B idging o sepa a ing? Co-accessibili y as a measu e o po en ial
place-based encoun e s
Vasileios Milias
*
, Achilleas Psyllidis , Alessand o Bozzon
Depa men o Sus ainable Design Enginee ing, Del Uni e si y o Technology, Del , he Ne he lands
ARTICLE INFO
Keywo ds:
Accessibili y
Mobili y
Pedes ians
Popula ion g oups
Place-based encoun e s
ABSTRACT
Accessibili y is a widely used concep ac oss a ious disciplines o e alua e he deg ee o which indi iduals can
each desi ed des ina ions. Con en ionally, accessibili y is de e mined by he a ac i eness o a des ina ion and
he associa ed a el cos o each i . Howe e , exis ing place-based accessibili y measu es do no di e en ia e
be ween des ina ions accessible o indi iduals om a single demog aphic g oup and hose accessible o in-
di iduals om di e se demog aphic g oups. We p opose a measu e o assess he po en ial o dis inc des ina ions
o b ing di e en indi iduals and demog aphic g oups oge he , de ining his p ope y as co-accessibili y. We
demons a e how measu ing co-accessibili y can enhance exis ing accessibili y measu es, desc ibe i s compo-
nen s, and p o ide a ma hema ical o mula ion o quan i ying i . To illus a e he p ac ical applica ion o ou
measu e, we conduc a case s udy in Ams e dam, he Ne he lands, compa ing he accessibili y and co- accessi-
bili y o a ious des ina ions. This sample case s udy highligh s he complexi ies and challenges inhe en in
measu ing co-accessibili y. Building on exis ing li e a u e and ou analysis esul s, we discuss he po en ial
implica ions o co-accessibili y, iden i y key challenges in i s assessmen , and ecommend di ec ions o u u e
esea ch.
1. In oduc ion
Accessibili y se es as a undamen al concep ac oss di e se disci-
plines, including land-use planning, anspo a ion planning, and u ban
design, whe ein i plays a pi o al ole in assessing he ease wi h which
indi iduals can each essen ial ac i i ies and se ices, oge he e e ed
o as oppo uni ies (Hansen, 1959;Pi ie, 1979;Geu s and Van Wee,
2004;Ba y, 2009;Le ine, 2020;Handy, 2020). The e a e a ious ap-
p oaches o measu ing accessibili y, bu one p e ailing and widely
accep ed p inciple is ha accessibili y is de e mined by he a ac i e-
ness o a desi ed des ina ion and he associa ed cos equi ed o each i
(Handy and Niemeie , 1997;Geu s and Van Wee, 2004;Le inson and
Wu, 2020). The a ac i eness o a des ina ion encapsula es a a ie y o
ac o s, such as he numbe and ype o ac i i ies, ameni ies p o ided, o
employmen oppo uni ies a ailable a ha loca ion. In u n, a el cos
could e e o ime, mone a y expendi u es, o o he cos s equi ed o
an indi idual o each a desi ed loca ion.
The concep o accessibili y, including i s associa ed measu es and
ma hema ical o mula ions, has been u he specialized in o ac i e and
passi e accessibili y. Ac i e accessibili y e lec s he ease wi h which an
indi idual can each a des ina ion o engage in ac i i ies a a speci ic
loca ion (e.g., wo k, educa ion, leisu e). I is he mos p e alen concep-
ualiza ion o spa ial accessibili y and aligns wi h he undamen al de i-
ni ion o Hansen (1959). In con as , passi e accessibili y indica es he
ease wi h which an oppo uni y can be eached by he popula ion (Pi ie,
1979;Papa and Coppola, 2012;Casce a e al., 2013). Despi e hei
conside able po en ial and expanding applica ions, passi e accessibili y
measu es ha e ecei ed limi ed a en ion compa ed o measu es o ac i e
accessibili y (Casce a e al., 2013;Lopes e al., 2019;Lee and Salih,
2024). In bo h cases, he op imiza ion o accessibili y en ails maximizing
he a ac i eness o des ina ions while minimizing he cos s o in-
di iduals o each hem. Ne e heless, his op imiza ion goal exhibi s
ce ain limi a ions. Fo ac i e accessibili y, i canno di e en ia e be-
ween a ious des ina ions being accessible o di e en indi iduals and
he same des ina ion being mu ually accessible o mul iple indi iduals. In
con as , passi e accessibili y measu es can o e come his sho coming by
conside ing he numbe o people who ha e access o each des ina ion.
Howe e , mos passi e accessibili y measu es ha e ano he limi a ion:
hey do no di e en ia e be ween des ina ions accessible o indi iduals
om a single demog aphic g oup and hose accessible o indi iduals om
* Co esponding au ho a : Landbe gs aa 15, 2628CE Del , he Ne he lands.
E-mail add ess: [email p o ec ed] (V. Milias).
Con en s lis s a ailable a ScienceDi ec
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Recei ed 13 May 2024; Recei ed in e ised o m 13 Sep embe 2024; Accep ed 9 Oc obe 2024
Jou nal o T anspo Geog aphy 121 (2024) 104027
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0966-6923/© 2024 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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di e se demog aphic g oups. Gi en ha access o sha ed spaces is c i ical
o physical encoun e s and in e ac ions among di e en indi iduals and
g oups (Le ine e al., 2019;Lanza e al., 2023), hese limi a ions hinde
ou abili y o unde s and he po en ial o des ina ions o acili a e such
encoun e s.
Conside ing he sho comings o bo h ac i e and passi e accessibili y
measu es, his a icle in oduces co-accessibili y as a measu e o e alu-
a ing he ex en o which a des ina ion is mu ually accessible o in-
di iduals om a ious demog aphic g oups (e.g., age, e hnici y,
income). Co-accessibili y accoun s o he di e ences in ac o s in lu-
encing accessibili y o each demog aphic g oup. These ac o s may
include a ailable a el modes, ypes o ac i i ies, and he needs and
p e e ences speci ic o di e en demog aphic g oups o indi iduals. Ou
p oposed measu e can be used o examine seg ega ion phenomena by
ex ending esea ch beyond he usual ocus on esiden ial, wo kplace,
and educa ional en i onmen s (Milias and Psyllidis, 2022). Addi ion-
ally, co- accessibili y me ics could guide he design o des ina ions o
be e mee he p e e ences and needs o he di e se indi iduals and
demog aphic g oups who can access hem.
