility model.

2.3 Theme Park with Multiple Landmarks

The mobility model can be easily applied to model a com-plete theme park scenario. Each smaller park in a largetheme park would be modeled as a landmark. For eachpark, real dimension lengths are used to specify the 2D rect-angle area of a landmark. OpenStreetMap [15] can be usedto determine the sizes of the theme parks.

In the real scenario, the number of attractions and typesof those attractions are generally known; however, if this isnot the case, the queue types of the attractions and the num-bers specified in this paper can potentially be used. Withthis approach, a portion of a theme park can be modeled asa landmark.

Each visitor in this scenario has a total hangout time,which is the amount of time to spend in the theme park.Initially, visitors decide on the parks (landmarks) tovisit in an order such that the transportation (minimumweights) between them is minimized. A visitor also plansto visit particular attractions when entering a new land-mark. After finishing the hanging out time in the park,the visitor goes to the next planned park through theroad connecting the two parks.

Fig. 6 contains three main parks (landmarks) of the Dis-ney World theme park in Orlando; namely, Epcot, AnimalKingdom and Hollywood Studios. OpenStreetMap [15] isused to illustrate the model on this map and the MagicKingdom park is not included here for illustration pur-poses. In this figure, landmarks are the vertices and thelines connecting landmarks are the edges with differentweights. As you can see, the parks have labels L1, L2 andL3, and the weights of the edges between them have labelsW1, W2 and W3. The landmarks can be generated accord-ing to the actual sizes of the areas of the main parks, andthe weights are set with the actual transportation times.Dimensions and numbers of attractions are also set foreach park. The simulation of the model is applied to thereal scenario by this graph theoretical approach, whichgenerates realistic synthetic traces of visitor mobility forthe theme parks included in the scenario.


3 SIMULATION STUDY

3.1 Simulation Environment and Metrics

In this section, the experiments are carried out to validateour mobility model in landmarks and observe the effects ofthe unique parameters of the model. The simulation of ourmodel generates synthetic mobility traces of visitors in a 2Dterrain. The terrain is specified by dimensions, number ofattractions and the noise point ratio. Fig. 7 shows an outputexample of a simulation run with 20 mobile nodes, which istaken when simulation time is 3,600 seconds.

Mobile nodes in the simulation draw their trajectorylines while moving. These trajectory lines are the consecu-tive points in the figure, which illustrate the movement ofthe mobile nodes in the landmark. The waiting pointsare the points of intersections of consecutive trajectorylines. The waiting points are either noise points or theyare located inside the attractions. Fig. 8 demonstratesanother simulation with 200 mobile nodes after 3,600 sec-onds of simulation time. In this figure, by looking at thepositions of the mobile nodes represented by smallcircles, one can observe the expected human mobilitybehavior to gather in common places, which are the denseregions of fractal points in the model. The use of fractalpoints and planning trips according to the least actionprinciple represent this social behavior.

We conducted simulations for square landmarks withdimensions of 1,000 � 1,000 meters and 2,000 mobilenodes. For all experiments, total simulation time is 10 hourswith a sampling time of 10 seconds. Mobile nodes havehangout times which are exponentially distributed between2 hours and 10 hours. For a 1,000 � 1,000 landmark, weused 15 queues and approximately 10 percent noise pointratio. Then we changed these parameter values to observetheir effects on the metrics.

We considered three metrics throughout the simulations:1) flight length that specifies the distance between a pair ofconsecutive waiting points of a mobile node; 2) number ofwaiting points that analyzes the wait frequency of a mobilenode in a time interval and; 3) waiting time of visitors thatspecifies the time spent by a mobile node at noise points orinside attractions.

Attractions have two parameters: (expected) service timeand number of service channels that represent the numberof visitors leaving the attraction per round of service. The

number of service channels is set to 40 for main rides(RD ¼ 40), 20 for medium-sized rides (M�RD ¼ 20) and 20for live shows (LS ¼ 20), unless otherwise specified in thefigures. The service times are 60 seconds for rides and res-taurants, 120 seconds for medium-sized rides, and 300 sec-onds for live shows. When a mobile node reaches to anattraction, if the queue is full, the mobile node waits nearbythe attraction and enters the queue afterwards.

