ORIGINAL PAPER

Fundamental diagrams of pedestrian flowcharacteristics: A review

Lakshmi Devi Vanumu1& K. Ramachandra Rao1 & Geetam Tiwari1

Received: 13 August 2016 /Accepted: 5 September 2017 /Published online: 26 September 2017# The Author(s) 2017. This article is an open access publication

AbstractIntroduction The dimensionality of pedestrian infrastructurefacilities have a great influence on pedestrian movements anda considerable impact on natural environment of the facility.Understanding the pedestrian movements are crucial to esti-mate the capacity of the system accurately, especially in thetransportation terminals such as railway stations, bus termi-nals, airports and so forth, where large crowd gathers andtransfers. To have a safe and comfortable movement in normalsituation and also a quick evacuation in emergency situation,pedestrian movement patterns should be analysed andmodelled properly.Purpose Once the behaviour of pedestrians is established interms of speed and density with respect to the environment,even for the colossal systems, the pedestrian flow characteris-tics can be modelled by applying extremely efficient simula-tions. The main modelling element in the context of flowmodels is the fundamental relationship among speed, flowand density. The objective of this study is to review the fun-damental diagrams of pedestrian flow characteristics devel-oped for various flow types and geometric elements. Thispaper also discusses the design values of flow parametersand walking speeds of pedestrians at various facilities.

Methods In order to achieve the goal of this paper, we pre-sented a systematic review of fundamental diagrams of pedes-trian flow characteristics developed by using various ap-proaches such as field, experimental and simulation.Conclusions After a thorough review of literature, this paperidentifies certain research gaps which provides an opportunityto enhance the understanding of fundamental diagrams of pe-destrian flow characteristics.

Keywords Fundamental diagrams . Pedestrian flowcharacteristics .Walking speed . Pedestrian infrastructure

1 Introduction

Understanding the pedestrian movement is complex whencompared to vehicular movement as pedestrians have freedomto move in two dimensions. Also the graphical representationof pedestrian trajectories in both longitudinal and lateral direc-tion is complicated. May [1] emphasized that BThe two majordifferences between pedestrian and vehicular flow are the nu-merical values of flow characteristics and the use of lanes orwidth to define stream files. The lanes for the vehicular facil-ities may be well-defined whereas for pedestrian facilities, thefacility width may vary over time and flow condition^. Whilecomparing the vehicular flow and pedestrian flow, Treiber andKesting [2] illustrate that every pedestrian has a desired direc-tion in addition to the desired walking speed. Hence the de-sired velocity of a pedestrian is a vectorial quantity. Moreover,presence of cultural differences make the design values ofpedestrian facilities in different regions to vary greatly. So itmay not be appropriate to adopt one region design values forthe design of another region’s pedestrian facilities. Many re-searchers [3–18] have conducted considerable amount of stud-ies on pedestrian dynamics and developed numerous models

* K. Ramachandra Raorrkalaga@civil.iitd.ac.in

Lakshmi Devi Vanumulakshmidevivanumu@gmail.com

Geetam Tiwarigeetamt@gmail.com

1 Department of Civil Engineering, Indian Institute of Technology,Delhi, Hauz Khas, New Delhi 110016, India

Eur. Transp. Res. Rev. (2017) 9: 49DOI 10.1007/s12544-017-0264-6

over the past decades. For developing these models, re-searchers adopted different approaches such as experimental,field and simulation.

Empirical data from the field observations are essential forcalibration and validation of any model. Acquiring permis-sions for collecting such data in public transport stations andsome restricted areas is difficult because of security and pri-vacy issues. Apart from these, the camera arrangements, track-ing of pedestrians, lighting conditions, uncontrollable condi-tions etc. would make the data collection process complicated.In order to overcome the above problems researchers conductexperiments by simulating the real situations under controlledconditions either in open or closed areas with pedestrians assubjects [4]. Moreover, obtaining the practical data in theemergency situations or experimenting the panic situations istroublesome and the data obtained from these two methodsmay not be accurate and reliable. Hence simulation modellingwould be a better approach to test Bwhat if scenarios^ in thecomplex systems, especially evacuation of people in emergen-cy situations. A field and an experimental study has beencarried out on the same stair case [9]. In this study, eventhough exact quantification of error is not given between thevalues of experimental and field observations, it was foundthat, for a particular density the corresponding flow values areslightly higher in experiments compared to field studies. Qu[19] compared the field observed walking speeds and simu-lated walking speeds on stairs and found the range of relativeerror 0.41 to 20.53 with an average relative error of 7.26%.