In he ollowing sec ions, we examine exis ing accessibili y mea-
su es, highligh some o hei inhe en limi a ions, and illus a e how co-
accessibili y migh anscend hese cons ain s. We hen de ine he
undamen al cons i uen s o co-accessibili y and p o ide a ma hema ical
o mula ion o quan i ying i . In highligh ing he in icacies and chal-
lenges in ol ed in he measu emen o co-accessibili y, we use a sample
case s udy o e alua e and compa e pedes ian accessibili y and co-
accessibili y ac oss a ious des ina ions in Ams e dam, he
Ne he lands. D awing upon he exis ing li e a u e and he ou comes o
ou analysis, we in es iga e he po en ial implica ions o co-
accessibili y, unde sco e he main challenges in i s measu emen , and
sugges a enues o u u e esea ch.
2. F om accessibili y o co-accessibili y
The concep ualiza ion o accessibili y and app oaches o measu ing
i a y be ween s udies and ac oss disciplines. A sha ed p inciple d i ing
mos app oaches is ha accessibili y is de e mined by he dis ibu ion o
po en ial des ina ions ac oss space, he cha ac e is ics o hese des ina-
ions, and he ease o eaching hem (Handy and Niemeie , 1997). The
mos common ma hema ical o mula ion o accessibili y in he li e a u e
builds upon he seminal wo k o Hansen (1959), and is de ined by wo
main componen s: he a ac i eness o des ina ions and he associa ed
cos s equi ed o each hem. Following he no a ion o Le inson and Wu
(2020), i s o mula ion is gi en by:
Aj
i=∑
J
j=1
Oj (Cij)(1)
whe e Aj
ideno es he accessibili y o o igin loca ion o zone i o des i-
na ion o zone j;Ojis he des ina ion a ac i eness, o en e lec ing he
numbe o oppo uni ies a ailable a des ina ion j; and (Cij)is he cos
o impedance o each des ina ion j om o igin i. Eq. 1, o mally de ines
ac i e accessibili y bu can be used o bo h ac i e and passi e accessi-
bili y depending on wha zone iand j ep esen (i.e., loca ion o in-
di iduals o oppo uni ies) (Le inson and Wu, 2020).
O e he yea s, nume ous me ics ha e eme ged in he li e a u e ha
expand Hansen's o mula ion, aiming o cap u e he mul i-dimensional
na u e o accessibili y (Wu and Le inson, 2020). Some o hese
ex ended me ics en ich he cos componen (Cij), conside ing di e en
a el modes and a ic condi ions (Moya-G´
omez and Ga ´
cıa-Pal-
oma es, 2015), ime schedules o indi iduals, (H¨
age s and, 1970;
Mille , 1991;Neu ens e al., 2008;Tang e al., 2016), indi idual pe -
cep ions o a el cos s (Ca ion and Le inson, 2019), o how di e en
popula ion subg oups such as mino i ies o pe sons wi h disabili ies
expe ience access (Ma ens, 2016). Addi ionally, he des ina ion
a ac i eness (Oj), ini ially used o e lec he numbe o accessible
des ina ions o jobs in a ea j(Hansen, 1959;Geu s and Van Wee, 2004),
has e ol ed o encompass a wide a ay o ac o s pe aining o why
indi iduals a e a ac ed o pa icula des ina ions. This includes con-
side a ions such as he ype o ac i i ies a a des ina ion, he size and
quali y o acili ies, o indi iduals' li es yle-based p e e ences (Ki amu a
e al., 1997).
To encompass and dis inguish he a ious pe spec i es wi hin
accessibili y- ela ed li e a u e, exis ing measu es ha e been ca ego ized
in se e al ways. Measu es o ei he ac i e o passi e accessibili y can be
u he dis inguished in o place-based and pe son-based measu es
(H¨
age s and, 1970;Mille , 2005;Kwan, 2009). Place-based measu es
assess he spa ial sepa a ion o di e en loca ions. Such loca ions o en
ep esen indi iduals' ancho loca ions (e.g., home o wo k) and key
des ina ions whe e ac i i ies occu . Pe son-based measu es e lec he
ex en o which indi iduals o speci ic g oups can access di e en des-
ina ions while accoun ing o each indi idual's spa ial and empo al
cons ain s.
Le inson and Wu (2020), building on Hansen's o mula ion (Eq. 1),
p oposed a gene alized measu e o accessibili y o encapsula e all he
di e en conside a ions o spa ial accessibili y (Eq. 2). This o mula ion,
while simila o Hansen's Eq. 1, allows a shi om pa ial o gene al
access (Le inson and Wu, 2020) by ep esen ing Ai,Oj, and Cij as
ma ices. These ma ices enable accoun ing o di e en ypes o des i-
na ions, imes o day, ime a ailabili y, a el modes, and all cos s
ela ed o accessing a des ina ion (e.g., money, noise, o conges ion). In
addi ion, unc ion gis used o e lec he unequal alue o des ina ions.
Ai=∑
J
j=1
g(Oj) (Cij)(ac i e)
A↺
i=∑
J
j=1
g(Oj) (Cji)(passi e)
(2)
Bo h ac i e and passi e accessibili y measu es ha e speci ic limi a-
ions. Ac i e accessibili y measu es do no dis inguish be ween di e en
des ina ions being accessible o di e en indi iduals and he same
des ina ion being accessible o mul iple indi iduals, a limi a ion we
e m isola ion accessibili y bias. Passi e accessibili y measu es can
add ess his bias. Howe e , passi e measu es o en e oneously equa e a
des ina ion accessible o indi iduals om a homogeneous g oup o a
des ina ion accessible o indi iduals om di e se demog aphic g oups,
a limi a ion we e m homogenei y accessibili y bias.
To illus a e hese biases, we p esen wo examples inspi ed by he
schema ic ac i i y space ep esen a ion p oposed om Flamm and
Kau mann (2007) and Pe choux e al. (2013) and depic ed in Fig. 1a and
b. This ep esen a ion se es as a means o depic he des ina ions an
indi idual can access using links o deno e people's mobili y pa hs and
nodes o ep esen he des ina ions hey ha e access o.
