Vol. XXI, No. 1 Pedestrian Flow Simulation Validation and … · 2014. 10. 3. · Running title...

Running title • November 2012 • Vol. XXI, No. 1

Pedestrian Flow SimulationValidation and Verification Techniques

Mohamed H. Dridi

Institute of Theoretical Physics 1University of Stuttgart

[email protected]

27/09/2014

Abstract

For the verification and validation of microscopic simulation models of pedestrian flow, we have performedexperiments for different kind of facilities and sites where most conflicts and congestion happens e.g.corridors, narrow passages, and crosswalks. The validity of the model should compare the experimentalconditions and simulation results with video recording carried out in the same condition like in reallife e.g. pedestrian flux and density distributions. The strategy in this technique is to achieve a certainamount of accuracy required in the simulation model. This method is good at detecting the critical pointsin the pedestrians walking areas. For the calibration of suitable models we use the results obtained fromanalysing the video recordings in Hajj 2009 and these results can be used to check the design sections ofpedestrian facilities and exits. As practical examples, we present the simulation of pilgrim streams on theJamarat bridge (see fig. 5).

The objectives of this study are twofold: first, to show through verification and validation thatsimulation tools can be used to reproduce realistic scenarios, and second, gather data for accuratepredictions for designers and decision makers.

Keywords: accreditation, data analysis, pedestrian simulation, statistical, validation, verification ofsimulation tools, optical flow.

1 Introduction

In this paper we attempt to explore the meth-ods that can be used to make the resultsmade by a software or simulation tool more

authentic or believable. A set of statistical datataken from real life experience can be used tocheck the output values created by the simu-lation tools to validate the simulation model.This method is referred to as statistical tech-nique method and can be applied to simulationmodels, depending on which real-life data isavailable [1]. In general lack of empirical datamakes the verification of any simulation modela complicated task.

In case the real data are not available - thesimulation data obtained by the simulation

tools are still guided by the condition of a sta-tistical theory and probability distributions onthe design of experiments [2].

In case only output data is available - thevalues carried by the simulation model can becompared with well-known statistical data [2].

If data can be collected on both systeminput and output trace-driven simulation be-comes possible, model validation can be donethrough comparing the collected data with thesimulation results. In trace-driven simulation,the simulation input data are identified by thetrace data collected by a myriad of instrumentsand methods [2].

What, however, does ’validation’ mean?The term validation will be used to refer tovarious processes. The process of examining

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whether the acceptability and credibility of theconceptual model is referred to as validation,it is an accurate method to check the actualsystem being analysed. Validation can help todevelop the right model. Verification is a pro-cess to check simulation output for acceptabil-ity and controlling whether the results madeby the computer program are compatible withthe real data collected about the same system[2].

Concerning this topic many books could bewritten to describe the philosophical and prac-tical aspects involved in validation (see, themonograph by Knepell, and Arangno 1993)[2].For this reason, I identify validation as sys-tematic examination of the simulation modelwhether (if) it displays or illustrates the realworld in a reasonable time, either as a pro-cedure to check for correctness or meaning-fulness of the resulting data. Validation is aprocess to check the ability of the model toreproduce the real system. In the next sec-tions we will concentrate on validation thatuses mathematical statistics and comparisonwith video recordings of real situations.

Conceptual ModelReal World System

Simulation Program

Validation

VerificationValidation

Figure 1: Validation procedure for a given simulationmodel.

Since modelling and simulating has becomevery important in many domains in modernscience, much literature on verification and val-idation of a simulation models have appeared:see the web (http://manta.cs.vt.edu/biblio/),and the detailed surveys in Beck et al. (1997)[3],Kleijnen (1995b)[4], and Sargent (1996)[5]. Im-portant work concerning the choice of statis-

tical tests to validate a model was made byKleijnen (1999)[6].

For the first step we try to compare ourvideo taking with the simulation results. A lotof phenomena (like the lane formation, oscil-lation effect and edge effect) can be seen, tomake sure if our simulation reproduces a partof the reality. For this investigation we need tomake scenarios for the next video observationin the great mosque in Mecca.

2 Validation

2.1 Verification, validation and test-ing techniques

This paragraph describes different validationtechniques and tests, used in model examina-tion and validation. Most techniques describedhere are found in literature, although somemay be described slightly differently. They canbe used either subjectively or objectively. Inthe "objectively" case we attempt to implementmathematical methods using a kind of statisti-cal test e.g. confidence intervals and hypothesistesting. A combination of techniques is gener-ally used. These techniques are used for theexamination and validation of sub-models andthe universal model [7].

• Comparison to other models: In a ver-ification and validation of a simulationmodel process, different results (e.g. out-puts) of the simulation model will becompared with the results of other mod-els. For example, (1) comparison of asimple case of a simulation model withwell-known results of empirical models,and (2) the comparison of the simulationmodel with other validated models withthe same properties.

• Event validity: The appearance of eventsin a simulation model will be comparedwith those of the real system to determineif they are identical.