The pedestrian flow characteristics in congested anduncongested conditions can be well explained byFundamental Diagrams (FDs) which shows the relationshipbetween speed-flow-density. These diagrams are the basisfor design of any infrastructural facility and helps in predictingthe capacity of the system. In spite of extensive research in thisarea, the results from various studies shows that there existwide variations in FDs. Even though the shape of the FDsremains same, the values of flow parameters vary immensely.These large variations encourage the researchers to studyabout FDs of pedestrian flow characteristics and different fac-tors effecting them. Daamen et al. [20] presented FDs of pe-destrian flow characteristics developed by different re-searchers based on the empirical studies conducted at differenttypes of infrastructure and flow compositions (Fig. 1).However, it may not be appropriate to present the FDs devel-oped for different conditions in a single diagram as they varyfor various flow situations and also for different infrastructuralelements. Personal and environmental characteristics influ-ence the pedestrian motion. Moreover, capacity of the systemdepends on self-organization phenomena that includes zippereffect, oscillations at narrow bottlenecks, lane formations inuni-directional and bi-directional flows and so forth. This pa-per reviews the FDs of pedestrian flow characteristics for dif-ferent geometric elements such as corridors, bottlenecks, stairs

and escalators with different flow situations being unidirec-tional, bidirectional and crossing in various pedestrian facili-ties. In addition the design values of flow parameters, walkingspeeds of pedestrians at various pedestrian facilities were alsopresented.

Rest of the paper is presented in five sections. Section 2presents an overall critique on FDs. Section 3 presents FDs ofdifferent flow types. Section 4 reviews the FDs of variouspedestrian infrastructural elements. Section 5 discusses thewalking speed of pedestrians at various facilities. Finally inSection 6 the paper concludes by giving future directions toresearchers.

2 Fundamental diagrams of pedestrian flowcharacteristics

Macroscopic variables such as speed, flow and density havebeen used in assessing the performance of pedestrian facilitiesand these variables constitute the Fundamental Diagrams(FDs) of pedestrian flow. The fundamental diagram is thebasic relation to characterise the pedestrian movements usingthe transport infrastructure. Firstly, the fundamental relation-ship helps in deriving the capacity and level of service valuesof the facility and thus allows for instant rating of emergencyexits. Secondly, pedestrian flow models (macroscopic or mi-croscopic) can be evaluated using empirical fundamental dia-grams and it justifies the model capability in simulating pe-destrian streams. Thirdly, pedestrian fundamental diagramsplays an important role in developing dynamic simulationmodels by providing equilibrium relationships between mac-roscopic variables. It can be concluded that, without properunderstanding of the fundamental diagrams, it is difficult todesign an efficient transport system.

An understanding of the fundamental relationship betweenflow - speed - density is important in the planning, design andoperation of pedestrian facilities. The shape of the fundamen-tal diagram is characterised by type of facility, gender, age,space requirements for the pedestrians and so on. In the earlystage of pedestrian research, linear relationship between speed- density was assumed but with different linear relationshipsfor different type of pedestrians. The linear speed-density re-lationship was used to develop a speed-space relationship andfinally converted into speed-flow and flow-density relation-ship [1].

Considerable amount of research has been done for devel-opment and application of pedestrian fundamental diagrams.Several factors have been considered such as width of thefacility, gradients and pedestrian characteristics. Critical in-vestigations have taken place in areas such as bottlenecks,escalators and staircases. Influence of different flow typessuch as uni-directional, bi-directional, merging and crossingsituations on fundamental diagrams is also studied.

49 Page 2 of 13 Eur. Transp. Res. Rev. (2017) 9: 49

Fundamental diagrams are critical in identifying congestedand uncongested condition while monitoring pedestrianmovement in small to large gatherings. Development of FDsare also relevant in emergency and evacuation planning.

Even though FDs are helpful in solving many problems,some issues are still persisting. They are as following.

1. Discrepancies in developing planning handbooks basedon fundamental diagrams for different elements like stair-cases, escalators, emergency routes etc.

2. Differences between field, experimental and simulationdata across different cultures and environments needs tobe established and suitable adjustment factors betweenthese studies should be proposed.

3. The flow density relationship for different geometric ele-ments is important and further analysis like spatial andtemporal development of the basic quantities (velocity,density and flow) on different elements like corridors,stairs and bottlenecks should be considered. Microscopictrajectory data offers the great opportunity to take a deeperlook at influences of measurement method and selectedmeasurement area. For example, till now these influencesare not scrutinized and even the shape of the function hasnot been completely understood. A direct comparison ofempirical data is possible only when the experiments un-der controlled conditions as well as field studies are con-ducted on the same facility. In general, field studies do notprovide the favourable circumstances for the analysis on amicroscopic scale, but they are helpful in gaining an over-view about the basic quantities. Selection of location ofthe measurement area on a particular element (Example:

entry or exit point of the stairs) could influence the devel-oped fundamental diagram [9].

4. Since the data compared is obtained under various exper-imental situations and different measurement methods, itis difficult to conclude whether and how the type of flow(uni- or bidirectional) influences the fundamental dia-gram. Till date there is no consensus on the origin ofdiscrepancies between various types of pedestrian flows[21].

5. The extent to which various factors such as pedestrian andenvironmental characteristics influence the fundamentaldiagrams is unknown [3]. Further studies are needed inthis direction.

