research article modeling the separating pedestrian flow...

Research ArticleModeling the Separating Pedestrian Flow in T-ShapedPassage Based on Guide Sign

Hong-fei Jia1 Yong-xing Li1 Li-li Yang12 and Ya-nan Zhou1

1School of Transportation Jilin University Changchun Jilin 130025 China2School of Management Jilin University Changchun Jilin 130025 China

Correspondence should be addressed to Li-li Yang yangll105126com

Received 4 June 2016 Accepted 11 July 2016

Academic Editor Chris Goodrich

Copyright copy 2016 Hong-fei Jia et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Considering the actual situation of separating pedestrian flow in T-shaped passage the guide sign is set to guide the pedestriansand subconscious strength is introduced to show the effect of guide sign Pedestrian subconscious strength model is establishedand the subconscious strength calculation result is added to the pedestrian simulation model which is based on cellular automataOn the platform of MATLAB software separating pedestrian flow simulation with the effect of guide sign is realized Simulationsindicate that compared with the separating pedestrian flow without guide sign the efficiency of pedestrians passing with guidesign is higher Analyzing the effect of guide sign in different positions the suitable position of guide sign is obtained

1 Introduction

T-shaped passage is the common pedestrian facilities in thehubWith the different walking directions pedestrians wouldwave in T-shaped passage and the crowing phenomenonmayhappen in some time [1] In T-shaped passage separatingpedestrian flow and merging pedestrian flow are the familiarwaving behaviors Researching thewaving phenomenon inT-shaped passage and taking some effective measures to reducepedestrian conflicts have important practical significance

At present many studies have been made on pedestrianflow at different cases for example pedestrian flow simula-tion in bidirectional passage [2ndash4] pedestrians evacuation onstairs [5] pedestrian evacuation with panic [6] pedestriansevacuation in roomswith internal obstacles andmultiple exits[7] and pedestrian flow analysis and simulation in T-shapedpassage [8ndash13] In T-shaped passage Boltes et al [8] andZhang et al [9] analyze the pedestrian flow dynamics withempirical data respectively and the pedestrian flow funda-mental diagram is obtained Tajima and Nagatani simulatethe merging pedestrian flow by using the lattice gas modelof biased random walkers [10] Chen et al establish a force-driving cellular automata model to investigate the evacuationbehaviors of pedestrians at a T-shaped intersection and

the evacuation behaviors of pedestrians are simulated interms of different pedestrian density [11] Peng and Choustudy the conformation of pedestrian congestion in a ldquoTrdquointersection by using multifloor fields cellular automata [12]Fu et al simulate the interaction of separating pedestrianflow interlaced in a T-shaped passage with a modifiedmultifield cellular automaton updating synchronously Andin the simulation they find how the entrance density andthe pedestrians expecting to move to the left exit affect thephase transition diagram of pedestrian flow interlacing andseparating [1]

For improving the efficiency of pedestrians passingsetting the guide sign is the usually used method Xiong etal study the impact of traffic sign on pedestrian walkingbehavior and the one-way pedestrian flow has been simu-lated based on cellular automata [13] Song et al analyze theeffects of direction sign in pedestrian evacuation process andbuild the pedestrian evacuationmodel [14]With the researchand the actual observation we can know that the efficiencyof pedestrians passing is not high because of the conflicts inthe separating process of pedestrians Setting the guide signin front of the separating of the pedestrians can reduce thepedestrian conflicts in the separating process of pedestrians[13ndash15]

Hindawi Publishing CorporationDiscrete Dynamics in Nature and SocietyVolume 2016 Article ID 5625286 7 pageshttpdxdoiorg10115520165625286

2 Discrete Dynamics in Nature and Society

Exit of LP Exit of RP

Entrance of LP and RP

Main passage

Branch passage

Lb = 100

La = 100

Wa = 20

Wb = 10

Figure 1 Simulation scenario of T-shaped passage

In this paper we transfer the effect of guide sign into thesubconscious strength and add the subconscious strength tothe pedestrian simulation model which is based on cellularautomata and in this way the effect of guide sign inseparating pedestrian flow is simulated

