Depósi o de In es igación de la Uni e sidad de Se illa
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The Ve sion o Reco d is a ailable online a : h ps://doi.o g/10.1007/s11116-017-
9771-5
1
Es ima ing a ic olumes on in e ci y oad loca ions using
oadway a ibu es, socioeconomic ea u es and o he wo k- ela ed
ac i i y cha ac e is ics
Noelia Cace es1 • Luis Rome o2 • F ancisco Mo ales2 • An onio Reyes2 • F ancisco G. Beni ez2
Abs ac T a ic olume da a a e key inpu s o many applica ions in highway design and planning.
Bu hese da a a e collec ed in only a limi ed numbe o oad loca ions due o he cos in ol ed. This pape
p esen s an app oach o es ima ing daily and hou ly a ic olumes on in e ci y oad loca ions combining
clus e ing and eg ession modelling echniques. Wi h he aim o applying he p ocedu e o any oad loca ion,
i p oposes he use o oadway a ibu es and socioeconomic cha ac e is ics o nea by ci ies as explana o y
a iables, oge he wi h a se o p e iously disco e ed pa e ns wi h he hou ly a ic pe cen dis ibu ion.
Tes esul s show ha he p oposed app oach signi ican ly p oduces accu a e es ima es o daily olumes o
mos loca ions. The accu acy a hou ly le el is a bi mo e educed bu , o pe iods when a ic is signi ican ,
mo e han hal o he es ima es a e wi hin 20% o absolu e pe cen age e o . Mo eo e , he main peak pe iod
is app oxima ely iden i ied o mos cases. These indings oge he wi h i s g ea applicabili y make his
app oach a ac i e o planne s when no a ic da a a e a ailable and an es ima e is help ul.
Keywo ds Clus e ing algo i hms, a ic olume es ima es, socioeconomic cha ac e is ics, wo k-
ela ed ac i i y, oadway a ibu es, hou ly a ic pe cen dis ibu ion, a ic pa e ns.
________________________________
Noelia Cace es
ncace [email protected]
1 T anspo a ion Enginee ing, AICIA, Camino de los Descub imien os s/n. 41092 Se ille, Spain.
2 T anspo a ion Enginee ing, Facul y o Enginee ing, Uni e si y o Se ille. Camino de los
Descub imien os s/n, 41092 Se ille, Spain.
2
In oduc ion
T a ic olume es ima ion is a c ucial opic in a ic planning and ope a ions. In o ma ion on daily olume is
used by Road Adminis a o s o highway planning o pa emen design. Changes o e ime a e also use ul
du ing he oad design phase o e en o he calib a ion and alida ion o a el demand models. These da a
a e collec ed in only a limi ed numbe o oad loca ions, usually main oads, due o budge a y es ic ions.
Fo oads whe e da a a e una ailable, es ima es a e adi ionally made based on s a is ical me hodologies ha
can lead o la ge e o s (Gas aldi e al. 2014). Nowadays, mobili y is becoming mo e di e se since
popula ion ac i i ies a e mo e and mo e nume ous and occupy mo e space and ime. In o de o p edic
a ic olumes ha can be expec ed on he oad ne wo k du ing speci ic pe iods, cognizance should be aken
on he ac ha a ic olumes changes conside ably a each poin in ime as a unc ion o local condi ions.
Fo example, o in e ci y a ic, la ge ci ies usually a ac mo e people han smalle ones, and ci ies close
oge he end o ha e a g ea e a ac ion. Acco ding o hese p inciples, his pape p esen s an app oach o
es ima ing a ic olumes on in e ci y oad loca ions based on clus e ing and eg ession modelling
echniques. The s udy has explo ed as explana o y a iables no only oadway a ibu es (e.g. numbe o
lanes, speed limi and dis ance o majo ci ies), bu also indica o s ha e lec he socioeconomic and o he
wo k- ela ed ac i i y cha ac e is ics su ounding a oad loca ion (e.g. popula ion and employmen ), selec ing
he mos ele an ones. The main ad an age is i s applicabili y; i can be applied o any in e ci y loca ion,
which is especially impo an whe e he e a e no coun s a ions.