Fig. 1a illus a es he isola ion accessibili y bias by con as ing wo
cases. On he le , he e a e h ee des ina ions (d1,d2,d3)and each
des ina ion is accessible o one indi idual. On he igh , he same single
des ina ion (d1) is accessible o all h ee indi iduals. While hese wo
cases a e di e en in e ms o he numbe o indi iduals who ha e access
o each des ina ion hey a e no di e en ia ed when solely examining
he numbe o des ina ions each indi idual has access o (one
des ina ion).
Fig. 1b, illus a es he homogenei y accessibili y bias by con as ing
wo di e en cases. The one on he le depic s h ee indi iduals ha ing
access o he same des ina ion. The one on he igh shows h ee in-
di iduals belonging o di e en demog aphic g oups ha ing access o
he same des ina ion. These wo cases a e conside ed iden ical in e ms
o he numbe o indi iduals who ha e access o he same des ina ion
since in bo h cases each des ina ion is accessible o h ee indi iduals.
Howe e , in he igh case, d1is accessible by indi iduals om di e en
demog aphic g oups.
V. Milias e al. Jou nal o T anspo Geog aphy 121 (2024) 104027
2
A possible way o o e come hese limi a ions is by employing a ime-
geog aphy app oach (H¨
age s and, 1970). In ime geog aphy, which
cons i u es he p ima y heo e ical amewo k o concep ualizing pe -
son- based accessibili y (Mille , 2005), an indi idual's accessibili y is
modeled using a space- ime p ism (Mille , 1991). The space- ime p ism
ep esen s he possible mo emen s o an indi idual h ough bo h space
and ime, conside ing ac o s such as pe sonal mobili y cons ain s and
ime schedules (Song e al., 2017). The in e sec ion o mul iple in-
di iduals' space- ime p isms ac oss he con inuous geog aphic space has
been concep ualized h ough join accessibili y (Neu ens e al., 2008;
Fa be e al., 2013, 2015).
In his wo k, we add ess he abo e-men ioned accessibili y biases by
p oposing co-accessibili y as a place-based measu e ha assesses a des-
ina ion's po en ial o b ing oge he di e en indi iduals and in-
di iduals om di e se demog aphic g oups by being accessible o hem.
I conside s spa ial cons ain s wi hou accoun ing o indi idual ime
cons ain s. This allows o i s measu emen wi hou being hinde ed by
he equi emen o de ailed da a on he p ecise na u e o an indi idual's
(comple ed) ac i i y pa e ns and ips, and he associa ed p i acy and
e hical conce ns (Pi ie, 1979;Lopes e al., 2019;B um-Bas os and Paez,
2023). To add ess he isola ion accessibili y bias, he co-accessibili y o a
des ina ion is de e mined by he numbe o indi iduals who ha e access
o ha des ina ion. To add ess he homogenei y accessibili y bias we need
o conside he indi iduals' demog aphic g oups and he co-accessibili y
o a des ina ion is de e mined by he numbe o indi iduals who ha e
access o ha des ina ion and he numbe o demog aphic g oups hese
indi iduals belong o.
In Fig. 2, we p esen six dummy examples o illus a e how measu ing
accessibili y and co-accessibili y could enable us o examine he deg ee o
which a ious des ina ions a e accessible o di e en indi iduals and
demog aphic g oups. In all ou examples we conside i e indi iduals
(Pn= {p1,p2,p3,p4,p5}) and h ee des ina ions (Dn= {d1,d2,d3}).
Fu he mo e, in hese examples, in alignmen wi h he commonly ound
o mula ion o accessibili y, o a des ina ion o be conside ed accessible
by an indi idual wo condi ions mus be me : he indi idual needs o be
able o each he des ina ion (low a el cos ) and o conside he des i-
na ion a ac i e (high des ina ion a ac i eness). To depic he accessi-
bili y o a des ina ion by an indi idual, meaning ha he indi idual can
each he des ina ion and conside s i a ac i e, we u ilize lines ha
connec he indi idual o he co esponding des ina ion.
The co-accessibili y o a des ina ion is indica ed based on wo
numbe s: he numbe o indi iduals who ha e access o ha des ina ion,
Fig. 1. Isola ion and Homogenei y accessibili y biases.
V. Milias e al. Jou nal o T anspo Geog aphy 121 (2024) 104027
3
and he numbe o demog aphic g oups o which he indi iduals wi h
access o ha des ina ion belong. The pu pose o hese examples is o
unde sco e he dis inc ions be ween he ou comes o (ac i e o passi e)
accessibili y and co-accessibili y measu es, and o demons a e how co-
accessibili y could add ess he isola ion and homogenei y accessibili y
biases p esen ed in Fig. 1a and b.
In examples (I) - (III) illus a ed in Fig. 2, we examine he limi a ions
o ac i e and passi e place-based accessibili y measu es owa ds
indica ing he deg ee o which des ina ions a e accessible o di e en
(g oups o ) indi iduals. In example (I), ollowing an ac i e accessibili y
app oach, each indi idual has access o one des ina ion and all h ee
des ina ions d1,d2, and d3a e conside ed o be equally accessible o
di e en (g oups o ) indi iduals. In example (II), ollowing a passi e
accessibili y app oach, des ina ions d2and d3a e accessible o wo in-
di iduals, while d1is accessible o only one indi idual. Mo eo e , des-
ina ions d2and d3a e equally accessible o di e en indi iduals and
Fig. 2. Dummy examples used o illus a e how accessibili y and co-accessibili y measu emen s can indica e he deg ee o which di e en des ina ions a e accessible
o a ious indi iduals and demog aphic g oups.
V. Milias e al. Jou nal o T anspo Geog aphy 121 (2024) 104027
4
g oups. In example (III), we illus a e he p oposed co-accessibili y
measu e, by ex ending passi e accessibili y o accoun o he di e en
demog aphic g oups. In his case, d2and d3a e accessible o wo in-
di iduals while d1is accessible o only one indi idual. When we u he
look a he demog aphic g oup o each indi idual, we also obse e ha
only d2is accessible o indi iduals om di e en demog aphic g oups
( ed and g een) since d1and d3a e accessible o only one g oup, ed and
blue espec i ely.