Initially, the mobile nodes are randomly distributed tothe fractal points as their start locations. We assume eachmobile node has a constant speed of 1 m/s. Minimum wait-ing time in a noise point is 30 seconds and Pareto alphavalue is empirically set to 1.5. Lee et al. [11] propose usingthe least-action trip planning on the waypoints of real-lifetraces to determine the alpha value in Algorithm 1. Thesame method is applied to the Disney World GPS traces.The alpha value of 3.0, resulting in the minimum error rate,is used in the simulation study. The flight length difference(error rate) is 1.94 percent for a ¼ 3:0. The error ratebecomes 6.01 percent for a ¼ 2:5, 22.57 percent for a ¼ 2,and 58.22 percent for a ¼ 1:5.

3.2 Simulation Results

We conducted simulation experiments and generated syn-thetic mobility traces of the theme park (TP) mobility model.

Fig. 6. An illustration of the application of model to a real-world scenario:Disney World parks in Orlando.

Fig. 7. Trajectories of 20 mobile nodes after 1 hour simulation time.

Fig. 8. Positions of 200 mobile nodes after 1 hour simulation time.


The mobility traces are analyzed by comparison with 41GPS traces from the CRAWDAD archive, which are col-lected from smartphones of 11 volunteers who spent theirThanksgiving or Christmas holidays in the Walt DisneyWorld parks [16]. The average duration of the mobilitytraces is approximately 9 hours with a minimum of 2.2hours and maximum of 14.3 hours. The GPS tracking logshave a sampling time of 30 seconds. We filtered out thedata, assuming the visitors are traveling by transportationvehicles when they exceed their regular movement speedsduring each sampling time. Moreover, we analyzed thevalidity of the results by comparing them with syntheticmobility traces of SLAW [11] and RWP [2] mobility modelsimulations. We examine fundamental characteristics ofmobility features, including distribution of flight lengths,average flight lengths, distribution of waiting times andwaiting rate (number of waiting points per hour) of themobile nodes.

For SLAW and RWP, equally sized areas (1,000 � 1,000meters) are used for the comparison with our model. Forthe GPS traces, we assume that a visitor is not walking if thevisitor moves for more than 150 m in 30 seconds samplingtime, which would exceed the average speed of a person.Accordingly, the data is filtered for the time when the visi-tors are not walking, but possibly traveling with a bus oranother vehicle in the theme park. If a mobile node is in acircular area with a radius of 10 m in consecutive samplingtimes of 30 seconds, we assume that the mobile node is wait-ing in a waiting point.

3.2.1 Flight Lengths

A flight length is the distance between two consecutivewaiting points of a visitor. A waiting point is defined by anattraction or a noise point. Flight length distribution is oneof the most significant characteristics of human mobilitymodels since it reflects the scale of the diffusion. Heavy-tailflight lengths in human travels is shown as the characteristicfeature of human mobility in several studies ([17], [18]). Theflight length distribution results also allow us to make real-istic comparisons of human mobility extracted from GPStraces with other mobility models. In this experiment, wecompared flight length distribution of the TP mobilitymodel with GPS traces, SLAW and RWP mobility models.The flight length distribution of the GPS traces represents

the mobility decision patterns of the real theme parkvisitors. For instance, the probabilities of theme park visi-tors to travel to far destination locations (e.g., 400 m) as wellas their tendency to prefer moving in shorter distances (e.g.,40 m) are analyzed with comparisons to the synthetic mobil-ity traces.

The first set of experiments are conducted by using onlyTP model with the same parameter settings to verify thatthe output traces of the simulations are consistent. The flightlength distributions of three randomly selected experimentsare given in Fig. 9. These experiments have flight lengthcounts between 64,000 and 68,000; however, all the experi-ments are normalized to the flight length count of 1,000.Flight length distributions are consistent, have similar char-acteristic, and there is no significant difference between thedistribution lines. The experiment shows the similarexpected outcomes of the synthetic simulation of the mobil-ity model, among different traces of the simulation model.

Next, flight length distribution of the simulation model iscompared to GPS traces, SLAW and RWP mobility simula-tion results. The normalized results of the simulations aregiven in Fig. 10. The flight length distribution of our modelis closer to the GPS traces compared to SLAW or RWPmobility models. SLAW has a similar characteristic butshorter flights and RWP model has a uniform distribution.Fig. 10 also shows that flight length distributions of RWPmodel is significantly different than the GPS traces. On theother hand, TP and SLAW mobility models representheavy-tail flight length distributions.