• Extreme condition tests: The model struc-ture and outputs should be credible for

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any extreme and improbable combina-tion of levels of factors in the system.

• Face validity: Experts or specialists in thesystem will be asked about the suitabilityof the model and its behaviour. For exam-ple, is the logic in the conceptual modeltrue and are the model input-output rela-tionships appropriate.

• Historical data validation: The systemcan take advantage of the historical col-lected data to calibrate itself, specificallythe data collected on a system for build-ing and examining the model, a part ofthe data can be used to establish themodel and the remaining data is usedto determine whether the model behavesas the system does. (This testing is ledby driving the simulation model samplesfrom the distributions or traces) [8, 9, 10].

• Multi stage validation: Another efficientmethod for validation a simulation toolwas proposed by Naylor and Finger(1967)[11]. It consists in associating threewell known methods of rationalism, em-piricism, and positive economics into amulti-stage process of validation. Thistechnique is based on (1) evaluation anddevelopment of the simulation modelwith respect to the theory, observations,and practical experience, (2) validatingthe model using possible existing empir-ical data, and (3) comparing the results(output) made by the simulation modelwith the real system.

• Operational graphics: Measured valuesof various performances e.g. using statis-tics for time series, are illustrated graphi-cally while the model runs over time; i.e.a visual indicator of performance showshow the program behaves during runtime to ensure the correct performance ofthe simulation tools.

• Sensitivity analysis: A sensitivity analy-sis is a powerful technique for validatingsystems. This validation method consists

in changing the input parameters of thesimulation or internal parameters of themodel to realize how the model’s outputwill be affected. If the system does theright things, the same relationships re-sulting from the model should be visiblein the real system. Using this techniqueboth qualitative (directions only of out-puts) and quantitative (both directionsand exact amount of outputs) propertiesof the system can be verified. Parame-ters cause important changes in the be-haviour of the model (sensitive parame-ters). These parameters have a high im-portance for the model and the simula-tion results (this may require iterationsin model development).

3 Calibration and validationof PedFlow model

In this section we present a variation of differ-ent techniques used to calibrate and validatethe PedFlow simulation model. PedFlow isa microscopic simulation model, which wasdeveloped by Löhner Simulation TechnologiesInternational, Inc. (LSTI) [12]. For verificationand validation, data was provided by the Insti-tute of Hajj research and the Ministry of Hajj,consisting of layout information, pilgrim num-bers, and Hajj schedules. We augmented thisdata with camera-based observations at severalstairways, gates and the piazza inside and out-side the Great Mosque in Mecca. This collecteddata can be used as input parameters of thesimulation and improves the acceptability andaccuracy of the data carried by the simulation.

PedFlow must model all processes that arerelated to pedestrians inside and outside theHaram at the normal and the busiest rushhours of the Hajj events such as: walking, per-forming activities, and route choice. In order tovalidate pedestrian flow modelling in PedFlowand to study pedestrian traffic flow movementduring the Hajj in detail, observations werecollected on the Haram in Mecca during theHajj 2009. These observations concerned the

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Tawaf, Sa’y, (individual) walking times, andother sites such as the Haram gates before andafter each prayer. These observations are veryhelpful in obtaining the data that will be usedto verify our simulation tool PedFlow. Thisdata concerns the numbers of pilgrims goingin and out of the Haram and individual walk-ing times and densities of pedestrians on theMataf. Finally, a comparison is made betweenthe observations and modelling results of Ped-Flow, in order to check the validity of PedFlowwith respect to pedestrian traffic flow opera-tions.

Since this investigation is concerned withstudying safety and fluidity of large scale pil-grim flows at pilgrimage places in Mecca, thevalidation of the simulation tool is mainly con-centrated on pedestrian traffic flow at the holyplaces. The main variables to be observed andcompared with the model predictions are:

• Walking speeds.

– On the stairs (upward and down-ward directions).

– On the piazza and the Mataf of theHaram.

• Densities over time and space.

– Video recording.

– Fundamental diagrams Predtechen-ski and Milinski [15].

• Layout information

– Data about the boundary conditionand environmental information.

3.1 Validation through comparisonwith other models

The credibility of the data produced by thepedestrian microscopic simulation model canbe validated through comparing with resultsobtained by other models having the same char-acteristics, although we mention that the com-parison with other simulation tools is necessaryfor the acceptance of the data but not sufficient.Different results (e.g. outputs) of the PedFlow

simulation model, being validated, are com-pared with results of other models. For ex-ample, emergent lane formation generated bymany simulation models, e.g. Blue [13], whoused a cellular automata model. Lane forma-tion in bidirectional flow and clogging effectsat bottlenecks in case of emergency situationwere realized by Helbing, Molnar, and Vicsek[14], who use a social force model. First asimple case of a simulation model is comparedwith known results of analytic models [15], andsecond the simulation model is compared withother simulation models that have been vali-dated, such as social-force models (see [16] andthe references therein) and cellular automata,e.g [17, 18].