In examples (IV) —(VI) shown in Fig. 2, we demons a e how u he
adjus ing he co-accessibili y measu e could p o ide a mo e e ined
indica ion o he deg ee o which des ina ions a e mu ually accessible o
di e en (g oups o ) indi iduals. Beginning wi h example (IV), simila
o (III), des ina ions d
2
and d
3
a e mu ually accessible o wo indi iduals
while d
1
is accessible o only one indi idual. Looking a he numbe o
g oups who ha e access o each des ina ion, we obse e ha d2is
mu ually accessible by wo g oups, while d1and d
3
a e accessible by
only one g oup. Thus, d2exhibi s a highe deg ee o co-accessibili y
o e all.
To measu e he co-accessibili y o a des ina ion while conside ing
he indi iduals' demog aphic g oups, we also p opose o accoun o he
ac o s ha impac he a el cos o each i and a e sha ed among he
people o each demog aphic g oup (e.g., in he case o pedes ians
belonging o di e en age g oups we would need o conside he
di e en walking speeds (Schimpl e al., 2011)). Ce ainly, wi hin he
same demog aphic g oup, indi idual di e ences s ill exis . None heless,
by ailo ing he ac o s ha impac accessibili y by each popula ion
g oup, we gain a mo e nuanced unde s anding o co-accessibili y
compa ed o ea ing all g oups as iden ical while a oiding he exces-
si e complexi y o conside ing each indi idual's unique p e e ences. In
example (V), we adjus he a el cos pe g oup o show how his
conside a ion could al e co-accessibili y. Fo ins ance, his adjus men
could accoun o he di e ences in walking speeds, a he han
assuming uni o m speeds o all, by conside ing a ia ions among chil-
d en, adul s, and he elde ly. We illus a e he adjus ed a el cos s,
using g oup-based colo s o each line. In his case, he des ina ion ha
shows he highes deg ee o co-accessibili y is d
2
.d
2
is mu ually acces-
sible by h ee indi iduals all belonging o di e en g oups. Then, d
1
ollows, which is mu ually accessible by wo indi iduals, also belonging
o di e en g oups ( ed and g een). Las is d
3
, a des ina ion only
accessible by a single indi idual.
Finally, we also accoun o he ac o s ha impac he a ac i eness
o each des ina ion and a e sha ed among he people o each de-
mog aphic g oup (Ki amu a e al., 1997) (e.g., playg ounds a e mo e
a ac i e o child en han o he elde ly). In example (VI), we u he
adjus he des ina ion a ac i eness pe g oup o show how his
conside a ion could al e co-accessibili y. We illus a e he adjus ed
des ina ion a ac i eness, using g oup-based colo s o each des ina-
ion. In his case, d
1
is mu ually accessible by wo indi iduals, also
belonging o wo di e en g oups, and i is he des ina ion wi h he
highes deg ee o co-accessibili y. Then, des ina ions d
2
and d
3
ollow,
each being accessible by only one indi idual.
3. Ma hema ical o mula ion o co-accessibili y
In his sec ion, we p opose a ma hema ical o mula ion o co-
accessibili y. To measu e he co-accessibili y o a des ina ion d o in-
di iduals om di e en demog aphic g oups, we i s need o measu e
he accessibili y o d o each demog aphic g oup g. As illus a ed in
Fig. 2, his in ol es conside ing ac o s ha in luence he a ac i eness
o dand he a el cos s associa ed wi h eaching i , which a e assumed
o be sha ed among membe s o each demog aphic g oup g. As
men ioned in he p e ious sec ion, indi idual dis inc ions pe sis e en
wi hin he same demog aphic g oup. Howe e , by adjus ing he ac o s
in luencing accessibili y o each g oup, we ob ain a mo e nuanced
unde s anding o co-accessibili y compa ed o ea ing all g oups as
iden ical, while a oiding he excessi e complexi y associa ed wi h
conside ing he unique needs and p e e ences o each indi idual. Thus,
wi hin he o mula ion o co-accessibili y, he a el cos depends on he
loca ion o he pe son pj∈gin ela ion o he des ina ion dand on
ac o s ha impac a eling and a e sha ed among he people who
belong in g oup g(e.g., income le el, a ailable a el modes, walking
speed, e c). Simila ly, he a ac i eness o a des ina ion depends on
ac o s ha impac how a ac i e des ina ion dis conside ed and a e
sha ed among he membe s o g oup g.
The passi e accessibili y o a des ina ion d o nindi iduals who
belong o he same demog aphic g oup g, allows us o add ess he
isola ion accessibili y bias p esen ed in Fig. 1a by exp essing he deg ee o
which dis mu ually accessible by membe s o gand is o mula ed as:
cd
g=h(Ad
p1,Ad
p2,…,Ad
pn),∀pj∈g(3)
whe e cd
gdeno es he (passi e) accessibili y o des ina ion d o in-
di iduals om g oup g. Ad
pjis he accessibili y o des ina ion d o a
pe son pj om g oup g (Eq. 2). Ad
pjis de e mined by ac o s ha impac
how a ac i e a des ina ion is conside ed and a e sha ed among he
people om g oup g, he loca ion o he pe son in ela ion o he des i-
na ion and ac o s ha impac a eling and a e sha ed among he
people om g oup g.Ad
pjcan adop a ious ypes o accessibili y mea-
su es depending on he unde lying assump ions made, as explained by
Le inson and Wu (2020).h ep esen s a unc ion ha is used o agg e-
ga e he accessibili y o des ina ion dby each pj∈gand p o ides he co-
accessibili y o des ina ion dby all indi iduals. We pu pose ully pe mi
h o be non-linea and ou pu di e en ypes o esul s such as single
alues (e.g., om summa ion) o dis ibu ions (e.g., om p obabili y
dis ibu ion unc ions). By emb acing non-linea i y in ou app oach, we
aim o p o ide a e sa ile o mula ion ha can yield a spec um o e-
sul s, ca e ing o he demands o analyzing co-accessibili y ac oss
di e en scena ios and con ex s. Fo ins ance, hcould be a summa ion
and p o ide he o al nube o people who ha e access o a des ina ion.
This app oach is commonly seen in passi e accessibili y measu es (Lee
and Salih, 2024;Lopes e al., 2019). When de eloping a co-accessibili y
measu e, h can be ailo ed o accoun only o indi iduals belonging o a
speci ic demog aphic g oup (e.g., he numbe o child en wi h mu ual
access o a pa k). In ha case, Eq. 2can also be adjus ed o he g oup
unde s udy. Al e na i ely, h could ep esen a p obabili y dis ibu ion
unc ion, p o iding insigh s in o he likelihood ha indi iduals om
demog aphic g oup g will access a des ina ion, We e e o Eq. 3as
g oup-based co-accessibili y, which essen ially se es as a specialized
passi e accessibili y measu e.