3 Fundamental diagrams of various flow types

Different types of flow situations exist in pedestrian facilitiessuch as uni-directional, bi directional and crossing.Unidirectional and bidirectional flow conditions can be com-monly observed in corridors, stairs and bottlenecks of pedes-trian facilities such as transport terminals, shopping malls etc.Crossing can be observed especially at junctions of transferstations. The research studies shows that the FDs and thecorresponding flow parameter values for all these flow situa-tions are different. The studies conducted for different flowsituations are as follows:

Daamen [3] conducted various experiments consisting ofunidirectional, bidirectional and crossing flow situations atDelft University of Technology, Netherlands. The estimated

Fig. 1 Fundamental diagrams ofpedestrian flow characteristicsfrom Literature (Daamen et al.[20])

Eur. Transp. Res. Rev. (2017) 9: 49 Page 3 of 13 49

free flow speed from unidirectional flow experiment is foundto be higher than the observations in literature. Also the aver-age walking speeds in bidirectional flow situations are foundlower than for unidirectional flows. From the single file ex-periment conducted by Lv et al. [4] found that the speed anddistance headway are correlated nonlinearly. Zhang andSeyfried [22] observed a clear difference in FDs of uni andbidirectional pedestrian streams with the maximum flow valueof 2 (ms)−1 and 1.5 (ms)−1 respectively. As there is a signifi-cant difference between uni and bidirectional flows, the designof pedestrian facilities should consider these characteristics.Figure 2 shows the FDs of unidirectional and bidirectionalflow developed from various studies.

Cheung and Lam [23] examined the influence of bi-directional pedestrian flows on stairs and passageways andobserved that with the increase in unbalanced pedestrian flowratio, there is an increase in reduction of effective capacity ofthe facilities for a specific direction. In minor flow direction,the reduction in walking speeds was observed at capacity. Astudy conducted by Lam et al. [5] revealed that the free-flowspeed was not influenced by the presence of counter flows.Further, it is noticed that effective capacity and at-capacitywalking speeds are decreasing with the increase in the in-equalities in the pedestrian flow ratios. Moreover presenceof bidirectional flows influences minor flow direction signif-icantly compared to major flow direction. Also the influenceof bidirectional flow is more on shopping areas compared tocommercial areas. Kretz et al. [24] found that as the group sizeincreases, the passing times for each opposing flow fractionincreases linearly. Zhang et al. [21] considered stable separat-ed lanes (SSL - Stable Separated Lanes - pedestrians are ad-dressed to choose the exits freely) and dynamical multi lanes(DML – Dynamic Multiple Lanes - pedestrians are addressedto choose specific exits) to categorize bidirectional flows.Also studied the influence of flow ratio on opposing pedestri-an flows by introducing Balanced Flow Ratio (BFR) andUnbalanced Flow Ratio (UFR). The outcomes of the study

reveals that, for different degrees of ordering there is no sig-nificant difference in the FDs for densities less than 2.0 m−2.Zhang and Seyfried [22] shows that head-on conflicts in thebidirectional streams has not affected the FD. Moreover theordering of the stream is improved by self-organized laneswhich provide relief to the conflicts.

There are limited studies available in investigating thecrossing flows. However Zhang and Seyfried [25] found thatFDs are not influenced by intersecting angles of 90° and 180°.

4 Fundamental diagrams for various infrastructuralelements

The fundamental relationship between pedestrian flow char-acteristics for different geometric elements was not yetcompletely understood. Capturing the realistic behaviour ofpedestrians in various pedestrian facilities with different geo-metric elements such as corridors, bottlenecks, stairs, escala-tors etc. is essential in order to estimate the flow parametersaccurately. The important parameters such as width of thebottleneck, slope of the stairs plays a vital role in decidingthe capacity of the respective element. Further, it is importantto identify how the variations in these parameters influence thecapacity. This section discusses the FDs of pedestrian charac-teristics for various elements such as corridors, bottlenecks,stairs and escalators. The FDs developed for pedestrian flowcharacteristics given by different planning guidelines and re-searchers are shown in Fig. 3. The line diagrams of theseinfrastructural elements are shown in Fig. 4.

4.1 Corridors

Corridors are simple and common elements in almost all typesof pedestrian facilities designed to provide unidirectional andbidirectional flows. A study conducted by Hankin and Wright[27] at London subway reveals that the maximum flow and

Fig. 2 Fundamental diagrams ofuni and bidirectional pedestrianflow from various studies (a)Density–speed and (b) density–specific flow (Zhang and Seyfried[22])

49 Page 4 of 13 Eur. Transp. Res. Rev. (2017) 9: 49

width of corridor are proportional to each other for a corridorwidth of at least above a minimum of 4 ft. Chattaraj et al. [6]found that FD is not influenced by corridor width. Zhang et al.[28] found that for densities less than 3 m−2, the specific flowapproach works well for different widths of corridors. Whilecomparing the FDs of same type of corridor with variouswidths it was found that the results were matching withHankin’s findings. Moreover, the outcomes of this study con-cur with the assumption that specific flow does not depend onthe facility width. Zhang and Seyfried [22] found that straightcorridors have highest flow when compared to bottleneckswhich can be considered as an important point in the design

of emergency exits. The experimental results of Zhang et al.[29] shows that FDs developed for various widths of the cor-ridor agrees well and supports the assumption that flow –density relations for the same type of facility can be combinedinto single diagram for specific flow. Moreover FDs devel-oped by various measurement methods show equal tendencyhowever with different accuracy.