3.1.1 Walking through a narrow passage;

Our first set of simulations consisted of pedes-trian flow through a hallway with a narrow pas-sage (see fig. 2) (a). The hallway was 80 m wideand the narrow passage was 16 m long and 4m at the narrowest point. Each pedestrian’sdesired speed was set at a walking speed foradult pedestrians in normal conditions vd = 1± 0.02 m/s; relaxation time: τ = 0.50 ± 0.1 s;(smaller times→ more aggressive) and pedes-trian radius: R = 0.2 ± 0.02 m; (smaller radius→ smaller repulsive forces). Repulsive poten-tials were assumed to decrease exponentially.The relaxation time is the time needed to reach90 percent of the desired velocity.

This experiment is realized with constantinflux, that means if a pedestrian has passedthrough the passage, he will be replaced by anew pedestrian at a random starting location,i.e. at the entrance of the hallway to keep thenumber of people in the hallway constant. Themean velocities (measured in the passage area)for different pedestrian influxes and the resultsare illustrated in figure 2 (d). These results areconsistent with those obtained by Predtetschen-ski and Milinski [15] and other fundamental di-agrams, who also found out reduced velocitiesdue to the tendency of pedestrians to convergeat the same time in the direction of the passagearea when the hallway is narrow. This caused

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(d)

(b)

(c)

(a)

Figure 2: This figures illustrates a pedestrian flow walking through a narrow passage: (a) bottleneck geometry; (b) thedensity index; the density map illustrates how the pedestrian density rises in the congested area. Red colorindicates high density which can reach 7 people/m2, while blue color indicates low pedestrians density; (c)the velocity index, the blue color indicates the lowest velocity; (d) decrease of the pedestrian velocity in thepassage area as a function of the local density, the measured data are represented by the crosses in the graph,they are consistent with the empirical data of Predtetschenski and Milinski [15] represented by the solid line.

blocking and the velocities to drop and the den-sity to increase with time, creating bottlenecksand clogging, (see fig. 3).

Pedestrian motion in passages is one of thefew cases where reliable empirical data exists.In order to assess the validity of the proposedpedestrian motion model, a typical passageflow was selected. The geometry of the prob-lem is shown in figure 2 (a). Pedestrians enterthe domain from the left and exit to the right.In this case, each pedestrian has the goal offirst reaching the entrance of the passage, thentraversing it to the other end, and finally to exiton the right. Typical snapshots during one ofthe simulations are shown in figure 3.

The resulting data of the simulation areshown as crosses in figure2 (d). The data flowsare shown in a graph besides the analyticaldata from Predtetschenski and Milinski. This

graph corresponds to specific parameters andillustrates a defined simulation state, althoughthey exhibit the relation between the input pa-rameters and the simulation results. In thelow density range the data are synchronizedwith a high accuracy. There are no deviationsof the simulation values and the analyticallydata. The walking speed drops in dependencyof density. The small deviation in the start-velocity, can be traced back to the input param-eters.

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Influx people/second

Figure 3: Step by step simulation of a pedestrian crowdwalking through a passage (PedFlow anima-tion results).

3.1.2 Example: simulation of the Tawafmovement

In this test we try to verify the simulation re-sponse by running a simplified version of thesimulation program with a known analyticalresult. If the output data resulting from thesimulation model do not exhibit a significantdeviation from the known empirical data, thisresult can then be used to validate the model.

Through the simulation of pedestrian flowon the well known geometry of the Mataf inthe Haram Mosque (see fig. 4) we intendedto check simulation output for credibility. Weperformed different simulation runs for severalinput scenarios and tested whether the outputis reasonable. It is easy to compare certain per-formed measurements with other computedresults. Using animation is another method toimprove the simulation model. The resultingdata of the simulated system is displayed ina series of snapshots of the animation of themodel users. Since the model developers andmodel users are familiar with the real system,they can ameliorate the performance of the pro-gram and detect programming and conceptualerrors.

Figure 4 (C) illustrates typical simula-tion results for Tawaf movement (circling theKaaba seven times in a counter-clockwise di-rection). The entire influx consists of three one-directional pedestrian flows coming from threeentrances. The velocity indicator shows that

the movement in the edges of the Mataf areais faster than in the area of the Kaaba. The pic-ture shows a snapshot of the simulation, whichhas a particularly high maximum density of6.5 persons/m2. Note that the pedestrian den-sity is very high at the places where the Tawafbegins and ends, and the clumping of pedes-trians going in opposite directions, when thepilgrims finish the Tawaf. The average densityfor many runs was 5 to 7 persons/m2. Figures4 (D; a) and (D; c) illustrate the velocity-densitydistribution on the Mataf area during the rushhour calculated according to Predtetschenskiand Milinski. This result agrees well with themeasured data shown in Figures 4 (D; b) and(D; d).