In he emainde o his pape , a li e a u e e iew on he subjec is p o ided i s . A e desc ibing he
cha ac e is ics o he s udy a ea, da a used, and analyses pe o med o de i e he explana o y a iable, he
p oposed app oach is hen desc ibed. Finally, he esul s a e discussed and conclusions p o ided.
Li e a u e e iew
Due o he le el o unce ain y in a ic o ecas s (as e iewed in Jong e al. 2007), o e many yea s
esea che s ha e ied o ind ways o p oduce be e a ic olume es ima es. Ad anced me hodologies (e.g.
neu al ne wo k, uzzy logic, eg ession o clus e ing echniques) ha e been applied as a means o es ima ing
a ic olumes using a ic in o ma ion, such as Annual T a ic Census (Lam e .al 2006), peak olumes o
imes o he peak hou s (Weije ma s and an Be kum 2005), o e en speed and densi y da a (Azimi and
Zhang 2010). Howe e , moni o ing is necessa y o ob ain such a ic in o ma ion. Mo e ecen app oaches
p oposed in he Fede al Highway Adminis a ion T a ic Moni o ing Guide (FHWA 2013) combine he use
o au oma ic a ic eco de s (e.g. pe manen loop de ec o s) aken on a small numbe o oad loca ions o
es ima e a e age a ic olume on o he loca ions wi h sho pe iod coun s (e.g. using mic owa e ada ).
This p ocedu e allows educing he need o ex ensi e moni o ing ac i i ies and a la ge amoun o pape s
ha e been published wi h in e es ing indings. Ne e heless, moni o ing is s ill necessa y.
The big challenge is o es ima e a ic olumes a anywhe e else in he oad ne wo k, especially o oads
ha do no ha e de ec o sys ems. In his ega d, new echniques ha e ecen ly been de eloped in o de o
es ima e a ic olume using non- a ic in o ma ion (e.g. oadway cha ac e is ics, land-use indica o s, o
socio-economic and demog aphic da a). The me hods de eloped in ol e no only clus e ing bu also o he
s a is ical me hods such as linea eg ession. Mohamad e al. (1998) used mul iple eg ession analysis o
de elop annual a e age daily a ic (AADT) p edic ion models o coun y oads om agg ega ed da a a he
coun y le el (popula ion, a e ial mileage, loca ion and accessibili y), and an R-squa ed o 0.75 was
achie ed. Simila ly, Xia e al. (1999) speci ied a model o AADT p edic ions by using explana o y a iables
such as unc ional class, numbe o lanes, a ea ype, au o owne ship, accessibili y o non-s a e oads o o he
coun y oads, and nea by employmen ; he esul ing R-squa ed was 0.60. This R-squa ed alue was
imp o ed by Zhao and Chung (2001) analyzing land use and accessibili y a iables mo e ex ensi ely; and by
Zhao and Pa k (2004) h ough geog aphically weigh ed eg ession echniques o p oduce mo e locally
speci ic model pa ame e s. Ande son e al. (2006) also de eloped a model wi h non- a ic explana o y
a iables, including unc ional classi ica ion, numbe o lanes, popula ion, employmen , and whe he he
oad is a h ough s ee o des ina ion s ee , esul ing an R-squa ed equal o 0.82.