4.2 Bottlenecks

Bottlenecks are the crucial elements of pedestrian infrastruc-ture where the capacity reduces drastically. Their capacities

Fig. 3 Fundamental diagrams forpedestrian movement in planarfacilities [Lines representspecifications given by planninghandbooks (SFPE: Handbook,PM: Predtechenskii andMilinskii, WM: Weidmann).Points represent observations ofexperiments] (Seyfried et al. [26])

(a) (b) (c)

(d) (e)

Fig. 4 Line diagrams of Geometric elements (a) Corridor (b) Bottleneck (c) T – Junction (d) Stair case (e) Escalator

Eur. Transp. Res. Rev. (2017) 9: 49 Page 5 of 13 49

should be examined with at most care especially to deal theevacuation of pedestrians in emergency situations. Severalexperimental and simulation studies have been performed toanalyse the pedestrian flow characteristics in bottleneck withunidirectional and bidirectional flows. Hoogendoorn andDaamen [7] found that, with the increase in bottleneck widththe capacity increases in a stepwise manner because of zippereffect. Whereas, Seyfried et al. [8], Tian et al. [30] shows thatflow is linearly increasing with bottleneck width. To analyse

the pedestrian microscopic movement characteristics, Tianet al. [31] conducted a series of experiments in a bottleneckthrough which the lane formation phenomena was observed.One, two and three lanes were observed when the bottleneckwidth is kept as 0.5–0.7 m, 0.8–1.1 m, 1.2–1.4 m respectively.Zhang and Seyfried [22] found that long bottlenecks havelower flow values compared to short bottlenecks which showsthat emergency exits should be planned and designed keepingin view of shape and geometry of the facility.

(a) Downwards

(b) Upwards

Fig. 5 Fundamental diagrams ofstairs given by different planningguidelines [PM: Predtechenskiiand Milinskii (1978) [32], NM:Nelson and Mowrer (2002) [33],FN: Fruin (1971) [34], WM:Weidmann (1993) [35]](Burghardt et al. [9])

(a) downwards (b) upwards

Fig. 6 Measurements of thefundamental diagram for stairsobtained from various field andexperimental studies. Full rangeof observation points has beenshown in the small diagramenclosed (Burghardt et al. [9])

49 Page 6 of 13 Eur. Transp. Res. Rev. (2017) 9: 49

Tab

le1

Reviewof

Fundam

entald

iagram

sof

pedestrian

flow

characteristics

Author

Purpose

Element

Type

ofFlow

Country

Designvalues

Rem

arks

FieldStudies

Lam

etal.[5]

Speed-flowRelationship

Indoor

walkw

ays

BHongKong,SAR,

China

Descriptio

nIndoor

walkw

aysin

Proposedageneralized

walking

time

functionwith

bi-directionalP

edestrian

flow

ratio

(GBPR)

Flow

Ratio

shopping

area

commercial

area

Effectivecapacity(ped/m

/min)

1.0

68.0

75.0

0.1

56.1

66.7

At-capacity

walking

speed(m

/min)

43.00

51.01

Lee

[11]

FD

Stairw

ays,Escalators

UNetherlands

Descriptio

nStairs

Escalators

Pedestrians

personalcharacteristics,

infrastructure

type

anddirections

ofmovem

entinfluencesfree

speeds

da

da

Vf(m

/s)

0.77

0.68

0.88

0.82

q max(m

s)−1

0.86

0.18

0.93

0.67

Seeret

al.[38]

FD

Meanders,stairs

UAustria

Descriptio

nMeanders

Stairs

Maxim

umandeffectivecapacitiesfor

meandersandstairswereestim

ated

from

thedevelopedFD

’s.

Maxim

umflow

rate

(Ped/m

in)

48.25

–

Medianflow

rate

(Ped/m

in)

47.6

111.11

Medianheadway

(sec)

1.26

–Alhajyaseen

etal.[39]

Speed-flowrelationship

Crosswalk

BJapan

Different

capacity

values

fordifferent

directionalsplitratioswith

different

agegroupof

pedestrians

Reductionin

capacity

ismaxim

umat

approxim

atelyequald

irectio

nalsplit.

Capacity

may

reduce

upto

30%

becauseof

presence

ofelderlypedestrians.

Burghardt

etal.[9]

Effecto

fstairgradient

onFD

Stairs

UGermany

q smax=1.1(m

s)−1

Kmax=3.4m

−2Flowdecreaseswith

increase

instair

gradient.F

lowvalues

foragiven

density

inexperimentsareslightly

higher

than

fieldobservations

Shahet

al.[40]

FD

Stairs

–India

Vavg(duringafternoon)

-29.70m/m

inVavg(duringevening)

-23.73m/m

inDifferent

design

values

ondifferentstaircases

Pedestrians

walkfaster

during

the

afternoonor

daytim

ecomparedto

evening.Presence

ofthepedestrians

with

luggagehassignificanteffect

onreductionin

theaveragewalking

speedof

pedestrian.