3.1.3 Example: Al-Jamarat Bridge

The simulation of high density pedestrian flowstreaming the Jamarat area during the rushhour of the Hajj period revealed a great techni-cal progress in the modelling, simulation andbetter understanding of how large crowds alter.In the past many fatal accidents happened inthis extremely dangerous area, where a largenumber of pilgrims stream through the siteand try to stone the pillars in a relatively shortperiod of time. Since the movement of pilgrimsis very slow an accumulation effect on bothsites of the pillars arises. This leads to phys-ical jamming, pilgrims trampling, and in theworst situation to the death of pedestrians un-derfoot. To accomplish the safety of millionsof pilgrims walking this overcrowded area ev-ery year and for better fluidity of pedestrianflow near the pillars, the proposal was madeto build a bridge with a 5-level structure toease the process of performing this ritual. Thebridge was designed to satisfy the internationalstandard criterion of pedestrians safety, espe-cially during overcrowding, and this conceptarose from the idea to conduct the pilgrimsflow in one direction without any counter flow.The Saudi government designated ProfessorDr. Saad A. AlGadhi (expert in transportationmanagement and design) and Dr. G. KeithStill (the crowd dynamics expert) to evaluate a

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Figure 4: Tawaf movement simulation. (A) This figure illustrates the Mataf area at rush hour divided in regular cells.The number of pedestrians in every cell as a function of time is determined through repeating the countingprocess many times. The average value is identified as local density ρ(~r, t); (B) velocity-density diagram:Empirical relation between density and velocity according to Milinski and Predtetschenski [15]. The partitionrefers to domains with qualitatively different decrease of the velocity; (C) pilgrims movement simulationwithin the Mataf area, the red color indicates the desired velocity 0.9 to 1 m/s while turquoise color the lowest;(D) velocity-density distribution as a function of the distance from the Kabaa wall, the curves (b, d) illustratethe simulation results while the curves (a, c) show the results obtained by a calculation according to thePredtetschenski and Milinski fundamental diagram.

model using crowd dynamic software tools toimprove the conceptual design [19]. This studyproduced a lot of data and information about:

• Sufficient arrival capacity

• Sufficient throwing area

• Sufficient space (density ≤ 4 Hajjis persquare meter)

• Sufficient passing area

• Sufficient egress capacity

in the Jamarat bridge area that can be usedto validate other pedestrian simulation tools.For example, published data about the Jamarat

bridge capacity, in-flux and out-flux, demon-strate that the total available ingress widthmust be greater than 28 meters to allow 125,000pilgrims per hour. This is a minimum require-ment and provision for security forces/civildefence, bi-directional/counter flow and hes-itation (pilgrims stopping to rest) where thelonger ingress ramps have additional widthrequirements [19].

Figure 5 illustrates how a combination ofmicroscopic and macroscopic techniques canassess the progression of queues approachingthe Jamarat (above - Simulex/Myriad, belowMyriad and site photograph)[20].

The other set of data about the Jamaratbridge was published by Helbing after the on-

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set of the crush event of 2006 in his paper: TheDynamics of Crowd Disasters: An EmpiricalStudy 2007 [21]. His video analysis revealed alot of data and information about the averagelocal speed, average local flows and the averagelocal densities in the Jamarat area before andafter the deathly crush accident. It was foundthat the pedestrian density near the pillars areacan reach a huge value of 9 persons/m2.

To assess the validity of the PedFlow simu-lation model and for improvements of resultingdata we apply analytical and comparative tests.These tests are used to compare the simulationoutput with the output from other simulationtools e.g. Simulex/Myriad [20]. Compared toother models PedFlow is more sophisticated topredict high density crowd dynamics. The sim-ulation result is shown in figure 5 (C) and (D).Of course the simulation input takes advan-tage of the published data to predict accurateresults.

3.2 Validation through visualizationand comparison with the realworld

The aim of most procedures and methods test-ing model validity is to determine the simi-larity between the results carried out by theconceptual model and the collected data. Thebetter the simulation output resembles the out-put from the real system the better the resultsin general. The animation and visualizationof the output simulation data are necessary toprove the credibility of the system, moreoverthis test is very important to examine how closethe data is to the real world.

3.2.1 Crowd visualization

A literature survey reveals several investiga-tions and animation methods which have beenproposed to provide more realism in the con-ceptual model simulating large scale pedes-trian motion. Treuille and Shao [22, 23] sug-gested a method that increases the degree ofaccuracy and realism of crowd simulations. Forexample a realistic human like character is an

essential role in the animation of high densitycrowd simulation. They illustrate the effectsand interactions between the individuals itselfwithin the crowd and the individuals and theirenvironment. This yields a better prospectabout the density distribution of pedestriansin a given site.

In the context of pedestrian animation weconsidered the technique of motion graphs [24]in order to provide advanced behavioural hu-man characters. We attempted to modify themotion graph approach to associate an existingdatabase of short MoCap (Motion Capture) ani-mations into a larger clip of continuous motion.However, in our approach the pedestrian move-ments are expressed as paths or trajectories ofthe character extracted from unlabelled motioncapture data. This technique modifies the char-acter’s position and orientation for the entireanimation clip. The trajectory and orientationof a character in a BVH (Biovision Hierarchicaldata) MoCap animation is interconnected, andone cannot be modified without influencingthe other, hence rendering the animation unre-alistic. Our technique allowed us to produce acontinuous and longer sequence of animationsusing an existing database of MoCap anima-tions and joining the animations together. Be-haviour is closely related to the correspondinganimation. It is this binding between behaviourand animation that we intended to utilize tovalidate our model.