2 Simulation Model of Separating PedestrianFlow Based on Guide Sign

21 Assumption Conditions There are four assumptions thathave beenmade in the separating pedestrian flow simulation

Assumption 1 All the pedestrians have the same expectationspeed

Assumption 2 It is without considering pedestrian individualdifference

Assumption 3 Thesight distance of the pedestrian is 6m andall the pedestrians are the same

Assumption 4 All the pedestrians are influenced by guidesign that is to say all pedestrians have the subconsciousbehavior to walk along the left-hand or right-hand side withthe effect of guide sign

22 Simulation Scenario Assume a T-shaped passage whichis composed of main passage and branch passage shown inFigure 1 The lengths of main passage and branch passageare all 100 cells The width of main passage is 20 cells andthe width of branch passage is 10 cells The size of each cellis 04m times 04m which is the typical space occupied by apedestrian [16 17] Only one pedestrian can be contained ina cell at most Pedestrians generated at the down origin ofmain passage andwhowalk away at the left side exit of branchpassage are set as LP Pedestrians generated at the origin of

main passage and who walk away at the right side exit ofbranch passage are set as RP Pedestrians move one cell eachtime-step

23 Floor Field The floor field has been proposed manyyears ago and it has been widely used in pedestrian flowsimulation [18] According to the relevant research [1 18] inthe calculation process of static floor field we can think thatthe target exit and nearest boundary are themain factorsThecalculation formula is as follows

119878119894119895= 119886 sdot 119878

1015840

119894119895+ 119887 sdot 119878

10158401015840

119894119895 (1)

where 119878119894119895is the value of static floor field at cell (119894 119895) 1198781015840

119894119895is the

value of static floor field at cell (119894 119895) formed by the exit 11987810158401015840119894119895is

the value of static floor field at cell (119894 119895) formed by the nearestboundary 119886 and 119887 are the coefficients

Pedestrians move from cell (119894 119895) to destination in hori-zontal vertical and diagonal directions The value of staticfloor field at cell (119894 119895) formed by the exit can be calculated asfollows

1198781015840

119894119895= (max119894119895

119889119894119895) minus 119889119894119895 (2)

where 119889119894119895is the distance from cell (119894 119895) to the exit

Considering the phenomenon that pedestrians tend tokeep a certain distance from the boundary [1] the value ofstatic floor field at cell (119894 119895) formed by the nearest boundarycan be calculated as follows

11987810158401015840

119894119895= 1198891015840

119894119895 (3)

where 1198891015840

119894119895is the distance from cell (119894 119895) to the nearest

boundaryOnly with the static floor field the problem of ldquodead endrdquo

may appear meaning that pedestrians moving in oppositedirections will get stuck into the same cell even though thereare other cells available nearby In the walking process thepedestrian would try to avoid the densely populated areafor comfortable walking Considering this the dynamic floorfield is introduced as follows

119863119894119895= 1 minus

119903119894119895

119873119894119895

(4)

where 119863119894119895is the value of dynamic floor field at cell (119894 119895) 119903

119894119895

is the number of cell (119894 119895) and its neighbors which have beenoccupied by pedestrians119873

119894119895is the number of cell (119894 119895) and its

neighbors

24 Addition of the Guide Sign Theguide sign is set to reducethe pedestrian conflicts and the position of guide sign isshown in Figure 2 The length of the guiding zone is 119871

119898and

the length of pedestrian sight distance is 119871119904 According to

related research [19] the length of pedestrian sight distance119871119904is equal to 15 cells (6m)The yellow zone shown in Figure 2

is the guide zone with the length 119871119898

+ 119871119904and width119882

119886

When pedestrians arrive at the guide zone under theeffect of guide sign LP (RP) generate the subconscious

Discrete Dynamics in Nature and Society 3



Branch passage

Main passage

Guide sign

Lb = 100

Lb = 100

Lm

Ls

Wa = 20

Wb = 10

Figure 2 Schematic diagram of the position of guide sign

behavior to walk along the left-hand (right-hand) side Thesubconscious strength 119872 is introduced to show the effectof guide sign The subconscious strength 119872 is calculated asfollows