Kaw

saret

al.[41]

FD

walkw

aysandstairs

inside

ahallroom

UMalaysia

Vf(m

/s)

Flow

rate(ped.(ms)−1)

Pedestrianflow

characteristicsare

differentfor

indoor

andoutdoorfacilities

min

max

Levelwalkw

ays

1.41

0.27

1.87

Stairs(a)

0.51

0.06

0.73

Stairs(d)

0.54

0.08

0.88

Corbetta

etal.[42]

FD

Corridorbetweenstairs

BNetherlands

–FDsshow

sthatco-flowspeedarehigher

fordescending

pedestriansthan

for

ascendingones.S

peedsin

counter-flow

sappear

tobe

higher

than

incorresponding

co-flows

Quet

al.[19]

FD

Stairs

UChina

–Pedestrians

walkeddownstairsfaster

than

upstairs.S

ub-group

behaviourandlane

form

ationwereobserved

Experim

entalS

tudies

Daamen

and

Hoogendoorn

[43]

FD

Narrowbottleneck

UNetherlands

Vfm

in=0.86

m/s

Vfm

ax=2.18

m/s

Vavg=1.58

m/s

Capacity

=1.5(m

s)−1

Usage

ofbottleneckisdifferentd

uring

near-capacity

andcapacity

flow

conditions

comparedto

free

flow

situations

Seyfriedet

al.[44]

FDforsingle-file

motion

ofpedestrians

Corridor

UGermany

–Observedlin

earrelationbetweenSpeed

and

theinverseof

density

Seyfriedet

al.[8]

Capacity

estim

ation

from

FDBottleneck

UGermany

Different

flow

parameter

values

fordifferent

bottleneckwidths

Observedlineargrow

thof

flow

with

width

Seeret

al.[38]

FD

Meandersandstairs

UAustria

Meanders

Stairs

Maxim

umandeffectivecapacitiesfor

meandersandstairswereestim

ated

from

thedevelopedFD

’s.

Group

12

12

MedianFlowrate

(Ped/m

in)

55.6

53.6

96.46

120.45

Headw

ay(sec)

1.08

1.12

––

Flow

rate(Ped/m

in)

––

89.82

113.65

Eur. Transp. Res. Rev. (2017) 9: 49 Page 7 of 13 49

Tab

le1

(contin

ued)

Author

Purpose

Element

Type

ofFlow

Country

Designvalues

Rem

arks

Seyfried

etal.[26]

Influenceof

measurement

methodon

FDCorridor

UGermany

–Applicationof

differentm

easurementm

ethods

leadsto

largedeviations

intheresults

Chattarajetal.[45]

Effecto

fculture,lengthof

corridor

onFD

Corridor

UIndiaand

Germany

Vf(India)=1.27

(±0.16)m/s

Vf(G

ermany)

=1.24

(±0.15)m/s

Indian

subjectsspeeds

arehigher

than

those

ofGerman

subjects,

Corridorlength

hasno

impacton

thedistance

headway-speed

relatio

nZhang

etal.[21]

Influenceof

ordering

inbidirectionalflowson

FD

Corridor

BGermany

Vfavg=1.55

±0.18

m/s

q smax=1.5(m

s)−1

atK=2.0m

−2

q max2.0(m

s)−1

(U)

q max=1.5(m

s)−1

(B)

Upto

densities

of2m

−2thereisno

significant

difference

observed

intheFD

sforvarious

degreesof

ordering

(DML,S

SL,B

FRand

UFR

)Zhang

etal.[28]

Influenceof

measurement

methodon

FDcomparison

ofFDforT-Junctio

nand

corridor

T-Junctio

nandCorridor

UGermany

–Different

methods

produces

agreeableresults

with

somedifferences.FD

sof

various

elem

entscannot

becompared

Zhang

etal.[29]

FDCorridor

UGermany

–FD

sdevelopedby

variousmethods

show

equaltendencyhowever

with

different

accuracy.F

Dsforthesametype

offacilitycanbe

combinedinto

single

diagram

forspecificflow

.Tianet

al.[30]

FDCorridoractingas

bottleneck

UChina

–Observedalin

earrelationshipbetween

Flow

rateandbottleneckwidth.