Wi h he e olu ion o spa ial analysis echniques using geog aphic in o ma ion sys em (GIS) echnology
and he p og ess in da a mining, esea che s ha e s a ed o explo e o he me hods ha exploi he spa ial
con ex o a ic and o he supplemen a y da a (Gecchele e al. 2011; Song and Mille 2012). The k iging
echnique, which exploi s he spa ial aspec o obse a ions, has been explo ed by Wang and Kockelman
3
(2009) o mining ne wo k and coun da a, o e ime and space, using highway coun da a. The me hod
o ecas ed AADT alues a loca ions whe e coun s a ions a e una ailable. In his ega d, Selby and
Kockelman (2011) showed ha k iging can educe a e age-absolu e-e o by 16%-79%, depending on he
da a and model speci ica ion used. Neu al ne wo ks ha e also been applied o es ima e AADT, combined
wi h uzzy se heo y (Gas aldi e al. 2014), o using he e ec in oduced by he p inciple o demog aphic
g a i a ion on independen a iables based on land-use cha ac e is ics o he AADT es ima ion (Duddu and
Pulugu ha 2013).
Al hough me hods o es ima ing olume by no using a ic da a may no be necessa ily adequa e o mee
he needs o enginee ing design and planning (Gas aldi e al. 2014), hey a e a ac i e hanks o i s cos
e ec i eness and applicabili y. They can be applied o any loca ion in he oad ne wo k, which is especially
impo an o o he p ac ical applica ions ha do no equi e such a high le el o accu acy. Inspi ed by hese
ad an ages, his pape exploi s clus e ing analysis and eg ession modelling o es ima ing olumes on
loca ions o e oad ne wo k. O p ima y in e es is no only he o al daily olume o ehicle a ic as is
o en s udied, bu a he he changes o e ime o pa e n o hou ly olume h oughou he day. The app oach
hypo hesizes ha he a ic olume a a pa icula oad loca ion a ies as a unc ion o local condi ions
ega ding no only oadway ea u es, bu also ega ding cha ac e is ics o nea by ci ies. The idea ha
socioeconomic cha ac e is ics, ac i i y pa icipa ion and/o o he aspec s o li e can in luence a el beha io
has been s udied p e iously in he a el modeling ield (Ki amu a e al. 1997; Allah i anloo and Recke
2015). The app oach p oposed in his pape is a con inued e o ollowing a p e ious wo k (Cace es e al.
2012), in which a ic olumes o a gi en loca ion we e es ima ed using an a ac i eness ac o based on he
cha ac e is ics o nea by a eas (popula ion and dis ance), associa ing he ypical pa e n (ob ained by
clus e ing) wi h he loca ion. Howe e , he app oach did no wo k well o g oups whose membe s ha e
small simila i y in olume p o iles, especially because he clus e ing algo i hm did no lead o ind
homogenei y wi hin he g oups in e ms o olume p o iles bu acco ding o he a ac i eness ac o s. To
sol e his d awback, he p oposed app oach akes pa e ns di ec ly de i ed om he use o hou ly a ic
dis ibu ion as clus e ing a iable. This ac p oduces mo e compac g oups han in he p e ious wo k, and
hus p edic ion models may signi ican ly deli e be e esul s.
Inpu da a
Explana o y a iables
In o de o p edic a ic olumes, o cou se, physical oadway a ibu es a a pa icula poin (e.g. numbe o
lanes, capaci y, speed limi , and so on) ha e di ec e ec s on a ic olumes. Howe e , hese a ibu es do
no exhibi enough a iabili y o be use ul o p edic ion (e.g. i mos o he oad loca ions ha e wo lanes,
hen “numbe o lanes” is an inadequa e a iable). Then, he explana o y a iables need o ha e a iabili y,
and such a iabili y needs o be co ela ed wi h a ic olumes. Ci ies whe e people li e o wo k exe
s ong in luence o e in e ci y mobili y. The mo e people he e a e, he mo e mobili y he e will be; he mo e
shopping cen es he e a e, he mo e me chandize will a i e and mo e anspo a ion will happen. Then,
socioeconomic and o he wo k- ela ed ac i i y cha ac e is ics (popula ion, deg ee o economic ac i i y,
p opo ion o jobs, and so on) can e lec he spa ial a iabili y su ounding a oad loca ion, and hus ha e
been included as a pa o he possible a iables. To conduc he s udy, he anspo ne wo k co esponding
o he pilo a ea is abs ac ed in o a g aph model consis ing o a se o cen oids and links, which ep esen
ci ies and oad sec ions, espec i ely. Each cen oid con ains he a ibu es wi h he socioeconomic and o he
wo k- ela ed ac i i y cha ac e is ics o he ci y; while he links con ains he oadway a ibu es o be
analysed. This sec ion desc ibes he se o explo ed a iables.