Finally, he co-accessibili y o a des ina ion d o indi iduals
belonging o a se o nmu ually exclusi e demog aphic g oups G(e.g.,
[child en, adul s, olde pe sons] o [low income, medium income, high
income]), Cd
Gallows us o add ess he homogenei y accessibili y bias p e-
sen ed in Fig. 1b and can be o mula ed as:
Cd
G=H(cd
g1,cd
g2,…,cd
gn),∀gi∈G(4)
whe e His he unc ion used o agg ega e he co-accessibili y alues o
des ina ion d o each g oup in G, esul ing in he o e all co-accessibili y
o he des ina ion o all g oups in G. Like h, he selec ion o H.
depends on he con ex o he p oblem being s udied. H aims o
add ess he homogenei y bias and allows o he di e en ia ion o des-
ina ions based on hei accessibili y o indi iduals om di e en de-
mog aphic g oups. The e o e, H can be chosen o e lec he di e si y o
he people who ha e access o a des ina ion acco ding o hei de-
mog aphic g oup. Examples o widely known di e si y indices ha can
be used include Shannon's Equi abili y Index (Shannon, 1948), Simp-
son's Di e si y Index (Simpson, 1949), and he Gini Index (Gini, 1912).
Al e na i ely, o simplici y, H could be a summa ion e lec ing he
numbe o di e en demog aphic g oups wi h access o d.
V. Milias e al. Jou nal o T anspo Geog aphy 121 (2024) 104027
5
4. Sample case s udy
We employ a ep esen a i e case s udy o demons a e how he
p oposed co-accessibili y measu e can be compa ed wi h and comple-
men he mo e commonly used ac i e accessibili y measu es. The
simpli ied co-accessibili y measu e we use does no encompass all he
ac o s in luencing co-accessibili y as discussed in ea lie sec ions. I s
aim is o acili a e a discussion on he applicabili y o co-accessibili y
and o highligh he in icacies and challenges in ol ed in i s
measu emen .
Ou case s udy is de ined by ou key aspec s: he a ea o analysis, he
a el mode, he demog aphic a ibu es, and he ype o des ina ions
in ol ed. The a ea o analysis is he ci y o Ams e dam in he
Ne he lands. We chose Ams e dam due o i s di e se a ay o neigh-
bo hoods, which include bo h his o ic and mo e ecen ly de eloped
a eas. Addi ionally, Ams e dam ea u es a mix o pedes ian- iendly
s ee s and ba ie s, such as canals and high- a ic oads. As o he
a el mode, ou ocus is on pedes ians. Walking is chosen as i is he
mos a o dable and accessible a el mode o indi iduals o i ually
e e y popula ion g oup, i is a sus ainable means o anspo , and i has
been shown o posi i ely con ibu e o people's well-being. The de-
mog aphic cha ac e is ic we examine is age. The need o u ban spaces
ha b ing people o di e en ages oge he and encou age in e gene -
a ional encoun e s is uni e sal and ele an o mos coun ies and ci ies,
as unde sco ed by he Uni ed Na ions' Sus ainable De elopmen Goal
11.7 (UN Gene al Assembly, 2015). The selec ion o des ina ions is
guided by he concep o hi d places in oduced by Oldenbu g (1989),
encompassing enues whe e indi iduals o di e en ages can encoun e
each o he beyond he ealms o home and wo k. Speci ically, we
selec ed des ina ions ha a e accessible o indi iduals o all ages, such as
pa ks, playg ounds, and museums while delibe a ely excluding enues
ha impose age es ic ions o access, such as casinos o nigh clubs.
4.1. Measu ing accessibili y &co-accessibili y
To assess accessibili y and co-accessibili y, we employ an isoch one-
based measu e. Isoch ones show wha des ina ions can be eached om
an o igin loca ion wi hin a gi en a el cos h eshold (El-Geneidy and
Le inson, 2007;Le inson and Wu, 2020). Isoch ones a e selec ed
because o hei simplici y and ease o in e p e a ion, cha ac e is ics
ha also con ibu e o hei widesp ead adop ion by p ac i ione s
(O'Sulli an e al., 2000).
We make h ee main assump ions. Fi s , we conside all des ina ions
in ou analysis equally a ac i e o all g oups. Second, we assume all
people walk a he same speed: 1.26 m/s (i.e., he a e age o di e en
age g oups, as measu ed by Schimpl e al. (2011)). The eason o no
adjus ing he walking speed pe age g oup is ha conside ing he lowes
(1.2 m/s) and highes (1.29 m/s) a e age walking speeds ound by
Schimpl e al. (2011) would only esul in a di e ence o 81 m wi hin a
15-min walk. This di e ence canno be e lec ed in ou es ima ions due
o he spa ial esolu ion o he employed popula ion da a (100 ×100m
g id cells). Thi d, ega ding he a el cos we only accoun o he
walking ime and conside accessible e e y loca ion a pe son can each
wi hin a 15-min walk om hei home. We op ed o he 15-min walking
dis ance h eshold because i is inc easingly u ilized bo h in esea ch
and in p ac ice, wi h se e al ci ies in eg a ing i in o hei u ban plan-
ning s a egies in ecen yea s (Weng e al., 2019;Willshe , 2020;
Mo eno e al., 2021;Pozoukidou and Cha ziyiannaki, 2021;Caselli
e al., 2022). Howe e , we acknowledge ha assigning any ime
h eshold is somewha a bi a y in na u e. Based on hese h ee as-
sump ions, he accessibili y o a des ina ion d by an indi idual pj∈gis
o mula ed as:
Ad
pj={1i walking − ime be weend and pj≤15 minu es
0i walking − ime be ween d and pj≥15 minu es (5)
To iden i y which des ina ions a e accessible o each indi idual, we
model he pedes ian s ee ne wo k as a g aph, wi h nodes ep esen ing
s ee in e sec ions and edges ep esen ing s ee segmen s. We hen
o e lay a g id laye (100 ×100m) indica ing esiden ial a eas and
de e mine he closes in e sec ion o he cen e o each g id cell. These
in e sec ions ep esen indi iduals' home loca ions. Nex , we calcula e
15-min walking ips om hese home loca ions, conside ing he leng h
o each s ee segmen and he a e age walking speed de ined ea lie .