The processes used to describe animatedmovement of one or more objects or personsare presented in this paragraph. From tabularvalues carried by the microscopic simulationdata results the path and velocity vectors ofthe agents are determined. The coordinatesand velocity of every pedestrian at any time isgiven by the simulation data. The animation ofthe characters is designed in two steps: first weattach a polygon to every coordinate, and nextwe attach every polygon to a human character,(see fig. 6(C)). The motion tracking and motionanimation is applied in many disciplines andscientific fields like entertainment, and medicalapplications, and for validation of computervision [25]. However, we distinguish two types

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Figure 5: During Hajj, pilgrims flock to the Jamarat Bridge in Mina to cast stones at three pillars representing thedevil. The cylindrical pillars (A)(top) were replaced by short walls (A)(bottom) after a previous fatal stampedein 2004. The idea was to improve crowd flow and reduce congestion. (A) shows the geometry and the locationof the stoning pillars; (B) shows a huge number of pilgrims streaming toward the pillars; (C) Al-JamaratBridge microscopic simulations/PedFlow and (D) Microscopic simulations/Myriad [20] (red color means highdensity; yellow color means middle density; green and blue color means low density).

of animations: the film and game-makers, whotake advantage from this technique to repro-duce multitudinous number of avatars. Thesecond type of animation is based on exactsimulation results and illustrates more realism,which can be used to help the decision makerto manage huge crowds, detect critical pointsin a closed area and to help the architects anddesigner to establish the number of fire exitsrequired for a building. This animation cancontribute to the validation of the simulationtools.

3.2.2 Validation through comparison withthe real world

For validation of a simulation model, it is nec-essary to compare the simulation output withreal-world data, such as video recordings rep-

resenting the same circumstances of the simula-tion. This method can ascertain a lot of effectsand behaviours that appear in crowds.

Through observation of pilgrim flow weattempt to validate and verify the crowd dy-namic model tool PedFlow. The obtained realdata presented in paper [45] is used to ver-ify a microscopic crowd dynamics model de-veloped to solve complicated problems con-cerning high density crowd behaviours. Thecrowd dynamics model attempts to simulatethe global movement of each individual influ-enced by the temporal circumstances and thesurrounding crowd. A good agreement be-tween the predictions and observations willvalidate the prediction model.

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Figure 6: Crowd visualisation, real vs. virtual world: (A) The real world represented in the Mataf top view; (B)simulation snapshot of the Tawaf movement; (C) crowd visualisation (characters implementation); (D)illustrates the reproduced virtual world.

4 Validation of PedFlow us-ing optical flow method

4.1 The optical flow method

In the last years optical flow is consideredas one of the most important techniques con-cerning image processing and computer vision.Computing of optical flow vectors using con-secutive image sequences is achieved in twodifferent ways: gradient methods and correla-tion methods. Many studies show that opti-cal flow techniques can be successfully usedto identify or recognize moving objects, e.g.moving cars or walking person, [26]. Com-pared with other models this approach is ableto operate with relatively low computationalexpenditure or visibility requirements on a di-versity of entities, permitting reconstructionof object trajectories with high accuracy fromvideo recordings. The detection of movement

can be determined by the introduction of dif-ferent sets of image sequences - by consideringthe different details between two images - sincethis is more accurate in computational calcu-lation and prediction [27]. The difference inimage brightness can then be analysed furtherto extract movement vectors that describe themotion of the drops (entity) captured in therespective images. This method is based onvideo segmentation and position identification,rather than motion recognition by analysingframe by frame sequences of ordered images.

Over the last decades, computer scientistshave worked in different ways to reconstructthe trajectory of moving objects. Many stud-ies and investigations appearing in differentscientific fields attempt to compute the opti-cal flow given by a sequence of images (seethe comprehensive surveys [28, 29]). The gra-dient and correlation methods are the mainlyused techniques for computing and calculationof optical flows. In addition to these, there

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are other statistical methods which are able toestimate the motion parameters [30] and theuse of phase information [31]. The approachproposed by Hayton establishes a relationshipbetween optical flow and image registrationtechniques [32].

Let us denote by I(x, y, t) the image inten-sity function associated with to the pixel greyvalue at location (x, y) of the image at time t.Gradient-based techniques are predicated onthe intensity conservation assumption

I(x, y, t) = I(x + δx, y + δy, t + δt), (1)

which can be expanded in a Taylor series ne-glecting higher order terms [33]. In general,gradient-based techniques are accurate onlywhen the intensity is preserved, and the Taylorseries approximation stays reasonable whenframe-to-frame displacements due to subjectsmotion are a part of a pixel. To reduce theerrors resulting from using this technique andto compute flow vectors over a larger imageregion an iteration method is deployed.