Roadway Cha ac e is ics
These da a a e ela ed o he a ibu es o he oadway a he pa icula loca ion k, and include he numbe o
lanes (LANk) and he speed limi (SLk). The unc ional oad class (FRCk) has been inco po a ed in o he
analysis. The unc ional classi ica ion is he p ocess by which oadways a e g ouped in o classes acco ding
o he cha ac e o se ice hey a e in ended o p o ide. Fou classes ha e been used in his s udy: main oads
(mo o way, eeway, o o he majo oad), seconda y oads, local oads and o he s. The s udy also conside s
o he a iables ela ed o he dispe sion o popula ion and ac i i y in ci ies su ounding he loca ion. The
mo e dispe sed ac i i ies o se ices a e, he mo e a el is equi ed o each hem. Fo his pu pose, h ee
4
mo e a iable a e de ined. The i s one is DCPk, used o measu e he dis ance om he loca ion k o he
mean cen e o popula ion. This mean cen e o popula ion o he loca ion k (called CPk) is de e mined by
inding he spa ial mean cen e o all ci ies su ounding he loca ion (wi hin a adius o in luence o 15
kilome e s) weigh ed by i s popula ion. The X- and Y- coo dina es o he CPk a e calcula ed as ollows:
o each ci y whose ne wo k dis ance o he loca ion , , is less o equal o 15km
k
k
ii
i
CP
i
i
ik
ii
i
CP
i
i
PX
XPi k d
PY
YP

=

=




whe e Xi and Yi a e, espec i ely, he x- and y- coo dina es o he ci y i; Pi is he popula ion (in inhabi an s)
o he ci y i; and dki is he ne wo k dis ance (by oad) be ween he ci y i and he loca ion k. So ha he ci ies
used in de e mining he cen e o popula ion o he loca ion k (CPk) a e hose wi hin a adius o in luence o
15 kilome e s cen ed a he oad loca ion k. (The use o such a adius id explained in ollowing pa ag aphs).
Then, he a iable DCPk is calcula ed using bi d’s eye dis ances (in a s aigh line) be ween he loca ion k
and i s mean cen e o popula ion (CPk), measu ed in me e s by means o a GIS ool. This dis ance is he
only one measu ed his way (in a s aigh line), since a cen e o popula ion is usually loca ed in a poin no
connec ed o he oad ne wo k. Hence, i is no possible o ob ain he sho es a el dis ance by oad om he
GIS ool. Apa om his, wo mo e a iables a e de ined o measu e he dis ance om he loca ion k o he
mos popula ed ci y (DMPCk) and o he nea es ci y (DNCk). Bo h o hem a e based on he ne wo k
dis ance, measu ed (in me e s) as he sho es a el dis ance by oad (ob ained by means o a GIS ool)
be ween he loca ion k and he cen oid ep esen ing he nea es /mos popula ed ci y. A summa y o he oad-
based a iables in ol ed is lis ed in Table 1.
Table 1. Se o a iables based on oadway a ibu es o loca ion k.