Fig. 11 shows the flight length results of TP, SLAW,RWP, and the GPS traces with the confidence bounds for3,500 outputs of each trace. The average flight length ofthe mobility model is very close to the results of GPStraces and the model outperforms the other mobilitymodels. RWP has a very significant difference comparedto the other three results. In the 1,000 � 1,000 terrain,RWP produced an average value of 500 meters, becauseof the uniform random selection of next destinations. Onthe other hand, the flight lengths of SLAW are signifi-cantly less than the TP model and GPS traces. In SLAWmodel, consideration of all fractal points as waiting pointsproduced shorter flights. Table 2 shows the mean, medianand standard deviation values of the flight lengths for themobility models and the GPS traces.

Fig. 9. Flight length distributions of different traces of TP.Fig. 10. Flight length distributions of TP, SLAW, RWP, and GPS traces.


Additionally, we compared the TP traces to analyze theeffects of different parameter values on flight lengths. Theunique parameters of TP, number of attractions, noise pointratio, and number of service channels of the attractions areused for the analysis.

We start analyzing the effects of the unique parameters.Fig. 12 shows the normalized flight length distributions ofTP model with 10, 20 and 30 attractions. We observed thateven though the flight lengths do not change dramatically,compared to 10 attractions, the increased number of attrac-tions produced shorter flights for 20 and 30 attractions asthe distances between the attractions become shorter.

Noise points represent the waiting points of the visitorsbetween the time of visiting attractions. TP model repre-sents this behavior by giving distant noise points very smallprobabilities to be chosen as next destinations, compared tothe closer noise points. The effect of the ratio of non-clus-tered fractal points on flight lengths is shown in Fig. 13. Inthe case of no noise point (0 percent), the visitors alwaysselect attractions that are distant from each other. Therefore,0 percent noise point ratio produces longer flights. Theincrease in the noise point ratio causes the increase in theprobability of selection of a noise point. Therefore, theincrease in noise point ratio shortens the flight lengths ofthe visitors. The noise point ratio parameter must be config-ured by using the GPS traces from theme parks for similarmobility traces.

Fig. 14 shows that there is no significant effect of thenumber of service channels parameter for flight lengthdistributions. The number of service channels effects thewaiting time of a visitor in the queue of an attraction,while the waiting time in attraction does not change theselection of the next destination. RD, M-RD, and LS rep-resents the main rides, medium-size rides and liveshows respectively.

The number of visitors in theme parks differs accordingto date and time. If the data for the number of visitors (pop-ulation size) in different dates is available, the model can berun for each of these dates and the results would reflect theeffect of variation in the number of visitors over time. Inorder to observe the impact of the number of visitors, weconducted simulations of the TP model with various popu-lation sizes, ranging from 500 to 10,000.

The increase in the number of visitors causes spendingmore time on the attractions with the fixed service rates.We observe the effect of this parameter on the flightlength distributions in Fig. 15. While the parameter doesnot have a very significant impact on the results, simula-tions of smaller populations, such as 500, generatestraces with shorter flights compared to the larger ones.This is mainly because of spending less time on theattractions. During the hangout times of the 500 visitors,they have extra time to spend in the noise points andtraveling to noise points mostly produces shorter flightlengths.

3.2.2 Number of Waiting Points

In this experiment, we analyzed the number of waitingpoints averaged for one hour for the three models andthe GPS traces. Average number of waiting points of GPStraces is approximately 10.5, which means every visitor iswaiting at roughly 10 different locations in an hour on

Fig. 11. Flight lengths of TP, GPS traces, SLAW, and RWP.

TABLE 2Flight Length Results

Mean Median Standard Deviation

TP 116.6 m 45.7 m 163.5 mGPS 101.1 m 53.9 m 132.4 mSLAW 51.5 m 19.0 m 94.6 mRWP 500.6 m 502.7 m 254.1 m

Fig. 12. Flight length distributions of TP with 10, 20, and 30 attractions.

Fig. 13. Flight length distributions of TP with 0, 10, 15, and 25 percentnoise point ratios.


average. For SLAW mobility model, the average numbersof waiting points are close to 20 doubling the GPS traces,while it is approximately 7.5 for our simulation and 3.3for RWP model.

