Heliyon 9 (2023) e14275
A ailable online 4 Ma ch 2023
2405-8440/© 2023 The Au ho s. Published by Else ie L d. This is an open access a icle unde he CC BY license
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Resea ch a icle
Analysis o he use o beha io al da a om i ual eali y o
calib a ion o agen -based e acua ion models
Voj ˇ
ech Juˇ
ík
a
, Ondˇ
ej Uhlík
b
, Dajana Snopko ´
a
c
,
*
, Ondˇ
ej K a da
c
,
Tom´
aˇ
s Apel aue
b
, Jiˇ
í Apel aue
b
a
Depa men o Psychology, Facul y o A s, Masa yk Uni e si y, B no, Czech Republic
b
Ins i u e o Compu e Aided Enginee ing and Compu e Science, Facul y o Ci il Enginee ing, B no Uni e si y o Technology, B no, Czech Republic
c
Depa men o Geog aphy, Facul y o Science, Masa yk Uni e si y, B no, Czech Republic
ARTICLE INFO
Keywo ds:
Pa h inde
Vi ual eali y
E acua ion beha io
Agen modeling
Indoo na iga ion
E acua ion ime
ABSTRACT
Agen -based e acua ion modeling ep esen s an e ec i e ool o making p edic ions abou
e acua ion aspec s o buildings such as e acua ion imes, conges ions, and maximum sa e
building capaci y. Collec ion o eal beha io al da a o calib a ing agen -based e acua ion
models is ime-consuming, cos ly, and comple ely impossible in he case o buildings in he design
phase, whe e p edic ions abou e acua ion beha io a e especially needed. In ecen yea s
e acua ion expe imen s conduc ed in i ual eali y (VR) ha e been equen ly p oposed in he
li e a u e as an e ec i e ool o collec ing da a abou human beha io . Howe e , empi ical
s udies which would assess alidi y o VR-based da a o such pu poses a e s ill a e and
conside ably lacking in he agen -based e acua ion modeling domain. This s udy explo es op-
po uni ies ha he VR beha io al da a may b ing o e ining ou pu s o agen e acua ion
models. To his end, his s udy employed mul iple inpu se ings o agen -based e acua ion
models (ABEMs), including hose based on he da a ga he ed om he VR e acua ion expe imen
ha mapped ou e acua ion beha io s o indi iduals wi hin he building. Calib a ion and e al-
ua ion o models was based on empi ical da a ga he ed om an o iginal e acua ion exe cise
conduc ed in a eal building (N =35) and i s i ual win (N =38). This s udy ound ha he
esul ing p edic ions o single agen models using da a collec ed in he VR en i onmen a e
p oposed co ec ions ha e he po en ial o be e p edic eal-wo ld e acua ion beha io while
o e ing desi able a iance in he da a ou pu s necessa y o p ac ical applica ions.
1. In oduc ion
E acua ion is ypically unde s ood as a sys ema ic mo emen o a pe son om a dange ous place o a place o sa e y, i conduc ed
success ully he e acuee should a i e a designa ed assembly poin . This means ha e acua ion is conside ed a human-cen e ed
ac i i y and he whole p ocess can be ca ego ized as a pa h-sea ch o aided way inding in case o un amilia indoo en i onmen s
[1]. F om his pe spec i e, i is di ec ly de e mined by indi idual human cogni i e abili ies and ai s, including decision-making
s a egies, spa ial skills, o ap i udes o unde s anding indoo en i onmen s [2–4]. A wide ange o complex beha io al phenom-
ena occu du ing human e acua ion, such as p olonged eac ion o i e ala ms (p e-e acua ion beha io ) [5–10] o he equen use o
* Co esponding au ho .
E-mail add ess: [email p o ec ed] (D. Snopko ´
a).
Con en s lis s a ailable a ScienceDi ec
Heliyon
jou nal homepage: www.cell.com/heliyon
h ps://doi.o g/10.1016/j.heliyon.2023.e14275
Recei ed 26 Decembe 2022; Recei ed in e ised o m 27 Feb ua y 2023; Accep ed 28 Feb ua y 2023
Heliyon 9 (2023) e14275
2
e acing na iga ion s a egy, whe eby inexpe ienced indi iduals, in pa icula , e acua e by he same ou e hey en e ed he building
while ailing o no ice/ ollow e acua ion signs [5,6,11,12]. People also o en use o he han he p esc ibed eme gency exi s [13].
E acua ion beha io is also in luenced by he con ex ual en i onmen al in o ma ion ha is p esen a he ime [14,15]. P e ious
s udies ha e analyzed he impac o he p esence o na iga ion aids, signage, and landma ks [5,6,15,16], ligh [17,18], isual,
audi o y, o ol ac o y cues ha depend on he o m o he h ea ha igge s he e acua ion [19–21], and he a o dances p oposed by
he en i onmen al s uc u e i sel [11,22,23]. This has placed beha io al s udies o indi iduals in he speci ic en i onmen a he
cen e o cu en esea ch. Fo e ec i e p edic ion wi h ega d o building designs, i is necessa y o cap u e and inco po a e human
ac o s in o e acua ion models.