119872 = 120572 sdot 1198721sdot 1198722 (5)

where 119872 is subconscious strength of LP (RP) 1198721is the

subconscious strength formed by the horizontal positionof LP (RP) 119872

2is the subconscious strength formed by

the vertical position of LP (RP) 120572 is the undeterminedcoefficient and 0 lt 120572 le 1

In the guide zone when the distance between the LP(RP) and left (right) boundary of main passage is larger thesubconscious of LP (RP) to walk along left-hand (right-hand)side is stronger namely the value of 119872

1is bigger on the

contrary the value of1198721is smaller

The subconscious strength 1198721for LP is calculated as

follows

1198721= 1 minus

1

1 + exp ((119877 minus 04) 008)

119877 =

119882119886minus 1198891

119882119886

(6)

The subconscious strength 1198721for RP is calculated as

follows

1198721= 1 minus

1

1 + exp ((119877 minus 04) 008)

119877 =

1198891

119882119886

(7)

where 1198891is the distance between pedestrian and right

boundary of main passage and 0 lt 1198891lt 119882119886119882119886is the width

of main passage 119877 is the ratio of distance between LP (RP)and left (right) boundary and the width of main passage and0 lt 119877 lt 1

The distance between LP (RP) and down boundary ofbranch passage is also the main influence factor for subcon-scious strength When the distance between LP (RP) anddown boundary of branch passage is larger the subconsciousof LP (RP) to walk along left-hand (right-hand) side issmaller namely the value of 119872

2is smaller on the contrary

the value of1198722is biggerThe subconscious strength119872

2of LP

(RP) is calculated as follows

1198722= exp(minus

1198892

119871119898

+ 119871119904

) (8)

where 1198892is the distance between pedestrian and the down

boundary of branch passageWhen we assume that 119871

119898= 2m and 119871

119904= 6m

we can draw the curve of the subconscious strength 119872 forLP shown in Figure 3 and the curve of the subconsciousstrength 119872 for RP shown in Figure 4 From Figures 3and 4 we can clearly know the changing tendency of thesubconscious strength and it is consistent with the actualsituation

25 Transition Probability Cellular automata Von Neumannmotion rule [20 21] is used in this paper In Figure 5including the position occupied by himself or herselfthere are five positions for pedestrian to go Transitionprobability of pedestrian to each position is shown inFigure 6

With the cellular automata Von Neumann motion rulethe transition probability of pedestrian without guide sign iscalculated as follows

119875119894119895=

1

119873

sdot exp (119896119878sdot 119878119894119895) sdot exp (119896

119863sdot 119863119894119895) sdot (1 minus 120583

119894119895) sdot 120585119894119895

119873 = sum

119894119895

exp (119896119878sdot 119878119894119895) sdot exp (119896

119863sdot 119863119894119895) sdot (1 minus 120583

119894119895) sdot 120585119894119895

(9)

The transition probability of pedestrian with guide sign iscalculated as follows

119875119894119895

=

1119873 sdot [exp (119896119878sdot 119878119894119895) sdot exp (119896

119863sdot 119863119894119895) sdot (1 minus 120583

119894119895) sdot 120585119894119895] + 119872

1 + 119872

lef t-hand direction for LP (right-hand direction for RP)

1119873 sdot exp (119896119878sdot 119878119894119895) sdot exp (119896

119863sdot 119863119894119895) sdot (1 minus 120583

119894119895) sdot 120585119894119895

1 + 119872

otherwise

(10)


6 6

8

8

4

4

2

2

0

0

M

d1 (m)

d 2(m

)0

02120572

04120572

06120572

08120572

120572

Figure 3 The curve of the subconscious strength119872 for LP

66

8

8

4

4

2

2

0

0

M

d1 (m)

d 2(m

)0

02120572

04120572

06120572

08120572

120572

Figure 4 The curve of the subconscious strength119872 for RP

where 119873 is the normalized parameter 119896119878is the coefficient

of static floor field which reflects the degree of pedestriansrsquofamiliarity to the inherent characteristics of the scenario119896119863is the coefficient of dynamic floor field which reflects

the following trend of pedestrian in procession 120583119894119895is the

parameter which judges whether the cell is occupied bypedestrian or not and 120583