Pedestriansbehaviourin

thecorridor

hasasignificanteffecto

ntim

eheadwaysandtheirdistributionwhen

they

form

lanes

Yanget

al.[46]

Speed-flow

-density

relationship

Stairs

UChina

Different

values

ofparametersfor

differentstairsandalso

fordifferent

situations

Flow

rateanddensity

exhibiteddifferent

tendency

forstaircases

with

different

dimensions.In

emergencysituation,

theeffectof

velocity

ondensity

was

moresignificantcom

paredto

norm

alsituation

Lvet

al.[4]

Pedestrian

movem

ent

behaviour

Different

environm

ents

UChina

Vmax=1.56

m/s

Incorporatinglocald

irection-changing

mechanism

,self-slow

ingandvisual

hindranceinform

ation,a2-Dcontinuous

modelhasbeen

proposed

Burghardt

etal.[9]

Effecto

fstairgradient

onFD

Stairs

UGermany

q smax=1.1(m

s)−1

Kmax=2.6m

−2Flow

decreaseswith

increase

instair

gradient.F

lowvalues

foragiven

density

inexperimentsare

slightly

higher

than

fieldobservations

Zhang

and

Seyfried

[22]

FDCorridor

U&B

Germany

q max=2.0(m

s)−1(U

)q m

ax=1.5(m

s)−1(B)

Observedacleardifference

betweenthe

FD’sof

unidirectionaland

bidirectional

flow

sBandini

etal.[47]

FDCorridor

U&B

Italy

–Highdensity

conditionsaresimulated

byextendingthefloor-fieldCA

Zhang

and

Seyfried

[25]

Influenceof

intersection

ofpedestrian

flow

son

FDCorridorandotherscenarios

B&C

Germany

Different

flow

parametersfordifferent

flow

situationscenarios

Intersectin

gangles

of90°and180°

has

noinfluenceon

theFD

’sof

various

flow

types.

Flötterödand

Läm

mel[13]

FDStraight

corridor

and

roundcorridor

BGermany

–Proposed

aone-on-one

mapping

between

FDparametersof

uniand

bidirectional

flow

sSimulationStudies

Seyfried

etal.[14]

Effecto

fremoteactionand

required

spaceon

FDCorridor

UGermany

Intended

speedvalues

arenorm

ally

distributed

with

μ=1.24

m/s

σ=0.05

m/s

ModifiedtheSocialforce

model.T

hereplicationof

classicalF

Disachievable

byincreasing

therequired

spaceand

prevailingvelocity

ofaperson

Bruno

[15]

Speed-Density

Relation

Footbridge

–Italy

Vfavg=1.34

m/s

Proposed

amodelthatconsidersthe

influenceof

travelpurpose,geographic

area

andeffectof

lateralv

ibratio

nsof

platform

onSp

eed-Density

relation

49 Page 8 of 13 Eur. Transp. Res. Rev. (2017) 9: 49

4.3 T - Junction

While limited research is available on pedestrian characteris-tics in other geometric elements, Zhang et al. [28] comparedthe FDs for a T-Junction and straight corridor and expressedthat FDs of various facilities cannot be compared because ofthe inequality existed between inflow and outflowwhich leadsto a transition between low densities and high densities in thepedestrian flow.

4.4 Stairs and escalators

Stairs are considered as one of the most important part of theegress routes (Fig. 4d). Understanding the evacuation dynam-ics of pedestrians on stairs is crucial especially to analyse theemergency situations. Different planning guidelines, empiri-cal and experimental studies proposed FD’s and flow param-eter values for stairs in ascending and descending directions.To know the variation in flow parameters of different guide-lines, values obtained from different experimental studies thereader is advised to refer Burghardt et al. [9]. A comparison ofFD’s of stairs given by different planning guidelines, measure-ments of FD obtained from various field and experimentalstudies was published in Burghardt et al. [9] and is presentedin Figs. 5 and 6 respectively.

Cheung and Lam [23] observed higher values of capac-ities and walking speeds on stairways and passageway atHong Kong Metro stations compared to London under-ground stations. Further, it is found that the effect of bidi-rectional pedestrian flows on staircase are more significantcompared to passageway. Cheung and Lam [10] investigat-ed the relationship between speed and flow on stairs andescalators (ascending, descending) and found that pedes-trians behaviour differ when they use the facilities in bothdirections. It is noticed that the pedestrians are more sus-ceptible to relative delay on both the facilities in descend-ing direction compared to ascending direction. Further, it isobserved that 85% of pedestrians are desirous to use anescalator in descending direction when the relative delayis 7.8 s while in ascending direction it can be up to 17.4 s.This is interpreted by the fact that the effort in walking indescending direction of a staircase is perceived to be lessthan walking in ascending direction. Graat et al. [36] foundthat the capacity and speed are higher on stairs with normalslope (30°) than the stairs with steeper slope (38°) whichclearly shows that stair gradient effects the velocity andcapacity. Lee [11] conducted a study on escalators andstaircase in public transport facilities and observed thatdirection of movement, infrastructure type and pedestrianpersonal characteristics influences free speeds. Further, itis noticed that men walk faster than women. At Hong KongMTR stations Lee and Lam [37] investigated the walkingspeed variations on a unidirectional walkway and aT

able1

(contin

ued)

Author

Purpose

Element

Type

ofFlow

Country

Designvalues

Rem

arks

Hao

etal.[16]

FDUnknown

UChina

–Alattice

gasmodelwith

parallelu

pdate

rulesisused

tostudyunidirectional

pedestrian

flow

Chattarajetal.[6]

Singlefilepedestrian

movem

ent

Corridor

UIndia&

Germany

–DissimilaritiesexistinFD

dueto

cultural

differences

Lvet

al.[4]