1.1. Agen -based models o p edic ing e acua ion
Agen -based e acua ion models (ABEMs) a e used o a ious kinds o simula ions in o de o explo e, isualize and p edic po-
en ial scena ios in e acua ing people om buildings. Mos comme cially used agen models a e howe e limi ed o di ec ways o
agen mo emen . They possess no cogni i e o beha io al p edic o s; hey do no usually conside many o he speci ic cogni i e and
beha io al mani es a ions ha occu in e acuees [24]. ABEMs usually wo k on he basis o algo i hms ha calcula e he
spa io- empo al op imum o he agen mo emen (e.g., he sho es dis ance o sho es ime). Al hough smoo hing algo i hms o e
somewha mo e na u al cou ses o mo emen [6], ABEMs usually neglec he ac ha he dynamics and ajec o ies o human
mo emen in eal en i onmen s do no ully co espond o simula ed ones [25,26]. Fo ABEMs i is ypical ha agen s ha e p ede ined
pa ame e s based on which hey make decisions and choose hei pa hs. Al e na i e app oach is o ce-based models (e.g., social o ce
model [27]), whe e agen s adap hei beha io o o ces om o he agen s ha a ec hem and cellula au oma a, which is a speci ic
o m o ABEMs and a e disc e e in ime, space, and s a e a iables. I uses cells and disc e e mesh. E e y cell has a ini e numbe o
s a es and is upda ed based on a simple se o ules (in e ac ing wi h o he agen s and en i onmen [28]). In his s udy we wo ked wi h
he so wa e Pa h inde which uses con inuous iangula ion which acili a es con inuous mo emen o pe sons h oughou he model,
compa ed o cellula au oma a.
1.2. VR expe imen s as a da a sou ce on e acua ion beha io
Vi ual eali y (VR) expe imen s ep esen ecologically alid, con ollable [29,30] and po en ially cos -e ec i e ways o ga he ing
beha io al da a on human ac ions in a wide ange o si ua ions. VR seems o ac i a e b ain mechanisms simila o hose ha occu in
he eal wo ld [31,32]. In his ega d, i has been ound o e ec i ely simula e eal-wo ld scena ios [33]. Vi ual en i onmen s
p o ided ia imme si e head-moun ed displays (HMDs) possess a high le el o ealism and allow o he non-in asi e collec ion o
beha io al da a, which is u he p omo ed by a con ollable deg ee o i ual en i onmen ’s in e ac i i y [34] and ac i i y-logging
op ions [22,35,36]. Rega ding his, VR expe imen s
1
could sol e he p oblem o conduc ing complica ed and expensi e e acua ion
d ills in eal buildings o ga he he necessa y da a o model op imiza ions. Mo eo e , VR-based expe imen s can be easily pe o med
in i ual buildings ha do no cu en ly exis (e.g., p oposed buildings) [18,22,37–39] and can be applied o si ua ions ela ed o
dynamic haza ds, such as i e o he sp ead o oxins [40]. In his ega d, Building In o ma ion Modeling (BIM) echnology may be used
o p omo e he e ec i e design o VR en i onmen s, ollowing he need o human-cen e ed design assessmen [35,41]. Recen ad-
ances in VR ha e shown p omise in simula ions wi h ega d o iable op ions o cap u ing beha io al da a abou ac ual human
beha io du ing e acua ions [2,20,40,42–45]. Howe e , he eliabili y and usabili y o speci ic beha io al p ope ies in VR-based
esea ch emains unclea and needs o be explo ed in ela ion o he echnical oppo uni ies and limi s o VR ools and he speci ic
co espondence o VR-gene a ed expe imen s o eal e acua ion beha io . Fo example, he na iga ion mo emen as well as o he
beha io s in eal en i onmen s compa ed o i ual ones a e expec ed o a y based on he speci ic ea u es o he en i onmen s [46,
47]. P e ious esea ch sugges ed VR echnology o limi human pe o mance [48], aking in o accoun he unna u al "in ol emen " o
use s in simula ion scena ios [49] impe ec depic ion o p oblema ic me apho s o mo emen [50]. The mo emen ac i i y, espe-
cially, was ound o be less e ec i e in he i ual en i onmen s [51]. This no ion b ough us o he c ea ion o hyb id agen models
esol ing he mo emen me apho - see below. O he limi a ions o VR echnology include po en ial cybe sickness, i.e., he discom o
ha use s may expe ience while using VR equipmen , losses in ecological alidi y compa ed o ield s udies since pa icipan s in he
expe imen may be awa e ha hey a e pa o a simula ion, and echnical limi a ions [40,52,53]. These aspec s should be always
conside ed when in e p e ing he ou comes o VR-based esea ch. In he cogni i e p ocesses such as decision o eac ion imes and
choice o exi , howe e , he assump ions abou hei simila i y in eal and i ual en i onmen s sugges ed by p e ious s udies [31,54]
seems o be suppo ed [51]. Gene ally, we can conclude ha wi h an app op ia e me hod, he use s udies and especially he da a on
pa icipan mo emen and decision-making p ocesses om VR-based expe imen s may help p omo e he e ec i eness and p ecision o
agen models ega ding e acua ion p edic ions, as human ac o s a e undamen al a iables in he ou comes o building eme gencies
[5].