The results of the mobility traces of the models set aregiven in Fig. 16. Each trace set includes one trace of themodels. The figure shows that TP model performs signifi-cantly better than SLAW and RWP in terms of waiting ratesof the mobile nodes. RWP produces very long flights, 500 mon average, which causes longer times for reaching waitingpoints. In SLAW model, on the other hand, a mobile nodesmoves frequently between 1,000 fractal points. TP modelcombines the behavior of long movements between theattractions, while it allows shorter movements with a proba-bility of visiting some noise points. Therefore, TP model isthe best match for waiting frequency behavior of themepark visitors.

Furthermore, we analyzed the effect of the parameters onthe number of waiting points. In Fig. 17, the increase in thenumber of attractions slightly increases the number of wait-ing points since the attractions become closer to each other,the flight lengths become shorter. Thus, the visitors’ abilityto visit more attractions increases.

Fig. 18 includes the results for noise point ratios rangingfrom 0 to 25 percent. The noise point ratio has a significantimpact on the number of waiting points. As the ratio

increases from 10 to 25 percent, the mean value of the num-ber of waiting points increases approximately by 50 percent.On the other hand, 0 percent noise ratio cause the smallestmean value of the number of waiting points. Along with thelonger flight lengths, the proportion of the visitors whospend time in attractions becomes higher. This causes lon-ger waiting times in queues for the visitors.

As the number of visitors leaving the attractions in around of service increases, waiting times of the visitors inthe queues of the crowded attractions decrease. As shownin Fig. 19, the number of waiting points per hour increases.However, the effect on the number of waiting points is lim-ited with the decrease of waiting times at the attractions.Higher numbers of service channels in attractions do notproduce shorter flights.

Fig. 20 shows the results of the average number of wait-ing points for the population sizes ranging from 500 to10,000. The population size changes the number of waitingpoints significantly because it affects the waiting times atthe attractions. Average number of waiting points becomesapproximately 1.5 per hour for 10,000 visitors.

3.2.3 Waiting Times

There are several studies on the waiting times in humanwalks. These studies ([19], [20]) show that the waiting time

Fig. 14. Flight length distributions of TP with three settings for the num-ber of service channels. (RD = main rides, M-RD = medium-size rides,and LS = live shows)

Fig. 15. Flight length distributions of TP with 500, 1,000, 2,000, 5,000,and 10,000 visitors.

Fig. 16. Number of waiting points per hour for TP, GPS traces, SLAW,and RWP for five trace sets.

Fig. 17. Number of waiting points per hour for TP with 10, 15, 20, 25, and30 attractions.


distributions have a truncated power-law distribution.While we reflect this in our model for waiting times at thenoise points by generating the waiting times synthetically,the waiting times at the attractions are determined accord-ing to the service rates and the number of people in thequeues. In this experiment, we compare waiting time distri-bution of TP with GPS traces and SLAW. Due to constantwaiting time of the mobile nodes, we did not include theRWP model in this experiment. The results are normalizedto 1,000 waiting times.

Fig. 21 shows that waiting time distribution of the pro-posed model is similar to the GPS traces. Compared toSLAW, TP and GPS traces have shorter waiting times. Theresults of GPS traces start at 30 seconds, due to the 30 secondssampling time. By setting noise point ratio, number of attrac-tions, and number of service channels parameters realisti-cally, one can obtain more accurate results to represent thereal-world scenario of theme park visitors mobility.

Fig. 22 shows the waiting times of TP model with 10 to 30attractions. We observed that the number of attractions doesnot have a significant effect on the waiting times as the wait-ing times stay at approximately the same level. This is dueto a tradeoff between visiting more attractions and havingless number of people in the queues. Visiting more attrac-tions causes longer average waiting times since the waiting

times at the noise points are mostly shorter. On the otherhand, as the visitors are distributed to more attractions,fewer people wait in each queue. As a result, the waitingtimes in the queues decrease.

As shown in Fig. 23, noise point ratio does not have a sig-nificant effect on the waiting times, since the waiting timesare mostly effected by the attractions. Still, the waiting timesbecome slightly less because the probability of waiting in anoise point increases. Moreover, the standard deviationbecomes smaller. This result shows that variation of thewaiting times at the noise points is smaller than the varia-tion at the attractions. The waiting time in an attractionhighly varies because of the number of people waiting inthe queue.

Fig. 24 shows the waiting time distributions of TP modelwith three settings of the parameter, the number of servicechannels. Comparing the first setting which is 20, 10, and 10for main rides, medium-sized rides, and live shows respec-tively, with the third setting, it can be seen that waitingtimes of the first setting is higher than the third one. Sincethe attractions serve more people with higher numbers ofservice channels, the waiting times at the attractionsdecrease. This effect becomes more significant with thedecrease in the number of attractions and with the highernumbers of mobile nodes.