This p ocess allows us o measu e all des ina ions wi hin he each o
hese walking ips o each indi idual.
To measu e he co-accessibili y o a des ina ion by a pa icula g oup
we need o de ine he unc ion has shown in Eq. 3. In ou analysis, we
de ine has a summa ion o align wi h he a o emen ioned isoch one-
based measu emen o accessibili y. Thus, he g oup-based co-accessi-
bili y o a des ina ion by he nindi iduals om g oup gis o mula ed as:
cd
g=∑
n
j=1
Ad
pj,∀pj∈g(6)
A e ha ing calcula ed he co-accessibili y o des ina ions pe g oup
we can calcula e he co-accessibili y o each des ina ion by all g oups. To
do so, we need o de ine he unc ion deno ed as Hin eq. 4. In ou case,
we a e in e es ed in he deg ee o which a des ina ion is mu ually
accessible by a se Go ndi e en age g oups (g1is child en, g2is adul s,
g3is elde ly). The e o e, His chosen o ep esen he age di e si y o he
people who can access each des ina ion by means o Shannon's Equi a-
bili y Index (Shannon, 1948). Shannon's Index is selec ed as i is among
he mos commonly used di e si y indices and summa izes in a single
numbe a pa ial desc ip ion o species ichness and e enness (Daly
e al., 2018;Mendes e al., 2008). Thus, Eq. 4is now:
Cd
G=
−∑
n
i=1
Pd
gi×lnPd
gi
ln(n),∀gi∈G(7)
whe e Pd
giis he a io o he co-accessibili y o dby each age g oup (cd
gi)
o e he o al numbe o indi iduals wi h access o d(∑n
i=1cd
gi);nis he
coun o age ca ego ies. The Cd
G alues ange om 0 o 1, wi h 1 indi-
ca ing a pe ec balance in he p opo ions o each age ca ego y.
4.2. Da a
We use h ee di e en ypes o da a: popula ion demog aphics,
pedes ian s ee ne wo k da a, and loca ion-based da a. S a ing wi h
he popula ion demog aphics, o collec in o ma ion e lec ing peoples'
esidence loca ion and age we use he Du ch Cen aal Bu eau oo de
S a is iek (2020) (spa ial esolu ion o 100 ×100m). The collec ed da a
pe ain o he yea 2020. In o al, he popula ion demog aphics da a
include 6949 g id cells e lec ing he en i e Ams e dam. We g oup es-
iden s in o h ee popula ion age ca ego ies: child en (0–15 yea s old),
adolescen s and adul s (16–64 yea s old), and he elde ly (equal o abo e
65 yea s o age).
The da a ela ed o he pedes ian ne wo k e lec s ee s ha a e
conside ed o pedes ians such as sidewalks and pedes ianized s ee s.
We ob ain his in o ma ion om OpenS ee Map (2021), by collec ing
he s ee s o which he ne wo k_ ype is se o “walk”using he OSMNX
package (Boeing, 2017). Thus, we only collec s ee s o pedes ians and
exclude s ee s such as mo o ways, bike lanes, o se ice oads. The
s ee ne wo k o OpenS ee Map has been de e mined o be app oxi-
ma ely 83 % comple e in o e 40 % o coun ies wo ldwide (Ba ing on-
Leigh and Milla d-Ball, 2017). When ocusing on he pedes ian s ee
ne wo k s udies ha e sugges ed ha OpenS ee Map da a p o ide a ee
and adequa e al e na i e in si ua ions whe e comme cial pedes ian
da a se s a e no a ailable (Ziels a and Hochmai , 2012). The da a
collec ion was ealized in No embe 2021. The collec ed s ee segmen s
V. Milias e al. Jou nal o T anspo Geog aphy 121 (2024) 104027
6
lie wi hin he adminis a i e bounda ies o Ams e dam, as delinea ed
om he open Du ch land use da ase Basis egis a ie G oo schalige
Topog a ie (BGT) (Kadas e , 2020), ex ended by a bu e o 1 km o
minimize po en ial bounda y e ec s (Hillie e al., 1993).
Las ly, he loca ions a e also collec ed om OpenS ee Map. In
pa icula , we selec and collec loca ions ha lie wi hin he adminis-
a i e ci y bounda ies o Ams e dam ex ended by a bu e o 1 km and
come om he ollowing p ima y ea u e g oups: Ameni y,En e ainmen ,
A s &Cul u e,Leisu e, o Shop. OpenS ee Map has been conside ed a
alid sou ce o such da a wi h an accep able le el o comple eness
(Zhang and P ose , 2019;Koukole sos e al., 2012;Logan e al., 2021).
The da a collec ion p ocess was ealized in Sep embe 2021. In o al, we
collec ed 10,483 loca ions.
4.3. Resul s
The esul s o he measu emen s o pedes ian accessibili y and co-
accessibili y a e illus a ed o e h ee ypes o maps. Fi s , he maps o
pedes ian (ac i e) accessibili y highligh he numbe o des ina ions
accessible om each g id cell wi hin a 15-min walk. Acco ding o Eq. 5,
hese maps show he o al numbe o accessible des ina ions o each
g id cell included in ou analysis. Second, he maps o pedes ian co-
accessibili y pe g oup (cd
g) (passi e accessibili y) display he o al
numbe o people wi hin a speci ic age g oup who can access a des i-
na ion, es ima ed using Eq. 6. Thi d, he maps o he co-accessibili y o
each des ina ion om all g oups (Cd
G) e lec he age di e si y o he
people wi h access o each des ina ion, as calcula ed h ough Eq. 7.
Fo he isualiza ions, we i s calcula e he a e age accessibili y o
(a) Accessibili y o des ina ions om each g id cell wi hin a 15-
minu e walk.
Numbe o accessible des ina ions wi hin a 15-minu e walk om each
g id cell.
•
Highe han a e age (>340)
•Nea -a e age (240 ±100)
•
Lowe han a e age (<140)
(c) Co-accessibili y o each des ina ion based on he age di e si y o
he people who ha e access o i wi hin a 15-minu e walk.
Des ina ions’ age di e si y based on he indi iduals who ha e access
o hem wi hin a 15-minu e walk.