1
In his ex , we use he e m “VR expe imen s” ins ead o “VR simula ions” o a oid po en ial con usion wi h “agen simula ions”.
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1.3. Aims o he s udy
I was demons a ed ha he e exis di e ences be ween he eal e acua ion p ocess and he e acua ion p ocess conduc ed in VR
condi ion [51], especially ega ding o al eg ess imes caused by he di e en mo emen me apho . Rega ding his, we suppose ha
VR e acua ion simula ions canno be di ec ly used o making p edic ions abou he e acua ion p ocess in a eal se ing. Human
beha io in he VR e acua ion exe cise, howe e , possesses se e al simila i ies o he eal e acua ion [51] and we a gue ha i can be
used o calib a ing ABEMs wi h he aim o b ing necessa y p edic ions applicable o enginee ing p ac ice. In his s udy we explo e
ways o how he VR e acua ion da a can be used in ABEMs wi h he aim o each p edic ions abou eal e acua ion beha io . Fo his
pu pose, he VR-based e acua ion expe imen [51] was b ough in o he con ex o agen -based e acua ion modeling. We adop ed aw
de-iden i ied da a abou he human indi idual e acua ion beha io in a eal and a co esponding i ual building (digi al win). All he
used da a we e ga he ed wi hin he expe imen conduc ed unde he esea ch p ojec , which was sol ed by he Masa yk Uni e si y,
B no, in coope a ion wi h B no Uni e si y o Technology, Czech Republic, and i s ou comes we e epo ed in a soli a y epo [51]
including also de ailed me hodology and p ocedu e o he expe imen . The conduc ed expe imen p ima ily ocused on compa ing he
beha io al mani es a ions o indi iduals e acua ing om a eal building and indi iduals e acua ing om he same en i onmen
c ea ed and p esen ed in VR unde equi alen condi ions. VR se ing in he o iginal expe imen employed cu en ly accessible VR and
con olling de ices (head-moun ed display o imme si e VR and compu e mouse and keyboa d) wi h he aim o app oach engi-
nee ing p ac ice. In he p esen pape , he aw da a om he men ioned VR expe imen we e e-used as key quan i ies o he
Pa h inde ABEM [55] wi h he goal o analyze he possibili ies o using such da a collec ed in cos -e icien and ime-e icien VR
expe imen s o agen models. The e alua ion o agen models is p oblema ic, as he e is a lack o da a on eal e acua ion o he
assessed building. In ou case howe e , we a e able o compa e he esul ing model agains he a ailable beha io al da a collec ed in
he eal building. The aim o his s udy, hough, is no o compa e beha io aspec s cap u ed in a eal and a co esponding i ual
con ex no he discussion on he mos e ec i e VR se ing o eco ding e acua ion beha io da a. Wi h he use o ABEMs, his s udy
aims o assess he po en ial iabili y o VR beha io al da a o making eliable e acua ion p edic ions. Model ou comes (mo e spe-
ci ically, e acua ion imes) can be s a is ically compa ed o he eal e acua ion da a in o de o s udy eliabili y o ABEMs calib a ed by
he VR da a and o obse e di e ences and simila i ies wi h o he calib a ion se ings. He e, an e acua ion model was un o a speci ic
building using he de aul pa ame e s o Pa h inde , and esul s ( o al e acua ion ime) we e hen compa ed wi h he simula ion esul s
based on VR and eal-wo ld expe imen da a ( eal-wo ld da a se ed as a baseline). By de aul se ings we mean ini ial pa ame e s used
in Pa h inde so wa e which a e based on empi ical da a wi h di e en con ex (e.g. Re . [56]) and canno conside local beha io al
pa e ns such as e acing s a egy o wai ing poin s. This se ing (o i s a ia ion) would be used in si ua ions whe e he e is no local
empi ical da a abou occupan s’ beha io and decision-making. Pu pose o hese se ings is o analyze he di e ence be ween ABEMs
esul s based on local da a (VR expe imen da a) and gene al ype o empi ical da a used o e acua ion modeling.
2. Ma e ials and me hods
2.1. So wa e
This s udy used Pa h inde so wa e ( e sion 2021.2.0525 ×64) [55,57], which was de eloped by Thunde head Enginee ing
company. Resea ch has shown ha Pa h inde is he mos used pedes ian e acua ion model in academic and indus ial ields [58]. The
model consis s o h ee modules: a g aphical use in e ace (GUI), a simula o , and a 3D esul s iewe . GUI is p ima ily used o c ea e
model geome y and model calib a ion. Suppo ed inpu geome y ile o ma s include BIM o ma s (i c), 3D o ma s (dae, bx) and 2D
(dwg, dx ). A e he geome y is impo ed, a iangula ed na iga ion mesh is c ea ed. Agen s a e p esen ed as au onomous en i ies
wi h a p ede ined se o pa ame e s [59].