Fig. 18. Number of waiting points per hour for TP with different noisepoint ratios.

Fig. 19. Number of waiting points per hour for TP with three settings ofthe number of service channels. (RD = main rides, M-RD = medium-sizerides, and LS = live shows)

Fig. 20. Number of waiting points per hour for TP with different numbersof visitors.

Fig. 21. Waiting time distributions of TP, SLAW, and GPS traces.


The waiting time distributions of our model with respectto the population size is shown in Fig. 25. More people intheme park cause longer waiting times, because of sharingthe same attractions. As it can be seen in the figure, waitingtimes increase with the increased population sizes. Whileattractions do not cause significant waiting times for 500 vis-itors, they require on average 15 minutes and up to 2 hourswaiting times for 10000 visitors. On the other hand, someattractions with less popularity may still not require longerwaiting times.

Overall, we observed that the proposed model outper-forms SLAW and RWP for the specified metrics, comparedto the GPS traces. Moreover, the model gives a consistentperformance. Among the tested parameters, noise point ratiois the most effective one, as it has a direct effect on the proba-bility of selecting attractions as the next destinations. Asexpected, population size affects the waiting times and theaverage number of waiting points since more people causeincrease in waiting times at the attractions.

4 RELATED WORK

Mobility affects the performance of network applicationsdesigned for a group of mobile users or nodes. As theusage of mobile elements in networked systems becomespopular, the effect of mobility becomes critical for variousapplications such as modern communication systems of

urban environments [21] and online services [22]. Consid-ering the impact of mobility, various approaches areproposed for problems including topology control of net-works [23], routing in mobile sensor networks [24], track-ing in sensor networks [25], [26], [27], analysis of socialnetworks [28], [29], disease spread simulation [30], andopportunistic communication [31]. Hara [32] analyzes theeffects of five random mobility models on data availability,while Carofiglio et al. [33] use Random Direction Mobilitymodel to provide optimal path selection for routing inmobile ad hoc networks.

Human mobility has several characteristic features,which have been observed by various measurement meth-ods. Instances of these features are truncated power-lawdistributions of pause times, inter-contact times, fractalwaypoints and heterogeneously defined areas of individualmobility. Rhee et al. ([34], [11]) show that these propertiesare similar to the features of L�evy walks and used theseproperties to design Self-similar Least Action Walk (SLAW)model. SLAW is a context based L�evy Walk model, whichproduces synthetic human walk traces by taking the degreeof burstiness in waypoint dispersion and heavy-tail flightdistribution as inputs. According to SLAW mobility model,the mobile nodes walk from one pre-defined waypoint toanother. The dense regions of waypoints form the areaswhere the people pause and spend most of the time.

Fig. 22. Waiting times of TP with 10, 15, 20, 25, and 30 attractions.

Fig. 23. Waiting times of TP with 10, 15, 20, and 25 percent noise pointratios.

Fig. 24. Waiting time distributions of TP with three settings of the numberof service channels.

Fig. 25. Waiting times of TP according to number of visitors from 500 to10,000.


SLAW models human mobility in a general contextwhere the waiting times at the waypoints are determinedaccording to a power law distribution. However, for ourparticular theme park scenario, the waiting times must bedefined according to the characteristics of the specific typesof attractions. The attractions at theme parks can be com-bined into groups of main rides, medium-sized rides, liveshows and restaurants [14]. Using the specific types, wemodeled the waiting times of visitors at these attractionsusing queueing theoretical models. Basically, in our model,queueing theory is integrated with the visitors’ movementdecisions, to create a realistic user mobility model for thetheme parks. A simple mobility model, SMOOTH [35] isproposed to represent the similar characteristic humanmobility features of SLAW model. Gonz�alez et al. [17] ana-lyze the trajectory of 100,000 mobile phone users for a timeperiod of six months and find that the trajectories have ahigh degree of temporal and spatial regularity. Social forcemodel [36] is proposed by Helbing and Johansson to repre-sent the micro-mobility behavior of the pedestrians incrowded areas. Song et al. [37] analyzed the mobile phoneusers trajectories and found a 93 percent potential predict-ability in mobility of the users.