119894119895= 1 if cell (119894 119895) is occupied and

120583119894119895

= 0 otherwise 120585119894119895is the parameter which judges whether

the cell is occupied by wall or barrier or not and 120585119894119895= 0 if cell

(119894 119895) is occupied and 120585119894119895= 1 otherwise

According to relevant research [1] and many simulationexperiments in order to be closer to reality we propose that119896119878

= 1 119896119863

= 04 119886 = 1 119887 = 04 and 120572 = 06 Withthe platform of MATLAB software the separating pedestrianflow simulation is realized

3 Simulation Results and Discussion

Separating pedestrian flow simulation is realized on theplatform of MATLAB software Separating pedestrian flow

Figure 5 Von Neumann motion rule

Pminus10

P0minus1P00

P10

P01

Figure 6 Transition probability

simulation process without and with guide sign is respec-tively shown in Figures 7 and 8 The blue solid circles are theLP and the red solid circles are the RP

In the simulation there are three stages without and withguide sign respectively

The First Stage At the down origin of main passage LP andRP are generated and walk towards the left side and right sideexit of branch passage respectively

The Second Stage Without the effect of guide sign LP and RParrive at the waving zone and interweave

With the effect of guide sign the pedestrians see the guidesign and generate the subconscious behavior LP tend to walkalong the left-hand side and RP tend to walk along the right-hand side When pedestrians walk away from the guide zone


(a) (b) (c)

Figure 7 The simulation of separating pedestrian flow without guide sign (a) LP and RP are generated at the down origin of main passage(b) LP and RP arrive at the waving zone and interweave (c) LP and RP arrive at the exit and walk away

(a) (b) (c)

Figure 8 The simulation of separating pedestrian flow with guide sign (a) LP and RP are generated at the down origin of main passage (b)LP and RP see the guide sign and generate the subconscious behavior (c) LP and RP arrive at the exit and walk away

and arrive at the branch passage the subconscious behaviordisappears

The Last Stage LP and RP arrive at the left side and right sideexit of branch passage respectively and walk away

In the simulation of separating pedestrian flow withoutguide sign the ldquoXrdquo shaped separating pedestrian flow appearsin the waving zone (see Figure 7(c)) and pedestrians crowedat the turning corner These are all consistent with the actualsituation In the simulation of separating pedestrian flowwithguide sign LP walk along the left-hand and RP walk alongthe right-hand side respectively The weaving behavior isweakened and pedestrians crowed at the turning corner

Assuming that the rate of pedestrian generation is con-stant and taking 50 times independent simulation experi-ments when the pedestrian flow is stable the number ofpedestrians passing the passage during 200 time-steps isshown in Figure 9

From Figure 9 we can know that the number of pedes-trians passing the passage with guide sign is bigger thanthat without guide sign The mean number of pedestrians

Separating pedestrian flow simulation without guide signSeparating pedestrian flow simulation with guide sign

2 4 6 8 10 12 14 16 18 20 22 24 26 28 300Experiment times

200

220

240

260

280

300

320

Num

ber o

f ped

estr

ians

pass

ing

the p

assa

ge

Figure 9 The number of pedestrians passing the passage withoutand with guide sign

passing the passage without and with guide sign is 248 and275 respectively It indicates that the guide sign is usefulfor reducing the conflicts and improving the efficiency ofpedestrians passing



04 08 12 16 2 24 28 32 36 4 44 48 52 56 60Distance between guide sign and the down

boundary of branch passage

220

240

260

280

300

320

Mea

n nu

mbe

r of p

edes

tria

nspa

ssin

g th

e pas

sage

Figure 10 The mean number of pedestrians passing the passagewith different position of guide sign