A he beginning o he simula ion, o each agen he e is an iden i ied local exi in he ac ual oom. Then Pa h inde uses he A*
sea ch algo i hm [60] o gene a ing seek cu es in he na iga ion mesh [61]. Simula ion can be pe o med in SFPE (Socie y o Fi e
P o ec ion Enginee s) mode o STEERING mode. SFPE implemen s he concep s in he SFPE Handbook o Fi e P o ec ion Enginee ing
[62]. This mode is based on a low model, whe e walking speeds a e de e mined by agen densi y in each oom, and low h ough he
doo is con olled by doo wid h. In his model, agen s canno in e ac wi h each o he , hey can occupy he same space in he geome y
and a e no able o change hei ajec o y. In STEERING mode (which was used in ou case), agen s in e ac wi h each o he and he
en i onmen . Agen s use a combina ion o he s ee ing mechanism (way inding) and collision handling o con ol how hey ollow
hei seek cu e ( hei ajec o y o he nex doo , waypoin , e c.) [63,64]. In e e y ime s ep, he agen ’s nex posi ion is calcula ed,
based on he ac ual dis ance om o he agen s as well as om he su ounding walls, pilla s and so on [61]. This makes he agen
mo emen mo e na u al and complex.
2.2. Da a
Comple ely anonymized aw da a in a o m o spa io empo al coo dina es o indi idual pa icipan s mo emen h ough he
building used o he agen -based models was ob ained om he empi ical expe imen conduc ed unde he esea ch p ojec n .
TL02000103 called “Cogni i e psychology and space syn ax in i ual en i onmen s o agen modeling” in es iga ed by Masa yk
Uni e si y and B no Uni e si y o Technology, Czech Republic. The s udy ollowed all e hical s anda ds o psychological esea ch, he
expe imen was conduc ed acco ding o guidelines o he Decla a ion o Helsinki. In o med consen was p esen ed o all pa icipan s
whe e hey we e in o med abou he na u e o he expe imen , also ha hei pa icipa ion was olun a y and ha hey could lea e he
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expe imen al session any ime hey wan ed wi hou any nega i e consequences. In he case o he p esen s udy, seconda y use o he
da a was applied. In a be ween-subjec s expe imen al design, he p ojec aimed o explo e he e acua ion beha io o use s in wo
di e en condi ions: an e acua ion om a eal building (35 pa icipan s, M =15, W =20) and an e acua ion om i s digi al win - i.e.,
om an equi alen building p esen ed in imme si e i ual eali y using head-moun ed display (38 pa icipan s, M =22, W =16). The
i ual en i onmen was de eloped om he sou ce BIM model and u he modi ied in he game g aphics engine Uni y [41]. The
de ailed me hodology, expe imen p ocedu e, and s a is ical compa isons o he o iginal empi ical da a on human e acua ion beha io
in eal and i ual en i onmen s we e p esen ed in a sepa a e p ojec epo [51]. In gene al, in bo h condi ions, he expe imen al
session s a ed in on o he unknown building (see Fig. 1) whe e pa icipan s we e one by one ins uc ed o na iga e o a speci ic
loca ion in he building - a lec u e oom. When in he oom, pa icipan s we e dis ac ed wi h a simple cogni i e ask ( inding di -
e ences on wo pic u es), du ing whose solu ion an e acua ion ala m sounded so hey we e o ced o e acua e. Since he pu pose o
he expe imen was o explo e e acua ion beha io and decision-making, pa icipan s we e p e en ed om e u ning by he same
ou e as hey en e ed he building by placing an obs acle in hei pa h (closing ba s), which o ced pa icipan s o look o an al e -
na i e e acua ion ou e. Du ing he e acua ion, he posi ion in ime and gaze ac i i y o he pa icipan s we e moni o ed (wi h he use
o came as and eye- acking echnology in eal condi ion, and au oma ic logging and embedded eye- acking in VR condi ion). An
illus a ion o one pa icipan ’s e acua ion ajec o y is displayed in Fig. 1. F om he ga he ed aw da a, we de i ed de ailed beha io al
me ics abou he pa icipan s’ passages h ough he building (see below). The calcula ed da a we e u he used o e ine he ou pu o
he agen e acua ion models (Pa h inde [55]).
3. Calcula ions
Taking in o accoun he op ions o cu en agen simula ion ools, we selec ed key beha io al me ics ob ained om he abo e-
men ioned s udy [51] o e ine Pa h inde ABEM. Na iga ion mo emen and o he beha io s in eal en i onmen s, in compa ison
wi h i ual ones, a e expec ed o a y based on he speci ic ea u es o he en i onmen s [46,47]. P e ious esea ch has sugges ed ha
VR echnology limi s human pe o mance [48] in ela ion o he unna u al “in ol emen ” o use s in simula ion scena ios [49],
impe ec depic ion, o p oblema ic me apho s o mo emen [49]. The in e ace me apho o mo emen in VR (i.e., he speci ic
se ings o mo emen con ol in he VR in e ace such as, o example, a keyboa d o joys ick) was pa icula ly iden i ied as p ob-
lema ic whe e a keyboa d-mouse con ol in e ace was used [51]. Such a se up does no simula e eal pa e ns o changes in speed
(accele a ions) in a a a mo emen s and only o e s ei he cons an speed mo ion o s anding. In cogni i e p ocesses such as decision
o eac ion imes and choice o exi , howe e , he assump ions as o hei simila i y in eal and i ual en i onmen s sugges ed by
p e ious s udies [31,54] seems o be suppo ed [30]. In his case, con incing analogies we e obse ed in he analyzed da a, ei he in
he o e all a e ages o he measu ed a iables o based di ec ly on simila ends iden i ied ia isual analysis.