•
Highe han a e age (>0.66)
•
Nea -a e age (0.61 ±0.05)
•
Lowe han a e age (<0.56)
(b) Local spa ial au oco ela ion (Mo an’s I) o he numbe o
accessible des ina ions om each g id cell wi hin a 15-minu e
walk.
Numbe o accessible des ina ions wi hin a 15-minu e walk om each
g id cell.
•High alues
•No signi ican
•Low alues
(d) Local spa ial au oco ela ion o he age di e si y o he people
who ha e access o each des ina ion wi hin a 15-minu e walk
(Mo an’s I).
Des ina ions’ age di e si y based on he indi iduals who ha e
access o hem wi hin a 15-minu e walk.
•
High alues
•
No signi ican
•
Low alues
Fig. 3. Accessibili y and co-accessibili y (based on age di e si y) o di e en a eas in Ams e dam.
V. Milias e al. Jou nal o T anspo Geog aphy 121 (2024) 104027
7
all g id cells and he a e age co-accessibili y o all des ina ions. Then we
clus e ou alues in h ee g oups and colo hem acco dingly: Highe
han a e age,Nea -a e age, and Lowe han a e age. To iden i y he s a-
is ically signi ican clus e s o high and low alues we u he c ea e a
connec i i y ma ix using queen con igui y-based spa ial weigh s and
measu e he spa ial au oco ela ion using Mo an's I co ela ion
coe icien .
4.4. Compa ison o accessibili y and co-accessibili y
We display ou a ea-based esul s h ough Figs. 3 and 4. Panels 3a
and 3b highligh he spa ial inequi ies in accessibili y. In pa icula ,
panel 3a shows he numbe o accessible des ina ions wi hin a 15-min
walk om each g id cell and 3b u he unde pins he spa ial clus e s
o g id cells wi h a signi ican ly high (o low) numbe o accessible
des ina ions, compa ed o he mean. Then, panels 3c and 3d p esen he
des ina ions' co-accessibili y in e ms o how age-di e se is he se o
people who ha e access o each des ina ion. Fig. 4 ollows he same
s uc u e while ocusing on he accessibili y and co-accessibili y o
di e en a eas pe age g oup (i.e., child en and elde ly).
As indica i e examples, we conside h ee a eas deno ed as A,B, and
C. People esiding in a ea Aha e access o he highes numbe o des-
ina ions in compa ison o any o he a ea. Indica i ely, people in he
icini y o Aha e access o a signi ican ly high numbe o des ina ions
compa ed o o he a eas, as can be seen om panel 3b, anging om
a ound 2250 o 400.
Rega ding co-accessibili y, he des ina ions loca ed in a ea Aa e
accessible wi hin a 15-min walk by a signi ican ly low o nea a e age in
e ms o age-di e si y se o people compa ed o o he des ina ions as
depic ed in panels 3c and 3d. These esul s a e also suppo ed when
looking a he g oup-based co- accessibili y (panels 4a—d): he des i-
na ions wi hin he Aa ea a e accessible by a signi ican ly lowe numbe
o child en, compa ed o he mean. Thus, by compa ing he esul s o
accessibili y and co-accessibili y o he a ea Awe see ha a highe
numbe o accessible des ina ions does no di ec ly ansla e o a highe
numbe o des ina ions ha a e simul aneously accessible by mul iple
age g oups.
The people esiding wi hin he Ba ea, ha e access o a mo e limi ed
ange o des ina ions ypically a ying be ween 10 and 180. In ce ain
cases, he numbe o accessible des ina ions is s a is ically signi ican ly
Fig. 4. Accessibili y and co-accessibili y (based on child en and elde ly) o di e en a eas in Ams e dam.
V. Milias e al. Jou nal o T anspo Geog aphy 121 (2024) 104027
8
lowe han he mean, as indica ed by panel 3b. Rega ding co-
accessibili y, he des ina ions wi hin a ea Ba e mu ually accessible by
a signi ican ly b oade age ange o people compa ed o o he des ina-
ions. Rega ding he numbe o child en who ha e access o he des i-
na ions in ha a ea, we can obse e di e se esul s wi h small clus e s o
des ina ions ha a e accessible o ei he a nea -a e age o signi ican ly
highe numbe o child en. When looking a he elde ly, we see esul s
ha a e close o he mean.
Simila ly o he Ba ea, he people esiding wi hin he Ca ea ha e
access o a s a is ically signi ican ly lowe numbe o des ina ions,
compa ed o he mean, as shown in panel 3b. When looking a co-
accessibili y, he es ima ed age di e si y alues o he des ina ions
wi hin a ea Ca e no signi ican ly highe o lowe han hose o o he
des ina ions. Howe e , when ocusing on speci ic g oups we obse e
ha he des ina ions wi hin he Ca ea, a e ound o be accessible by a
signi ican ly low numbe o elde ly.
In summa y, he esul s o accessibili y and co-accessibili y p o ide
complemen a y insigh s. While accessibili y p o ides in o ma ion
ega ding he ex en o which des ina ions a e accessible o people, co-
accessibili y indica es he deg ee o which he des ina ions o each a ea
p omo e encoun e s among indi iduals belonging o he same age g oup
( ackling he isola ion accessibili y bias) o di e en age g oups ( ackling
he homogenei y accessibili y bias) by being accessible o hem.
5. Discussion and conclusion
This wo k lays he g oundwo k o a me hodological amewo k o
measu ing co-accessibili y, which assesses he deg ee o which a ious
des ina ions a e mu ually accessible o indi iduals om di e en de-
mog aphic g oups. We demons a ed how a measu e o co-accessibili y
could enhance adi ional accessibili y me ics and alle ia e inhe en
biases such as he isola ion and homogenei y bias. We also ou lined he
componen s o co-accessibili y and p oposed a ma hema ical o mula-
ion o i s measu emen . In he ollowing pa ag aphs, we highligh
po en ial oppo uni ies and p ospec i e measu emen challenges o
suppo u u e esea ch endea o s in ela ed ields.