Pedestrian

movem

ent

behaviour

Different

environm

ents

UChina

ForEvacuationsimulation,Vmax=0.75

m/s

ForBottleneck

simulation,q s

obtained

is2.25(m

s)−1

Simulationof

passageandbottleneck

werecarriedoutu

sing

2-Dcontinuous

model

Bandini

etal.[47]

FDCorridor

U&B

Italy

Pedestrian

Speed=1.2m/s

Highdensity

conditionsaresimulated

byextendingthefloor-fieldCA

Quet

al.[19]

FDStairs

UChina

Different

simulationresults

fordifferentstaircases

Estim

ated

theevacuatio

ntim

eandcapacity

ofstairsusingsimulations

Flötterödand

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mel[13]

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corridor

and

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–Proposed

aone-on-one

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uniand

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flow

sFu

etal.[48]

Lock-step

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onFD

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desiredSp

eed=1.6m/s

Influenceof

lock-stepwas

analysed

byEstim

ating-CorrectionCellular

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aton

(ECCA)model

Eur. Transp. Res. Rev. (2017) 9: 49 Page 9 of 13 49

bidirectional stairway and observed that, when the pedes-trian flow is reaching the capacity of the facility, the vari-ation in the walking speed is found to be minimal. In ad-dition, it was also observed that the walking times are nor-mally distributed. To predict the pedestrian walking speedson staircase a linear regression model is developed byFujiyama and Tyler [12] by considering stair gradient, legextensor power of pedestrian and weight of the participant.This model shows that the walking speeds are different onvarious gradients of stairs, while the designers generallyneglect these differences. In addition the model is present-ing a specific profile in predicting the walking speeds ofpeople. Burghardt et al. [9] conducted an experimentalstudy and a field study on the same staircase and observeda maximum density of 2.9 m−2 and 3.4 m−2 respectively.Further, it was observed that the flow values for a givendensity in experiments are slightly higher than the fieldvalues.

A comprehensive review of FDs of pedestrian flow char-acteristics is presented in Table 1. The studies described inTable 1 mostly discuss FDs and factors effecting it for exclu-sive pedestrian facilities.

Pedestrian walking speed is of special interest to transpor-tation engineers and planners because it greatly influences thelevel of service and capacity of the system. For instance, if thepercentage of women and older pedestrians increases thespeeds decreases thereby capacity of the system also reducesbecause of their smaller step length and less step frequencyetc. Hence, to understand the capacity of a facility and also toknow the evacuation characteristics, it is important to under-stand the walking speeds in various environments. From var-ious sources it is observed that individual pedestrian charac-teristics and external conditions are influencing the pedestrianspeeds. Some of the factors mentioned are age, culture, gen-der, shy away distance, temperature, travel purpose, type ofinfrastructure, walking direction [3].

5 Walking speeds at various facilities

Pedestrian walking speed is an important parameter in thedesign of walking infrastructure as it decides the capacity ofa facility. Pedestrian speeds are greatly influenced by pedes-trian environment and the characteristics of the surroundingcrowd. For example, pedestrians in shopping and commercialareas walk slowly when compared to walking in the publictransport places [3]. Pedestrian walking behaviour may differwith respect to geographic location due to the presence ofcultural differences. Hence it is necessary to consider this par-ticular aspect of pedestrian dynamics for the design of facilityspecific to a country or region. For instance Indians maintainhigher speeds and less headways when compared to Germans[45]. From the previous studies, [49–53] it is evident thatyounger pedestrians maintain higher speeds when comparedto old pedestrians. Also men walk at higher speeds whilecompared to women [17, 49–55]. Tanaboriboon et al. [49]reported the mean walking speed in Singapore as 74 m/minwhich is relatively slower than the walking speeds inAmerican counterparts. Further, the maximum flow rate ob-tained is 89 pedestrians/m/min which is higher than the valuesobtained in western countries. This is interpreted by the reasonthat the Singaporeans require less space for the movementbecause of their smaller physique. Koushki [54] in Riyadh,found the average walking speed of pedestrians as 65 m/minwhich is less when compared to the walking speeds of UnitedStates, England and Singapore. Young [55] reveals that themoving walkway in the corridor affects the walking speedsof pedestrians those who use it. The standing persons on themoving walkways becomes obstacles to the following pedes-trians who are using the system next to them results in con-gestion on the system thus reduces the average walking speedsand leads to increased travel times. Montufar et al. [51] showsthat walking speeds in summer are greater than in winter forboth younger and older pedestrians. Further, they found that

1.23

1.46

1.47

1.08

1.32

1.5

1.17

1.41

1.3

1.15

1.43

0.88

1.28

1.17

1.27

1.46

1.36

1.61

0.9

1.35

1.14

1.36

0 0.5 1 1.5 2

Tanaboriboon (sidewalk)

Fitzpatrick (signalised)

Montufar (signalised-normal)

Montufar (signalised-crossing)

Finnis (township)

Koushki (Sidewalk)

Young (walkway)

Laxman (walkway)

Pedestrian Speed (m/sec)