Fo e ining he VR-based models, we ocused on he beha io al pa ame e s ha we e iden i ied as co esponding in eal and
i ual en i onmen s [51]. The pa ame e s ha we e selec ed o he op imiza ion o compu ed models will be p esen ed in mo e de ail
(see Table 1 o a gene al compa ison). They a e di ided in o wo g oups: gene al pa ame e s ha ha e he applica ion po en ial in
agen models simula ions o un in buildings wi h he same unc ion bu a di e en spa ial con igu a ion, while he second g oup o
pa ame e s is speci ic o he simula ion in ou s udied building. The Pa h inde model allows us o e lec he dis ibu ion o he
Fig. 1. Visualiza ion o he building used in eal and VR expe imen s. Blue is used o ma k he incoming ou e, which was manda o y o each
pa icipan , and lead hem o he oom whe e he e acua ion s a ed. E acua ions ou es a e ma ked wi h g een lines, he dashed-line al e na i e
e acua ion ou e (wi hou e acua ion signs) leading o he exac exi ha was used by pa icipan s o en e he building.
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5
e acuees (agen s) on he basis o gende a he inpu [59]. The e o e, all he alues o inpu pa ame e s used in his s udy e lec he
speci ic gende dis ibu ion o pa icipan s in each expe imen and a e agg ega ed on ha basis, i no s a ed o he wise.
3.1. Gene al quan i ies
-P e-e acua ion ime (Ala m eac ion ime) [s]: When he ala m goes o in he eme gency, people do no s a o e acua e imme-
dia ely, making i he key quan i y in he es ima ion o he e acua ion ime. Howe e , s anda d me hods in he Czech enginee ing
con ex as e lec ed by ˇ
CSN (Czech Technical S anda ds), do no usually conside his pa ame e [65] The b ain mus ini ially
p ocess he pe cei ed signal, and depending on he a ious en i onmen al and indi idual aspec s, he e is a delay in he human
eac ion. Since his delay should be inco po a ed in o a i icial agen models, we conside i s co ec ion c ucial in app oaching he
beha io al alidi y o he model. The p e-e acua ion ime ( he ime i ook he pa icipan s o lea e he oom om he momen he
ala m sounded) was se in he model on he basis o obse a ions om Re . [51]. A log-no mal dis ibu ion was i ed o his da a,
which in gene al co esponds o p e-e acua ion ime, based on [58].
- Unimpeded walking speed [m/s]: Speed was one o he me ics o which i was impossible o ensu e compa able condi ions be ween
eal and i ual en i onmen s (because o he abo e-men ioned mo emen in e ace me apho ). In he eal en i onmen , he speed
o he pa icipan s was no limi ed in any way, while in he i ual en i onmen , i was cons an (which is ela ed o he chosen
me hod o mo emen con ol: a keyboa d-mouse in e ace). In o de o be able o supp ess hese unwan ed di e ences be ween
en i onmen s, we agg ega ed he ime i ook pa icipan s o go h ough ce ain segmen s o he ou e (speci ically he wo longes
segmen s on he 4 h loo ). Thus, indi idual sho e s ops we e also included in he walking ime, which in he case o he i ual
en i onmen we e ela ed o mo emen con ol skills. The esul ing calcula ed speed hus came close o eali y. A e age speeds
we e agg ega ed based on gende o bo h segmen s and in e pola ed wi h a no mal dis ibu ion (see Table 1), which se ed as he
model inpu .
- S ai case walking speed [m/s]: The di e ences be ween en i onmen s wi h ega d o unimpeded walking speed applied o he speed
o mo emen on he s ai s, and he e o e we ollowed he same p ocedu e. The pa icipan s’ (downwa d) speed on he s ai case was
de i ed om six iden ical ligh s o he main s ai case. The wo a hes measu ed poin s o he ajec o y we e de e mined on each
ligh , hen he dis ance be ween hem [m] and he ime [s] a eled we e calcula ed. Based on his, an a e age speed on he gi en
ligh o s ai s was ob ained. Subsequen ly, he a e age speeds we e agg ega ed on he basis o gende o all ligh s o he s ai case.
A e di iding by he a e age unimpeded walking speed, a coe icien was ob ained (see Table 1) by which he unimpeded walking
speed o mo emen assigned o he indi idual agen s was mul iplied o he s ai case ou e segmen s.
- Accele a ion ime [s]: This is he ime i akes o he agen o each maximum speed. This was no possible o de e mine on he basis
o he empi ical expe imen , so i was es ima ed acco ding o he de aul se ings. Wi h ega d o he ea u es o he VE se ing
Table 1
Explici alues o inpu pa ame e s o he model simula ions. (Se e al alues we e aken om he da a collec ed in Re . [22]. Fo an exac expla-
na ion, see he desc ip ions o he pa ame e s abo e.)