Correlation-based techniques will be use-ful if the image sequences do not meet theconditions required for gradient-based tech-niques, that means the brightness intensity isnot preserved, for example in cloud [34] andcombustion [35] images. Such techniques tryto establish correspondences between invariantcharacteristics between frames. Typical fea-tures might be blobs, corners and edges [36].

4.2 Motion analysis and objecttracking

As already mentioned optical flow is a methodto estimate object motions through brightnessintensity changes in sequences of consecutivelyordered images. A brightness intensity regionvariation related to the average pixel intensityof each image in a sequence of crowd imagesis used to estimate the pedestrian density dis-tribution at various sites.

The technique permitting pedestrian’smovement capture e.g. extracting informationabout pedestrian speed, using video footageobtained from CCTV observation of urban

crowd movement surveillance and image pro-cessing can be traced back to Velastin [37] and[38], who use algorithms operating on pixelintensities under a certain condition (such asa high frame rate) [39]. Other techniques andmethods to compute the optical flow regardingchanges in pixel intensities in a series of imagessequences are developed by [40, 41, 27, 42].

Optical flow is defined as an apparent mo-tion of image brightness. Let I(x, y, t) be theimage brightness that changes in time to pro-vide an image sequence. Two main assump-tions are made:

• Brightness I(x, y, t) smoothly depends oncoordinates x, y in a greater part of theimage.

• Brightness of every point of a moving orstatic object does not change in time.

Let some object in the image, or some point ofan object, move and denote the object displace-ment after time dt by (dx, dy). Using Taylorseries expansion for brightness I(x, y, t):

I(x + dx, y + dy, t + dt) = I(x, y, t)

+∂I∂x

dx +∂I∂y

dy +∂I∂t

dt + ......, (2)

where ..... are higher order terms, then, accord-ing to assumption 2:

I(x + dx, y + dy, t + dt) = I(x, y, t), (3)

and

∂I∂x

dx +∂I∂y

dy +∂I∂t

dt + ...... = 0, (4)

Dividing (3) by dt and defining

dxdt

= u,dydt

= v (5)

results in

− ∂I∂t

=∂I∂x

u +∂I∂y

v, (6)

usually called the optical flow constraint equa-tion, where (u, v) are components of the opticalflow field vector in x and y coordinates respec-tively.

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The movement recognition in this work isbased on the optical flow method extractingdata from picture sequences using the Lucasand Kanade algorithm [43]. It considers agroup of adjacent pixels and supposes that allof them (the group of adjacent pixels) have thesame velocity. It finds an approximate solutionof the above equation (6) using the least-squaremethod by solving a system of linear equations.The equations are usually weighted. Here thefollowing 2× 2 linear system is used:

∑x,y

W(x, y)Ix Iyu + ∑x,y

W(x, y)I2y v

= −∑x,y

W(x, y)Iy It, (7)

∑x,y

W(x, y)I2xu + ∑

x,yW(x, y)Iy Iyv

= −∑x,y

W(x, y)Ix It, (8)

where W(x, y) is the Gaussian window and thesubscripts denote derivatives. The Gaussianwindow may be a representation of a compo-sition of two separable kernels with binomialcoefficients. Iterating through the system canyield even better results. It means that theretrieved offset is used to determine a newwindow in the second image from which thewindow in the first image is subtracted, whileIt is calculated.

5 Pedestrian tracking usingOpenCV software

To determine pedestrian dynamics in themosque of Mecca, with millions of peopleperforming their rituals, we chose to use theOpenCV tools from Intel. This section de-scribes the structure, operation, and functionsof the open source computer vision library(OpenCV) for the Intel Corporation architec-ture [44]. The OpenCV library is mainly usedfor real time computer vision. Some exampleareas are human-computer interaction (HCI);object identification, segmentation, and recog-nition; face recognition; gesture recognition;

motion tracking, ego motion, and motion un-derstanding; structure from motion (SFM); andmobile robotics.

5.1 Results

Image sequences were obtained from videoscollected by hd-cameras at the Hajj-2009.

The flow fields in figure 7 (C) show exam-ples of the rotational movement of pilgrimsaround the Kaaba. We can clearly observe akind of oscillation in the pilgrim paths aroundthe Kaaba, this oscillation is caused by theshock-wave effect as a result of the repulsiveforces between pedestrians in high densitycrowd dynamics. This was generated by apply-ing the algorithm to every eighth pixel positionon a pair of 1920×1080 pixel images of a sur-face similar to figure 7 (A, B). The rotation fieldin 7(C) was obtained by rotating pedestriandisplacement in the Mataf area near the Kaabawall. Through OpenCV tracking tools, it ispossible to see that the movement around theKaaba is not a perfect circular movement. Thetracking of a simple individual in the pilgrimstream indicates some oscillation movementaround the main path of the individual. Thesephenomena are due to the huge physical re-pulsive and attractive forces influencing thepedestrians movement. The pedestrian mo-tion disturbance caused by high density crowdmovement was also clearly visible in our pedes-trian tracking on the Mataf area (see fig. 9).This finding agrees with the video observationon the piazza of the Haram. For verification ofthe PedFlow approach we compare our simula-tion results with those of the optical flow. Withhelp of this approach a lot of phenomena (likethe lane formation, oscillation effect and edgeeffect) can be seen, showing that our simula-tion reproduces a part of the reality. Thereforewe stress that optical flow methods are veryefficient for image analysis, structural analysis,image recognition, motion analysis and objecttracking.