V averageV maleV femaleV youngV elderV older

Fig. 7 Pedestrian walking speedsfrom various studies

49 Page 10 of 13 Eur. Transp. Res. Rev. (2017) 9: 49

the normal walking speed is less than the crossing walkingspeed for different age groups in different seasons. In contrast,Avineri et al. [53] shows that irrespective of different agegroups, pedestrian walking speeds are higher on sidewalksor footpaths while compared to the signalized andunsignalised intersections. While analysing the group behav-iour of pedestrians Moussaid et al. [18] observed a continuousdecrease in walking speeds with the increase in group size.Based on fundamental relationships HCM [56] presents thatwalking speeds differ for different classes of pedestrians suchas shoppers, students and commuters. Laxman et al. [17] con-ducted a study in India under mixed traffic conditions andfound that the pedestrian free speed is 84 m/min which ishigher than in Singapore and China and a little lower thanGermany. Further, the means speeds are reduced by 10%when they are carrying baggage. Among the explanatory var-iables such as longitudinal gradient, effective footway width,age, individuals or group, gender and time of the day Silvaet al. [57] found that the longitudinal gradient of the footway isthe most significant variable in explaining the walking speed.Figure 7 shows the comparison of pedestrian walk speedsfrom various studies. It is quite evident that barring a coupleof studies, most speeds are in the range of 1.0–1.5 m/s.Further, the differences amongst various age groups and gen-der are also shown. Travel purpose is found to influence thewalking speeds of pedestrians. According to Daamen [3]higher walking speeds were observed for pedestrians travel-ling for business followed by commuters, shoppers and thenpedestrians walking in leisure. Especially, higher free speedsare observed in transfer stations compared to shopping areas.The possible reason may be because the pedestrians are inhurry to catch a train or bus thus increasing their walkingspeeds whereas the shopping is a leisure trip and with main-taining lower speeds.

Vf – Free speed, Vfavg –Mean free speed, Vmax =MaximumSpeed, Vavg –Mean Speed, qmax –Maximum flow, qs - Specificflow, qsmax – Maximum specific flow, K – Density, Kmax –Maximum density, d – descending, a – ascending, U -Unidirectional flow, B – Bidirectional flow, C – Crossing.

6 Conclusions and future directions

The paper presented a comprehensive review of FDs of pe-destrian flow characteristics. Based on the review, this paperdraws the following conclusions and identifies the researchgaps and hence the scope for further studies. Exploring thesegaps will enhance the understanding of FDs of pedestrian flowcharacteristics. This would also help improve the modellingbased on the suggestions made.

& Even though a considerable amount of literature on devel-opment of FDs based on theoretical and experimental

concepts is available, literature based on empirical find-ings are limited. From the previous studies it is observedthat mostly the research is focused on experiments. As theemotional status of the participants is relaxed during theexperiments, they cannot at times reflect the actual behav-iour of pedestrians which exists in real life situations.Hence there is a great need to focus on development ofFDs by conducting field studies for various pedestrianinfrastructure elements with different flow situations.

& Because of the favourable controlled conditions, re-searchers [3, 4, 6–9, 22, 24–26, 28–31, 43–46] are inter-ested in conducting experimental studies. The results ob-tained in experiments can be comparable only if the fieldstudies are conducted on the same element [9]. Otherwisethe accuracy of the experimental results cannot be justi-fied. Moreover, differences between filed, experimentaland simulation data across different cultures and environ-ments needs to be established and suitable adjustment fac-tors between these studies should be proposed.

& Zhang et al. [29] shows that the FDs of same element withdifferent widths can be combined into a single diagramwhereas for different elements it cannot be combined.For instance, the FDs of T-junctions and corridors cannotbe combined as the inflow and outflow are different [28].This shows that FDs are different for different elements aswell as different flow conditions. So further deep exami-nation is needed in this area.

& Cultural differences do influence the pedestrian flow char-acteristics as well as capacities of the pedestrian infrastruc-tural facilities [10, 12, 36, 45, 58]. In order to understandthe cultural differences, it is suggested to conduct the re-search in various regions and compare the design values offlow parameters across various cultures. In addition, it isobserved that individual pedestrian characteristics and ex-ternal conditions are influencing the pedestrian speeds.Some of the factors are age, culture, gender, shy awaydistance, temperature, travel purpose, type of infrastruc-ture, walking direction. Moreover, the extent to whichthese factors influence the fundamental diagrams is un-known. [3] Future studies need to focus in this direction.

& Fundamental relationships of pedestrian flow characteris-tics for various classes of pedestrians are different [3, 56].This infers that pedestrians walking speed differs withrespect to the facility and trip purpose. Hence the applica-tion of walking speeds of one facility for the design ofother facility may not lead to fruitful results. As walkingspeeds decides capacity of the facility, it needs to be ex-amined with respect to the context.

& Even for a simple element like a corridor, the applicationof various measurement methods leads to a large variationin the observations of FD [26]. This reveals that measure-ment method does influence the results and hence itshould be examined further.

Eur. Transp. Res. Rev. (2017) 9: 49 Page 11 of 13 49

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