For the modeling of human movement in specific scenar-ios, a variety of mobility models have been proposed. Liuet al. [38] propose a physics-based model of skier mobilityin mountainous regions by considering the physical effectsof gravity and the steepness of the terrain. The goal of themodel is to evaluate the effectiveness of wireless communi-cation devices in improving avalanche safety. Kim et al. [39]propose a mobility model for urban wireless networks, inwhich the model parameters are derived from urban plan-ning surveys and traffic engineering research. ParkSim [40]by Vukadinovic et al. is a software tool simulating themobility of theme park visitors. The mobility model of Park-Sim is driven by the possible activities of the visitors in thepark. Munjal et al. [41] review the changing trends of therecently proposed mobility models used for simulations ofopportunistic communication networks.

In [42], we propose a human mobility model for thedisaster scenarios in theme parks. We consider the evacua-tion behavior of theme park visitors during the times of nat-ural or man-made disasters. Since the micro-mobility anddynamics of the pedestrian flows have significant effects onthe evacuation time, we focus on using real theme parkmaps and social force model for modeling human mobilityin disasters. In this paper, on the other hand, we aim to pro-vide a statistical match with ordinary visitor movementgiven basic parameters such as number of people, numberof attractions, size of the park, and so on.

5 CONCLUSION

In this paper, we presented a model for the movement ofvisitors in a theme park. In this model, we combined thenondeterministic behavior of the human walking patternwith the deterministic behavior of attractions in a themepark. We divided the attractions into groups of mainrides, medium-sized rides, live shows and restaurants.We used queueing-theoretic models to calculate timesspent by visitors at different attractions. We validated

accuracy of our model through extensive simulationsusing theme park statistics, GPS traces collected in DisneyWorld theme park and the data generated by simulationsof other mobility models. The results show that ourmodel provides a better match to the real-world datacompared to SLAW and RWP models.

We believe that an important outcome of our work is thegeneration of realistic mobility traces of theme park visitorsfor theme parks with various scales. The techniques devel-oped in this paper can be used to model human mobility inplaces which restrain people from using transportationvehicles. These places include airports, shopping malls,fairs, and festivals. For instance, in airports, travelers usu-ally spend time and walk between the pre-determined pla-ces (hot-spots), such as check-in locations, restaurants,gates, and security check points.

The mobility traces are used in the simulation of aWSN with mobile sinks model in [43]. Another exampleuse of mobility models would be in evaluating opportu-nistic forwarding protocol, considering visitors carryingsmart-phones to share data with each other. By studyinghuman mobility, we learned that the mobility behaviorsof people in various environments produce significantlydifferent movement patterns. While networks withhuman participants are becoming increasingly popular,there is still a need for further research in humanmobility models.

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G€urkan Solmaz is currently working toward thePhD degree in Computer Science from theDepartment of Electrical Engineering and Com-puter Science, University of Central Florida(UCF). He received his MS degree in ComputerScience from the University of Central Florida andhis BS degree in Computer Engineering fromMid-dle East Technical University (METU), Turkey.His research interests include mobility modeling,coverage in mobile wireless sensor networks, anddisaster resilience in networks. He is a student

member of IEEE and ComSoc.

Mustafa _Ilhan Akbas received the BS and MSdegrees from the Department of Electrical andElectronics Engineering, Middle East TechnicalUniversity (METU), Turkey. He received the PhDdegree in computer engineering from the Depart-ment of Electrical Engineering and Computer Sci-ence, University of Central Florida (UCF). Hisresearch interests include wireless networkingand mobile computing, urban sensing and socialnetworks. He is a member of the IEEE, ComSoc,and IoT.

Damla Turgut is an Associate Professor in theDepartment of Electrical Engineering and Com-puter Science of University of Central Florida.She received her BS, MS, and PhD degrees fromthe Computer Science and Engineering Depart-ment of University of Texas at Arlington. Herresearch interests include wireless ad hoc, sen-sor, underwater and vehicular networks, as wellas considerations of privacy in the Internet ofThings. She is also interested in applying bigdata techniques for improving STEM education

for women and minorities. Her recent honors and awards include beingselected as an iSTEM Faculty Fellow for 2014-2015 and being featuredin the UCF Women Making History series in March 2015. She was co-recipient of the Best Paper Award at the IEEE ICC 2013. Dr. Turgutserves as a member of the editorial board and of the technical programcommittee of ACM and IEEE journals and international conferences.She is a member of IEEE, ACM, and the Upsilon Pi Epsilon honorarysociety.

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