Co-accessibili y is a place-based measu e ha sha es some concep-
ual simila i ies wi h passi e accessibili y and o he pe son-based mea-
su es such as join accessibili y. The ad an age o pe son-based
measu es is ha hey conside bo h spa ial and ime cons ain s. How-
e e , hei implemen a ion in eal-wo ld case s udies can be challenging
due o he need o de ailed da a on indi idual spa io empo al ac i i y
pa e ns. Addi ionally, i is cumbe some o apply such measu es when
e alua ing u u e spa ial planning in e en ions since hey ely on da a
om pas ac i i ies and ips. These challenges ha e been well-
documen ed in he li e a u e (P ed, 1977;Pi ie, 1979). Co-
accessibili y o e s an al e na i e o examining how mu ually acces-
sible des ina ions a e o di e en indi iduals and demog aphic g oups
when de ailed da a canno be collec ed due o ime o mone a y cos s o
should no be collec ed because o e hical conce ns.
We in oduced co-accessibili y as a b oad concep bu subsequen ly
na owed ou ocus o measu e and apply i in a sample case s udy.
Speci ically, we measu ed co-accessibili y by ocusing on a single mode
o a el, namely walking, and a gi en demog aphic, namely age.
Ne e heless, co-accessibili y can be applied ac oss any mode o a el
o demog aphic g oup. Fo ins ance, when conside ing o he de-
mog aphic g oups, co-accessibili y could be aluable o s udying
seg ega ion phenomena, ypically cen e ed on e hnici y (Rea don and
O'Sulli an, 2004), income (Vaughan and A baci, 2011), o educa ion
le el (Go don and Monas i io is, 2006) by enabling o go beyond he
commonly s udied domains o esiden ial (Cha les, 2003), wo kplace
(Helle s ein and Neuma k, 2008), and educa ional se ings (F ankel and
Volij, 2011).
Simila ly, measu es o co-accessibili y could be employed o
compa e he e ec i eness o public anspo a ion sys ems in os e ing
place-based encoun e s. Such an examina ion could del e in o
unde s anding how conside ing di e en modes o a el, such as public
anspo a ion, p i a e ehicles, o cycling impac s co-accessibili y. This
app oach could p o ide insigh s in o he social dynamics acili a ed by
di e en anspo a ion modes and expand exis ing esea ch on he
impac o public anspo on social encoun e s (Lyons and Cha e jee,
2008;Bissell, 2016).
Mo eo e , measu es o co-accessibili y can be le e aged o guide he
design o des ina ions o be e mee he wan s and needs o hose who
can each hem. This app oach can help o add ess issues o spa ial
inequali y and spa ial jus ice by ensu ing equi able access o essen ial
se ices and oppo uni ies o all demog aphic g oups. S udying he co-
accessibili y ac oss di e en des ina ions migh also p o ide a nuanced
unde s anding no only o he capaci y o des ina ions o acili a e en-
coun e s among di e se indi iduals bu also o he in insic cha ac e -
is ics o a eas ha nu u e his po en ial. These cha ac e is ics ex end o
he su oundings o he des ina ions which, as Jane Jacobs a gued, can
gene a e mu ual suppo and “complex pools o use” ha encou age
people o use des ina ions a di e en imes o he day (Jacobs, 1961;
Talen, 2010). Addi ionally, p ospec i e in e en ions o u ban design
scena ios can be con e ed in o inpu da a o he p oposed measu e o
assess hei impac s on co-accessibili y. Howe e , his unde aking mus
be app oached wi h cau ion, as he e is a isk o de eloping u ban
des ina ions ailo ed o he p edominan popula ion g oups ha ha e
access o hem, inad e en ly ma ginalizing o he popula ion subg oups
(Rishbe h, 2001).
Las ly, ou sample case s udy highligh ed he complexi ies associa ed
wi h he measu emen o co- accessibili y, e ealing inhe en challenges
ha should be add essed. We iden i y h ee main challenges o
measu ing co-accessibili y. The i s challenge s ems om he necessi y
o iden i y and measu e he ac o s in luencing accessibili y o a ious
demog aphic g oups. This is illus a ed h ough examples (IV)-(VI) in
Fig. 2, whe e we adjus he a el cos and des ina ion a ac i eness pe
g oup. While i is impo an o accoun o demog aphic dispa i ies, i is
challenging o simul aneously iden i y and measu e such di e ences in a
ime and cos -e ec i e manne . The ac o s ha in luence accessibili y
a e g oup-speci ic, many, and in e wined (Ga giulo e al., 2018;Me lin
e al., 2021). As a esul , he e is he challenging ask o disen angling
he impac o each ac o and p io i izing hem o he di e en g oups.
Mo eo e , some ac o s can be e y subjec i e and hus di icul o
cap u e, pa icula ly when adjus ing o he di e en demog aphic
g oups. Fo ins ance, when conside ing pedes ian co-accessibili y, such
ac o s can be he pe cei ed sa e y o he a ac i eness o a s ee which
can in luence whe he a pe son can walk o a des ina ion (Ewing and
Handy, 2009;Milias e al., 2023).
Second, he p oposed ma hema ical o mula ion o co-accessibili y
(exp essed h ough Eq. 3 and 4) is pu pose ully qui e b oad, encom-
passing mo e o a concep ual o mula ion, aiming o guide and inspi e
he de elopmen o new con ex -speci ic co-accessibili y measu es,
a he han a “ eady- o- ollow” ecipe one can use o measu e co-
accessibili y. To apply a co-accessibili y measu e h ee main ques ions
need o be answe ed i s : How o measu e accessibili y (Eq. 2)? How o
agg ega e he accessibili y o a des ina ion o di e en indi iduals
belonging o he same g oup (Eq. 3)? How o agg ega e he co-
accessibili y o a des ina ion o mul iple g oups (Eq. 4)? Es ablishing a
consis en selec ion p ocess p o ocol o de ining hese unc ions p o es
challenging, as his decision is in luenced by a a ie y o ac o s such as
he con ex (e.g., demog aphics), he da a a ailabili y, and he speci ic
aspec o he p oblem unde in es iga ion (e.g., assessing co-
accessibili y s a ically o dynamically based on ime, season, o
wea he ). In his ques , o he scien i ic ields can p o ide aluable in-
sigh s. Fo ins ance, he ple ho a o accessibili y s udies can aid he se-
lec ion o he mos ele an accessibili y measu e o he p oblem unde
s udy. In ano he example, when selec ing agg ega ion unc ions o
measu e he di e si y o indi iduals wi h espec o hei demog aphic
ai s, one can d aw insigh s om exis ing s udies on he po en ial and
limi a ions o di e en di e si y indices (DeJong, 1975).
V. Milias e al. Jou nal o T anspo Geog aphy 121 (2024) 104027
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