Inpu pa ame e s De aul
Se ings
Real E acua ion (M =15, W =20) Vi ual E acua ion (M =22, W =16)
Gende – 43% men 57% women 58% men 42% women
P e-e acua ion ime [s] loca ion (shape) [min;
max]
0 [s] 1,73 (0,38) [3,55;
9,95]
1,65 (0,35) [3; 8,6] 1,82 (0,44) [3.38;
15,72]
1,82 (0,46) [4,23;
14,96]
Unimpeded walking speed [m/s] mean (SD)
[min; max]
1.19 1.82 (0.278) [1.42;
2.25]
1.78 (0.379) [1.3;
2.68]
2.22 (0.158) [1.96;
2.54]
2.09 (0.223) [1.66;
2.34]
S ai case walking speed [m/s] mean [m/s]
(coe icien [−])
1.19 (1) 1.294 (0.71) 1.176 (0.66) 2.22 (1) 2.09 (1)
Accele a ion [s] 1.1 1.1 1.1 0 0
Wall bounda y laye [m] mean (SD) [min; max] 0.15 0.922 (0.245)
[0.559; 1.41]
0.894 (0.279)
[0.465; 1.38]
0.91 (0.333)
[0.387; 1.53]
0.9 (0.284) [0.372;
1.44]
S ai case pilla s bounda y laye [m] mean (SD)
[min; max]
0.15 0.642 (0.183)
[0.409; 0.954]
0.647 (0.211)
[0.37; 1.00]
0.676 (0.239)
[0.29; 1.06]
0.625 (0.242)
[0.286; 1.03]
Decision ime in on o he ba s ime [s]
(dis ibu ion [%])
– 0-5 (33)
5-10 (40)
10-15 (7)
15-20 (13)
45-50 (7)
0-5 (30)
5-10 (30)
10-15 (20)
15-20 (5)
20-25 (10)
50-55 (5)
0-5 (50)
5-10 (27.5)
10-15 (5)
15-20 (12.5)
30-35 (5)
0-5 (25)
5-10 (50)
10-15 (13)
15-20 (6)
35-40 (6)
Decision ime in on o he s ai s on 4. Floo
ime [s] (dis ibu ion [%])
– 0 (86.6)
5 (6.7)
T y o use ele a o
(6.7)
0 (95)
T y o use ele a o
(5)
0 (87)
T y o use ele a o
(13)
0 (93.75)
T y o use ele a o
(6.25)
Decision ime in on o he s ai s on 1. Floo
ime [s] (dis ibu ion [%])
– 0-2 (53)
2-4 (26)
4-6 (14)
8-10 (7)
0-1 (50)
2-4 (25)
4-6 (5)
6-8 (20)
0-2 (55)
2-4 (45)
0-2 (68.5)
2-4 (18.5)
4-6 (13)
Re acing [boolean ] – 20.0% yes
80.0% no
30.0% yes
70.0% no
36.4% yes
63.6% no
43.8% yes
56.2% no
V. Juˇ
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Heliyon 9 (2023) e14275
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(whe e he speed is cons an and limi ed by mo emen con ols), he accele a ion ime was no se o models based on he i ual
condi ion.
- Wall bounda y laye [m]: Du ing he building walk h ough, agen s in models ollow he ideal ajec o y o mo emen , i.e., he mos
spa ially e ec i e pa h. Human mo emen in buildings does no copy his ideal ajec o y. In Re . [56], Gwynne de ines laye s
be ween occupan and s a ic objec s ha can be used o e acua ion modeling. Wall bounda y laye was measu ed a iden i ied
co ne s o he building co ido s (C1-5 in Fig. 1), o which he minimum a oidance was eco ded. A no mal dis ibu ion wi h he
pa ame e s desc ibed in Table 1 was hen applied o he agg ega ed da a, e lec ed by gende .
- S ai case pilla s bounda y laye [m]: The minimum dis ance pa icipan s main ained om he co ne s o he s ai scase pilla s was
moni o ed (S1-12 in Fig. 3). The subsequen de e mina ion p ocedu e o he model inpu was iden ical o ha ela ing o he wall
bounda y laye .
3.2. Building speci ic quan i ies
- Decision ime on p ede ined decision poin s [s]: The decision p ocess is a c ucial human ac o , which has been ound o be simila in
eal and i ual e acua ion expe imen s [51], al hough i is no usually conside ed in agen simula ions [57]. Since he decision
ime and he choice o ou e depend on he speci ic spa ial con igu a ion o he building, we canno abs ac he gene al pa ame e s
applicable o e e y simula ion scena io. Th ee decision poin s (poin s equi ing a cogni i e assessmen o he su ounding si u-
a ion due o a change in di ec ion, obs acles on he ou e, e c.) we e iden i ied and app oxima ed o polygons on he e acua ion
ou e (see Fig. 3). The i s decision poin (A) was a s op a he ba s ha blocked he ou e ha he pa icipan s had p e iously used
o en e he lec u e oom. The second s op (B) was he junc ion on he 4
h
loo , whe e i was possible o u n owa ds he ele a o
(which i was o bidden o use du ing he e acua ion) o go down he s ai s. The hi d decision poin (C) was he poin a he bo om
o he s ai s on he 1
s
loo , whe e he pa hs sepa a ed in o an o icially ma ked e acua ion ou e and a ou e e u ning he same
way he pa icipan s had p e iously en e ed he building. In he s udy o S achoˇ
n e al. [51], he ime [s] ha pa icipan s spen in
hese polygons was moni o ed and used as inpu o ou calcula ions o he models. In addi ion, whe e he pa icipan s made a
longe de ia ion om he ou e a hese poin s (usually owa ds he ele a o ), i was manually in oduced in o he model (see
Table 1).