The above mentioned techniques can behelpful for the validation and verification ofsimulation tools but is not sufficient, since there

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Figure 7: Picture Analysis through Optical Flow Tools. Pedestrian flow walking around the Kaaba in the Haram inMecca: (A) and (B) illustrate two consecutive images in the sequence; each one of them consists of 1920×1080images pixels, (C) shows a set of velocity vectors obtained by the Lucas and Kanade technique computing ateach point of a 64×64 grid centred on the 1920×1080 pixels, (D) shows the echo effect.

are many effects affecting the credibility of thismethod, for example: ambiguity, aliasing, andthe aperture effect. One of these effects the’aperture problem’, has been extensively de-tailed in optical flow literature [33]. However,the other two short-comings (ambiguity, alias-ing) are discussed to a lesser extend. Com-puter scientists and algorithms developer areworking to resolve this problem so that the pro-grams can take into account the three points.

5.2 Echo Effect After Effects

’Adobe After Effects R©’1 is a digital mo-tion graphic and composition software pub-lished by Adobe Systems R©, used in the post-production process of film and television pro-duction. It is used for creating motion graphicsand visual effects.

After Effects helps us to understand the flu-

idity of the pedestrian flow and the densitywaves observed in the video recording duringthe rush hour on the Haram. These densitywaves are generated by huge pedestrian forcesthat propagate with the help of body contactthrough a crowd.

In figure 9 we show the path of individualswithin the crowd. One clearly recognizes thatthe movement around the Kaaba is not a circlemovement. The tracking of a single individualin the pilgrims stream indicates some oscilla-tion movement around the main path of the in-dividual, as already mentioned it is caused bythe physical repulsive and attractive forces act-ing on the individual. Physical forces becomeimportant when an individual comes into phys-ical contact with another individual/obstacle.When a local density of 6 persons per squaremeter is exceeded, free movement is impeded

1http://www.adobe.com/de/products/aftereffects.html

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http://www.adobe.com/de/products/aftereffects.html


Figure 8: Density waves (echo-effect): gray cloud-like structures near the Kaaba.

and local flow decreases, causing the outflowto drop significantly below the inflow. Thiscauses a higher and higher compression in thecrowd, until the local densities become criticalin specific places on the Mataf platform. Thistechnique has helped to demonstrate the den-sity waves, and that the movement around theKaaba is not circular but disturbed movementscaused by this density shock waves. The distur-bance in the path of the pilgrims is generatedby the enormous contact forces that come intoplay in this region especially near the Kaaba(see fig.8). These waves appear in figure 8 asgray structures around the Kaabe.

5.3 Discussion

We have used a multi-stage validation method.One of the most important parameters was ver-ified, the pedestrian density distribution onthe Mataf area as a function of the position~rand velocity ~v. It served in a first step of acomparison of the simulation density resultswith the observed density behaviour on the

Mataf area at different times during the day,before and after the prayer. The maximumregistered density obtained by the statisticalmethod was 7 to 8 persons/m2. One can clearlyrecognise the similarity between the statisticaldata and the results given by the simulation,which can reach 7 persons/m2, especially inthe congested area (see fig. 10 (A) and (B)).

From observation of the Mataf it is well-known that the area indicating the beginningand the end of the Tawaf is the area mostcongested and accumulated by pilgrims, (seefig.10) (D). This phenomenon is obviously re-produced by the simulation (see fig. 10 (A)).This area appears in the picture on the rightlower corner of the Kaaaba, known as blackstone corner where the observed pilgrim den-sity reached over 9 persons/m2. All statisticalresults illustrating the density distribution atthe Mataf area at different time intervals aredemonstrated in the paper [45].