With the constant rate of pedestrian generation weanalyze the influence of the position of guide sign for the effi-ciency of pedestrians passing Taking 50 times independentsimulation experiments with different position of guide signthe change of mean number of pedestrians passing is shownin Figure 10

In the separating pedestrian flow simulation without andwith guide sign when the distance between guide sign andthe down boundary of branch passage is less than 2m thedifference of the number of pedestrians passing the passageis small In the separating pedestrian flow simulation withguide sign with the increasing of the distance between guidesign and the down boundary of branch passage the conflictsreduce and the number of pedestrians passing the passageincreases When the distance between guide sign and downboundary of branch passage is bigger than 4m the differencein the number of pedestrians passing the passage is no longerincreasing It indicates that when we set the guide sign thedistance between guide sign and down boundary of branchpassage is suitable for bigger than 4m

4 Conclusion

(1) With the effect of guide sign pedestrians generatethe subconscious behavior for walking along the left-hand or right-hand side Subconscious strength isintroduced to show the effect of guide sign Pedestriansubconscious strength is added to the pedestrian sim-ulation model which is based on cellular automataSeparating pedestrian flow simulation with the effectof guide sign is realized

(2) In the separating pedestrian flow simulation of T-shaped passage compared with the separating pedes-trian flow without guide sign the efficiency of pedes-trians passing the passage is improved with the effectof guide sign

(3) Through many independent simulation experimentswe analyze the changing of the efficiency of pedestri-ans passing the passage with the changing positionof guide sign and suitable distance between guide

sign and the down boundary of branch passage isobtained

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The research is supported by the National Natural ScienceFoundation of China (Grant nos 51278221 and 51378076)and the Science Technology Development Project of JilinProvince China (Grant no 20140204027SF)

References

[1] Z J Fu L Z Yang P Rao and T L Zhang ldquoInteractions ofpedestrians interlaced in T-shaped structure using a modifiedmulti-field cellular automatonrdquo International Journal of ModernPhysics C vol 24 no 4 Article ID 1350024 2013

[2] H Yue H Guan J Zhang and C Shao ldquoStudy on bi-directionpedestrian flow using cellular automata simulationrdquo Physica AStatisticalMechanics and its Applications vol 389 no 3 pp 527ndash539 2010

[3] J Ma W-G Song J Zhang S-M Lo and G-X Liao ldquok-nearest-neighbor interaction induced self-organized pedestriancounter flowrdquo Physica A Statistical Mechanics and Its Applica-tions vol 389 no 10 pp 2101ndash2117 2010

[4] W Guo X L Wang and X P Zheng ldquoLane formation inpedestrian counterflows driven by a potential field consideringfollowing and avoidance behavioursrdquo Physica A StatisticalMechanics and its Applications vol 432 pp 87ndash101 2015

[5] Y C Qu Z Y Gao Y Xiao and X G Li ldquoModeling thepedestrianrsquos movement and simulating evacuation dynamics onstairsrdquo Safety Science vol 70 pp 189ndash201 2014

[6] J H Wang L Zhang Q Y Shi P Yang and X M HuldquoModeling and simulating for congestion pedestrian evacuationwith panicrdquoPhysicaA StatisticalMechanics and Its Applicationsvol 428 pp 396ndash409 2015

[7] H-J Huang and R-Y Guo ldquoStatic floor field and exit choicefor pedestrian evacuation in rooms with internal obstacles andmultiple exitsrdquo Physical Review E vol 78 no 2 Article ID021131 2008

[8] M Boltes J Zhang A Seyfried and B Steffen ldquoPedestriandynamicsmdashexperiments analysis modelingrdquo in Proceedings ofthe IEEE International Conference on Computer Vision Work-shops (ICCV rsquo11) pp 158ndash165 Barcelona Spain November 2011

[9] J Zhang W Klingsch A Schadschneider and A SeyfriedldquoTransitions in pedestrian fundamental diagrams of straightcorridors and T-junctionsrdquo Journal of Statistical MechanicsTheory and Experiment vol 2011 no 6 Article ID P06004 2011