- Re acing s a egy [boolean]: As wi h he p e ious pa ame e , e en e acing depends on he a ious aspec s o he building,
al hough he a io o people who used he e acing s a egy o lea e he building was simila in he eal and i ual en i onmen s
[51]. Compu ed models e lec he e acing beha io o pa icipan s by assigning he speci ic exi s o indi idual agen s a he las
wai ing poin on he i s loo . The speci ic dis ibu ion is depic ed in Table 1.
3.3. E acua ion model compu a ion
The Pa h inde agen model a he en ance equi es he geome y o he building and allows he se ing o inpu pa ame e s ha
u he dis inguish he cha ac e o indi idual agen s. Way inding is implemen ed by en e ing a se ies o e en s, a he end o which he
building is le by he app op ia e exi . Each e en akes place based on a speci ied p obabili y dis ibu ion, see Table 1. These e en s
include wai ing poin selec ion, walking o wai ing poin s, wai ing, and exi selec ion.
The inpu da a o he simula ions we e gene a ed by he Mon e Ca lo me hod [66]. In each ile, e e y agen was assigned a unique
andom numbe (a so-called andom seed) which gene a ed he new pa ame e alues in each simula ion wi hin he speci ied dis-
ibu ions (e.g., mo emen speed, see Table 1.) o each agen . This mechanism gene a es a ia ions in he ajec o ies o he agen s and
calcula ed e acua ion imes, so he ou comes o he simula ions could be subjec ed o s a is ical analysis. In his s udy, he numbe o
Fig. 2. Me hod o es ima ion o he minimum equi ed numbe o simula ions based on con e gence o o al e acua ion ime and i s s an-
da d de ia ion.
V. Juˇ
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Heliyon 9 (2023) e14275
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simula ions o he VES model was de e mined acco ding o Ronchi’s me hod [67]. To al e acua ion ime con e gence (TET con ) and
s anda d de ia ion con e gence (SD con ) we e de i ed. The o he me ics ha e no been used because hey assume he e acua ion o
a g oup o people, no an indi idual. Th eshold alues we e se up o bo h me ics: TET con - 1%, SD con - 5%. 300 simula ion es
uns we e pe o med o es ima ion o he minimal equi ed numbe o simula ion uns based on his me hod (see Fig. 2). Based on he
con e gence g aph in Fig. 2, he numbe o 150 simula ion uns was de e mined as su icien o u he analysis. I is e iden om he
g aph ha a la ge numbe o simula ions would no longe a ec he a iance in he esul ing e acua ion ime. The chosen numbe o
simula ions includes all beha io al phenomena de ined by he pa ame e s in Table 1, e en hose ha we e no so nume ous (e.g.,
ying o use an ele a o ). In case o models wi h de aul se ings, he inpu pa ame e s a e used wi hou any dis ibu ion, so he e is no
a iabili y in esul ing e acua ion imes. One simula ion is su icien in his case, howe e , 35 simula ions we e pe o med whe e he
missing a iabili y is seen. Eigh examples o hese simula ions a e a ailable in he o m o sho ideos in he Supplemen a y
Ma e ials.
The key ou pu o he simula ions o his s udy was he o al e acua ion ime, since i is he key and o en he only moni o ed
pa ame e in enginee ing p ac ice gene ally conside ed ele an by in es o s and local au ho i ies. In his s udy, e acua ion ime is he
ime om he ala m sounding o eaching he exi and is c ucial o mos e acua ion simula ions. Fo his eason, i was selec ed as an
assessmen c i e ion and hen became he subjec o a compa ison o he ou pu s o he models.
The speci ic geome y o he model was c ea ed based on he 3D building documen a ion (. bx) c ea ed in Re i A chi ec u e (The
same model ha was used o c ea e he i ual en i onmen ). A simpli ied isualiza ion o he e acua ion pa h and adjoining co ido s
can be seen in Fig. 3.
3.4. P oposed co ec ions
In he con ex o his s udy, we conside e acua ion ime a undamen al a iable o po en ial applica ion since i ep esen s he key
and e y o en he only moni o ed pa ame e in enginee ing p ac ice. E acua ion ime is he p incipal ou pu o he models, and as i is
he key measu e in he e acua ion p edic ions. I is p ima ily dependen on walking speed; howe e , i is one o he ac o s whe e he e
is no equi alence when we compa e he esul s ob ained om empi ical VR and eal expe imen [51] due o di e en in e ace
me apho s o mo emen . The inpu da a o his s udy we e aken om a VR expe imen using a s anda d keyboa d-mouse con ol
in e ace, which limi s he possibili y o accele a ion. The pa icipan can ei he s and o mo e a a cons an speed se a 3 m/s, while
he pa icipan s eg essing he eal building we e no limi ed in any way.