The second step of the multi-stage verifi-cation was to compare the velocity-density di-agram made by the simulation with all well-

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1 2

3

4

5

Figure 9: Pilgrims paths. With a new computer algorithm developed during this research, the trajectories or movementsof pedestrians across the infrastructure over time are determined. Microscopic pedestrian fields require largeamounts of trajectory data of individual pedestrians. Every red solid curve corresponds to one pedestriantrajectory. The oscillation in the pilgrims paths results from the huge pedestrian forces acting on everyindividual in the crowd.

known fundamental diagrams. According toPredtetschenski and Milinski the average walk-ing speed depends on the the walking facil-ity and the local density which can reach 9persons/m2 [15]. In figure 10 one clearly rec-ognizes density waves with maximum densitynear the Kaaba wall. There the average lo-cal density can reach a critical value of 7 to8 persons/m2. In the congested area the lo-cal density increases with significant droppingin the pedestrian velocity. The average localspeed ~v(~r, t) as a function of the local densityρ(~r, t) made by the simulation is comparedwith the Predtetschenski and Milinski densi-ties in figure 10 (C). Our own data is shown asred crosses in figure 10 (B). Moreover the anal-ysis of the data of the Mataf area showed thata reduction of the available navigation spaceis responsible for the speed reduction and the

density increase. The small deviation in pedes-trian walking speeds at lower density can beexplained by the fitness level of the pedestrian.Through this comparison two phenomena areclearly demonstrated, the density effect in theMataf area and the edge effects: the edges of acrowd move faster than the center of the crowd.This phenomenon was clearly demonstrated inthe statistical results shown in figure 10 (D).

Comparing the results of PedFlow with re-sults of other models in the simulation of aspecial cases like the Jamarat bridge (see fig. 5),showed that the critical points in the Jamaratfacility made by microscopic simulations withMyriad [20] are the same critical points exhib-ited by the PedFlow microscopic simulationsof the Jamarat bridge.

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(C)

(B)(A)

(D)

Figure 10: (A) A snapshot of tawaf simulation results made by PedFlow with velocity index, the blue color indicates thepedestrian stand still while the red color indicates their maximal walking speed; (B) velocity-density diagram:PedFlow simulation results; (C) Predtetschenski and Milinski fundamental diagram; (D) velocity-densitydistribution as a function of the distance from the Kabaa wall, the curves (b, d) illustrate the simulationresults while the curves (a, c) show the statistical results and indicate the density behaviour on the Matafarea at different times during the day, obtained by a calculation according to the Predtetschenski andMilinski fundamental diagram [45].

6 Conclusions and recom-mendations

For people working in software developmentand simulation program evolution the verifi-cation and validation of the model is a vitalprocedure to make sure that the tools apply toreality. The validation of the simulation pro-gram ensures the users and decision makersthat the simulation results are credible andapplicable in the development of the project.Moreover Turing and face validity tests con-tribute to progressive optimization of the pro-gram. The Turing test is a successful methodcomparing the real world with the simulationoutput. The output data obtained by the simu-lation can be presented to people attending the

same project and working with the same toolsknowledgeable about the system in the sameexact format as the system data. The discus-sion between the experts about the deviationof the simulation and the system outputs canbe helpful to validate the program, their expla-nation of how they did that should improvethe model.

The opinion of the project member andmodel user for development, progress and ver-ification of the simulation tools is very impor-tant. This method will be referred to as facevalidation. Face validation is necessary to iden-tify the behaviour of the simulation systemunder the same simulation condition. A pre-liminary examination of the model one candeduce that this method is useful, necessary,but not sufficient.

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In this paper we have discussed verificationand validation of microscopic simulation mod-els. Different approaches and methods for de-ciding verification and validation of the modeldevelopment process have been presented, ashave been various validation techniques.

As a practical example, the Haram Mosquein Mecca and the Jamarat Bridge in Saudi Ara-bia were used for high density crowd simula-tion: the huge number of pilgrims crammingthe bridge during the pilgrimage to Meccagave rise to serious pedestrian disasters in thenineties. Moreover, the analytical and numeri-cal study of the qualitative behaviour of humanindividuals in a crowd with high densities canimprove traditional socio-biological investiga-tion methods.

For obtaining empirical data different meth-ods were used, automatic and manual meth-ods. We have analysed video recordingsof the crowd movement in the Tawaf inMosque/Mecca during the Hajj on the 27thof November, 2009. We have evaluated uniquevideo recordings of a 105× 154 m large Matafarea taken from the roof of the Mosque, whereupto 3 million Muslims perform the Tawaf andSa’y rituals within 24 hours.

For the validation and calibration of thesimulation tools, different methods were used.

• Comparison of the simulation result withthe video recording.

• Comparison with other models: Differentresults (e.g., outputs) of the simulationmodel being validated, and comparedwith the results of other models. For ex-ample, (1) simple cases of a simulationmodel were compared with well-knownresults of analytic models, and (2) thesimulation model were compared withother simulation models that have beenvalidated.

• Parameter Variability - Sensitivity Anal-ysis: Applying this technique one candetermine the behaviour of the model orsimulation output, using different inputvalues.

• A comparison with Optical Flow resultswas also carried out.

At medium to high pedestrian densities, thetechniques used in PedFlow can produce real-istic crowd motion, with pedestrians movingat different speeds and under different circum-stances, following believable trails and takingsensible avoidance action.

7 Acknowledgements

I would like to express my sincerest thanksand gratitude to Prof. Dr. G. Wunner for acritical reading of the manuscript, for his im-portant comments and suggestions to improvethe manuscript. Many thanks to Dr. H. Cartar-ius for his support during writing this work.

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