[10] Y Tajima and T Nagatani ldquoClogging transition of pedestrianflow in T-shaped channelrdquo Physica A Statistical Mechanics andIts Applications vol 303 no 1-2 pp 239ndash250 2002

[11] C-K Chen J Li andD Zhang ldquoStudy on evacuation behaviorsat a T-shaped intersection by a force-driving cellular automatamodelrdquo Physica A StatisticalMechanics and its Applications vol391 no 7 pp 2408ndash2420 2012


[12] Y-C Peng and C-I Chou ldquoSimulation of pedestrian flowthrough a lsquoTrsquo intersection a multi-floor field cellular automataapproachrdquo Computer Physics Communications vol 182 no 1pp 205ndash208 2011

[13] H Xiong P F Yao X D Guo C L Chu and W HWang ldquoImpact of traffic sign on pedestriansrsquo walking behaviorrdquoMathematical Problems in Engineering vol 2015 Article ID826152 10 pages 2015

[14] B X Song Z Z Wu and Z H Xie ldquoStudy on occupantevacuation model considering influence of direction signrdquoChina Safety Science Journal vol 21 no 12 pp 27ndash33 2011

[15] J Lin R Song J Dai and P Jiao ldquoPedestrian guiding signsoptimization for airport terminalrdquoDiscrete Dynamics in Natureand Society vol 2014 Article ID 125910 14 pages 2014

[16] J Li S Y Fu H B He H F Jia Y Z Li and Y Guo ldquoSimulatinglarge-scale pedestrian movement using CA and event drivenmodel methodology and case studyrdquo Physica A StatisticalMechanics and Its Applications vol 437 pp 304ndash321 2015

[17] H Yue B-Y Zhang C-F Shao and Y Xing ldquoExit selectionstrategy in pedestrian evacuation simulation with multi-exitsrdquoChinese Physics B vol 23 no 5 Article ID 050512 2014

[18] C Burstedde K Klauck A Schadschneider and J ZittartzldquoSimulation of pedestrian dynamics using a two-dimensionalcellular automatonrdquo Physica A Statistical Mechanics and itsApplications vol 295 no 3-4 pp 507ndash525 2001

[19] Z-J Wang F Chen and Z-H Shi ldquoAgent-based realizationof social force model and simulation of pedestrians in subwaypassagewayrdquo Journal of South China University of Technologyvol 41 no 4 pp 90ndash95 2013

[20] M J Liao and G Liu ldquoModeling passenger behavior in non-payment areas at rail transit stationsrdquo Transportation ResearchRecord Journal of the Transportation Research Board vol 2534pp 101ndash108 2015

[21] L-L Lu G Ren W Wang and Y Wang ldquoModeling walkingbehavior of pedestrian groups with floor field cellular automa-ton approachrdquo Chinese Physics B vol 23 no 8 Article ID088901 2014

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Stochastic AnalysisInternational Journal of




Main passage

Branch passage

Lb = 100

La = 100

Wa = 20

Wb = 10

Figure 1 Simulation scenario of T-shaped passage

In this paper we transfer the effect of guide sign into thesubconscious strength and add the subconscious strength tothe pedestrian simulation model which is based on cellularautomata and in this way the effect of guide sign inseparating pedestrian flow is simulated

2 Simulation Model of Separating PedestrianFlow Based on Guide Sign

21 Assumption Conditions There are four assumptions thathave beenmade in the separating pedestrian flow simulation

Assumption 1 All the pedestrians have the same expectationspeed

Assumption 2 It is without considering pedestrian individualdifference

Assumption 3 Thesight distance of the pedestrian is 6m andall the pedestrians are the same

Assumption 4 All the pedestrians are influenced by guidesign that is to say all pedestrians have the subconsciousbehavior to walk along the left-hand or right-hand side withthe effect of guide sign

22 Simulation Scenario Assume a T-shaped passage whichis composed of main passage and branch passage shown inFigure 1 The lengths of main passage and branch passageare all 100 cells The width of main passage is 20 cells andthe width of branch passage is 10 cells The size of each cellis 04m times 04m which is the typical space occupied by apedestrian [16 17] Only one pedestrian can be contained ina cell at most Pedestrians generated at the down origin ofmain passage andwhowalk away at the left side exit of branchpassage are set as LP Pedestrians generated at the origin of

main passage and who walk away at the right side exit ofbranch passage are set as RP Pedestrians move one cell eachtime-step