The e o e, o he pu poses o his s udy, we applied ma hema ical co ec ions o he compu ed VES model. The i s co ec ed
model (Vi ual E acua ion Se ings Adjus ed - VESA model), was calcula ed using he same inpu da a as o he VES model, excep he
unimpeded and s ai case walking speeds we e adop ed om he da a collec ed in he eal expe imen (a eal e acua ion d ill). The
second co ec ed model (Vi ual E acua ion Se ings De i ed - VESD model) was de i ed om he VES model, in which we co ec ed
he esul ing e acua ion ime by a coe icien calcula ed as:
o al a e age walking speed VE
o al a e age walking speed RE
=2.184 m/s
1.754 m/s
=1.245
Fig. 3. Visualiza ion o he sample e acua ion ajec o y, impo an decision poin s and adjoining co ido s. Blue line illus a es he e acua ion
ajec o y. Co ido s highligh ed in ed we e used o unimpeded walking speed calcula ions. Poin s C1 – C5 ep esen co ido co ne s and poin s S1
– S12 ep esen s ai case pilla s.
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Heliyon 9 (2023) e14275
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The o e all p ocess o model calcula ions and applica ion o co ec ions is depic ed in Fig. 4.
3.5. Models e alua ion
The esul s o he calcula ed model could be e alua ed in ou s eps. In he i s s ep, we compa ed he esul s o he model (VES
model) wi h he model whe e e acua ion simula ions ook place wi h de aul inpu pa ame e s (DS model). In he second s ep, we
e alua ed he model esul s agains empi ical da a collec ed in i ual eali y (VE). Following he same expe imen p ocedu e in bo h
eal and i ual en i onmen s [51] allowed us o e alua e he model esul s also agains da a collec ed in a eal en i onmen (RE).
E en ually we conduc ed he compa isons also o he co ec ed models. The analysis was conduc ed using non-pa ame ic ANOVA
(K uskal-Wallis es ) and pos hoc Dunn’s es s wi h Holm’s p- alue and p- alue adjus men o be ween model compa isons (q- alues).
4. Resul s
In his sec ion, he esul s om he compa ison o he compu ed models a e p esen ed. The analysis was conduc ed using RS udio .
Ap il 1, 1106 [68]. Fo isualiza ions, he ggplo 2 [69] package was used. The esul ing e acua ion imes om all models we e es ed
o no mali y using he Shapi o-Wilk es . Since none o hem exhibi ed no mal dis ibu ion, we chose non-pa ame ic ANOVA
(K uskal-Wallis es ) and pos hoc Dunn’s es s wi h Holm’s p- alue and p- alue adjus men o be ween model compa isons (q- alues).
Fi s , we obse ed ha he simula ion wi h de aul se ings gene a ed a di e en ajec o y wi h no a iance. On he con a y, he
simula ed agen mo emen in he p oposed models o e lapped wi h he en elopes (conca e hulls) o eal mo emen ajec o ies o he
pa icipan s cap u ed in he empi ical expe imen (see Fig. 5). The a iance in ajec o ies was in oduced by using dis ibu ions o
model inpu quan i ies (see Table 1.) This means ha du ing he simula ions, agen s o e ined models isi ed simila spaces in he
building as eal people did, which allows o mo e de ailed in e p e a ions o he eliabili y o he p edic ions.
The eal (RE) and i ual (VE) empi ical obse a ions ep esen ing he beha io (i.e., e acua ion imes) o eal pa icipan s [51] a e
depic ed in he g aph (Fig. 6) nex o compu ed models in ol ing agen s, - i.e., he DS model, he VES model, he VESA model, and he
VESD model. The K uskal-Wallis es indica ed signi ican di e ences in e acua ion imes be ween obse a ions wi h la ge e ec size
(
χ
2 =272.73, d =5, p- alue <0.001,
η
2
=0.485). The speci ic di e ences we e calcula ed be ween indi idual condi ions and a e
depic ed in Fig. 6, wi h he p- alues, q- alues (calcula ed due o mul iple es ing p oblem) and es ima es shown in Table 2. The main
Fig. 4. The diag am o model calcula ion, co ec ion and e alua ion and p ocess.
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Heliyon 9 (2023) e14275
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Fig. 5. Visual compa ison o pa icipan and calcula ed agen ajec o ies.
Fig. 6. Box-plo depic ion o compu ed e acua ion imes om indi idual e acua ion models (De aul Se ings - DS; Vi ual E acua ion Se ings -
VES; Vi ual E acua ion Se ings Adjus ed - VESA; Vi ual E acua ion Se ings De i ed - VESD). G aph is complemen ed wi h he empi ical da a
abou e acua ion imes om he eal (RE) and i ual (VE) en i onmen s. Da a we e compa ed using K uskal-Wallis es and Dunn’s pos hoc es s,
p- alue adjus men s (q- alues) we e calcula ed and epo ed due o mul iple es ing p oblem (ns: non-signi ican , ****: p- alue <0.0001, ***: p-
alue =[0.0001, 0.001], **: p- alue =(0.001, 0.01], *: p- alue =(0.01, 0.05], ou lie s a e de ined as alues >1.5 imes and <3 imes he
in e qua ile ange beyond ei he end o he box).
V. Juˇ
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