23 Floor Field The floor field has been proposed manyyears ago and it has been widely used in pedestrian flowsimulation [18] According to the relevant research [1 18] inthe calculation process of static floor field we can think thatthe target exit and nearest boundary are themain factorsThecalculation formula is as follows

119878119894119895= 119886 sdot 119878

1015840

119894119895+ 119887 sdot 119878

10158401015840

119894119895 (1)

where 119878119894119895is the value of static floor field at cell (119894 119895) 1198781015840

119894119895is the

value of static floor field at cell (119894 119895) formed by the exit 11987810158401015840119894119895is

the value of static floor field at cell (119894 119895) formed by the nearestboundary 119886 and 119887 are the coefficients

Pedestrians move from cell (119894 119895) to destination in hori-zontal vertical and diagonal directions The value of staticfloor field at cell (119894 119895) formed by the exit can be calculated asfollows

1198781015840

119894119895= (max119894119895

119889119894119895) minus 119889119894119895 (2)

where 119889119894119895is the distance from cell (119894 119895) to the exit

Considering the phenomenon that pedestrians tend tokeep a certain distance from the boundary [1] the value ofstatic floor field at cell (119894 119895) formed by the nearest boundarycan be calculated as follows

11987810158401015840

119894119895= 1198891015840

119894119895 (3)

where 1198891015840

119894119895is the distance from cell (119894 119895) to the nearest

boundaryOnly with the static floor field the problem of ldquodead endrdquo

may appear meaning that pedestrians moving in oppositedirections will get stuck into the same cell even though thereare other cells available nearby In the walking process thepedestrian would try to avoid the densely populated areafor comfortable walking Considering this the dynamic floorfield is introduced as follows

119863119894119895= 1 minus

119903119894119895

119873119894119895

(4)

where 119863119894119895is the value of dynamic floor field at cell (119894 119895) 119903

119894119895

is the number of cell (119894 119895) and its neighbors which have beenoccupied by pedestrians119873

119894119895is the number of cell (119894 119895) and its

neighbors

24 Addition of the Guide Sign Theguide sign is set to reducethe pedestrian conflicts and the position of guide sign isshown in Figure 2 The length of the guiding zone is 119871

119898and

the length of pedestrian sight distance is 119871119904 According to

related research [19] the length of pedestrian sight distance119871119904is equal to 15 cells (6m)The yellow zone shown in Figure 2

is the guide zone with the length 119871119898

+ 119871119904and width119882

119886

When pedestrians arrive at the guide zone under theeffect of guide sign LP (RP) generate the subconscious




Branch passage

Main passage

Guide sign

Lb = 100

Lb = 100

Lm

Ls

Wa = 20

Wb = 10



119872 = 120572 sdot 1198721sdot 1198722 (5)






1is bigger on the



follows

1198721= 1 minus

1

1 + exp ((119877 minus 04) 008)

119877 =

119882119886minus 1198891

119882119886

(6)


follows

1198721= 1 minus

1

1 + exp ((119877 minus 04) 008)

119877 =

1198891

119882119886

(7)







2of LP


1198722= exp(minus

1198892

119871119898

+ 119871119904

) (8)



119898= 2m and 119871

119904= 6m




119875119894119895=

1

119873


119863sdot 119863119894119895) sdot (1 minus 120583

119894119895) sdot 120585119894119895

119873 = sum

119894119895

exp (119896119878sdot 119878119894119895) sdot exp (119896

119863sdot 119863119894119895) sdot (1 minus 120583

119894119895) sdot 120585119894119895

(9)


119875119894119895

=


119863sdot 119863119894119895) sdot (1 minus 120583

119894119895) sdot 120585119894119895] + 119872

1 + 119872



119863sdot 119863119894119895) sdot (1 minus 120583

119894119895) sdot 120585119894119895

1 + 119872

otherwise

(10)


6 6

8

8

4

4

2

2

0

0

M

d1 (m)

d 2(m

)0

02120572

04120572

06120572

08120572

120572


66

8

8

4

4

2

2

0

0

M

d1 (m)

d 2(m

)0

02120572

04120572

06120572

08120572

120572







120583119894119895





= 1 119896119863





Pminus10

P0minus1P00

P10

P01








(a) (b) (c)


(a) (b) (c)









200

220

240

260

280

300

320

Num

ber o

f ped

estr

ians

pass

ing

the p

assa

ge







220

240

260

280

300

320

Mea

n nu

mbe

r of p

edes

tria

nspa

ssin

g th

e pas

sage




4 Conclusion





Competing Interests


Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra












Branch passage

Main passage

Guide sign

Lb = 100

Lb = 100

Lm

Ls

Wa = 20

Wb = 10



119872 = 120572 sdot 1198721sdot 1198722 (5)






1is bigger on the



follows

1198721= 1 minus

1

1 + exp ((119877 minus 04) 008)

119877 =

119882119886minus 1198891

119882119886

(6)


follows

1198721= 1 minus

1

1 + exp ((119877 minus 04) 008)

119877 =

1198891

119882119886

(7)







2of LP


1198722= exp(minus

1198892

119871119898

+ 119871119904

) (8)



119898= 2m and 119871

119904= 6m




119875119894119895=

1

119873


119863sdot 119863119894119895) sdot (1 minus 120583

119894119895) sdot 120585119894119895

119873 = sum

119894119895

exp (119896119878sdot 119878119894119895) sdot exp (119896

119863sdot 119863119894119895) sdot (1 minus 120583

119894119895) sdot 120585119894119895

(9)


119875119894119895

=


119863sdot 119863119894119895) sdot (1 minus 120583

119894119895) sdot 120585119894119895] + 119872

1 + 119872



119863sdot 119863119894119895) sdot (1 minus 120583

119894119895) sdot 120585119894119895

1 + 119872

otherwise

(10)


6 6

8

8

4

4

2

2

0

0

M

d1 (m)

d 2(m

)0

02120572

04120572

06120572

08120572

120572


66

8

8

4

4

2

2

0

0

M

d1 (m)

d 2(m

)0

02120572

04120572

06120572

08120572

120572







120583119894119895





= 1 119896119863





Pminus10

P0minus1P00

P10

P01








(a) (b) (c)


(a) (b) (c)









200

220

240

260

280

300

320

Num

ber o

f ped

estr

ians

pass

ing

the p

assa

ge







220

240

260

280

300

320

Mea

n nu

mbe

r of p

edes

tria

nspa

ssin

g th

e pas

sage




4 Conclusion





Competing Interests


Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










6 6

8

8

4

4

2

2

0

0

M

d1 (m)

d 2(m

)0

02120572

04120572

06120572

08120572

120572


66

8

8

4

4

2

2

0

0

M

d1 (m)

d 2(m

)0

02120572

04120572

06120572

08120572

120572







120583119894119895





= 1 119896119863





Pminus10

P0minus1P00

P10

P01








(a) (b) (c)


(a) (b) (c)









200

220

240

260

280

300

320

Num

ber o

f ped

estr

ians

pass

ing

the p

assa

ge







220

240

260

280

300

320

Mea

n nu

mbe

r of p

edes

tria

nspa

ssin

g th

e pas

sage




4 Conclusion





Competing Interests


Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










(a) (b) (c)


(a) (b) (c)









200

220

240

260

280

300

320

Num

ber o

f ped

estr

ians

pass

ing

the p

assa

ge







220

240

260

280

300

320

Mea

n nu

mbe

r of p

edes

tria

nspa

ssin

g th

e pas

sage




4 Conclusion





Competing Interests


Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra













220

240

260

280

300

320

Mea

n nu

mbe

r of p

edes

tria

nspa

ssin

g th

e pas

sage




4 Conclusion





Competing Interests


Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article modeling the separating pedestrian flow...

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