Roadway ea u e
Va iable
Numbe o lanes a he oad loca ion k
LANk
Speed limi ed a he oad loca ion k (kilome es/hou )
SLk
Func ional oad class a he oad loca ion k
FRCk
Dis ance om he loca ion k o he mean cen e o popula ion (me e s)
DCPk
Dis ance om he loca ion k o he mos popula ed ci y (me e s)
DMPCk
Dis ance om he loca ion k o he nea es ci y (me e s)
DNCk
Socioeconomic and o he wo k- ela ed ac i i y cha ac e is ics
In his ega d, his s udy has used da a published yea ly by La Caixa Banking Founda ion (2011), wi h
abundan s a is ical in o ma ion and socioeconomic indica o s on each o he municipali ies in Spain wi h
mo e han 1,000 inhabi an s ( ep esen ing app oxima ely 96% o he o al na ional popula ion). Fo his case,
he a iables explo ed a e linked o he ci ies loca ed nea by he oad loca ion k, bu conside ing ha each
ci y a ec s he a ic load in a di e en manne . To model such in luence on each oad loca ion caused by
ac i i ies in nea by a eas, his pape has used he concep o loca ion-based accessibili y. This concep has
been widely ea ed in he ield o anspo and u ban planning (Koenig 1980; Geu s and an Wee 2004;
Lopez e al. 2009); and i has al eady been used o es ima e AADT a unmeasu ed loca ions ge ing good
esul s on he ield (Zhao and Chung 2001; Zhao and Pa k 2004). Acco ding o i , he in e ac ion be ween
loca ions declines wi h any inc ease in disu ili y (o cos ) be ween hem, ha usually depends on a el ime
o a el dis ance o a gi en loca ion. This measu emen es ima es he accessibili y o a loca ion k wi h
espec o oppo uni ies in all su ounding zones, in which smalle and/o mo e dis an oppo uni ies p o ide
diminishing in luences. Then, he accessibili y o oad loca ion k is de ined as ollows:
()
k i ki
i
A D F c=

(1)
whe e Di is he oppo uni y (socioeconomic and o he wo k- ela ed ac i i y ea u e showed in Table 2) a
zone o ci y i and F(cki) is he de e ence unc ion depending on he gene alized cos (cki) o eaching ci y i
om loca ion k. The explo ed a iables based on he cha ac e is ics a e showed in Table 2.
In his s udy he cos (cki) is modelled by he ne wo k dis ance (dki), so ha he de e ence unc ion
desc ibes he e ec o space. Rega ding de e ence unc ional o m, se e al s udies ha e used di e en

5
unc ions, such as powe -law, exponen ial, gaussian o logis ic unc ions. The g a i y model is a well-known
o mula ion o he spa ial in e ac ion, and specially, o he ip dis ibu ion (E lande and S ewa 1990).
G a i y models assume he in e ac ion be ween wo loca ions is p opo ional o hei impo ance (e.g.
popula ion), bu i decays wi h dis ance. In g a i y models, he gene al de e ence o m ollows a powe -law
unc ion o he in e ac ion be ween wo loca ions; ha is, F(
ki
c
)=1/
ki
d

whe e α e lec s he e ec o space.
In his s udy, he dis ance dki is based on he ne wo k dis ance and measu ed as he sho es a el dis ance (in
me e s) by oad om he loca ion k o he ci y i, which is ob ained by means o a GIS ool. The exponen o
he de e ence unc ion is a pa ame e whose alue depends on he sys em (Ba hélemy 2011). In o de o
de e mine i s alue, da a de i ed om a su ey ca ied ou by he Spanish Minis y o De elopmen in 2006-
2007 (MOVILIA 2006) was used, which con ained in o ma ion o enable unde s anding o he daily mobili y
pa e ns o Spanish esiden s. In pa icula , i o e ed he numbe o displacemen s be ween a pai o zones
oge he wi h he a e age dis ance a eled in hei displacemen s. Using his empi ical da a and he
popula ion in o ma ion associa ed o he zones om La Caixa Banking Founda ion (2011), he de e ence
unc ion was i ed by a powe -law wi h exponen α=1.52.
A las bu no he leas , i is impo an o highligh ha he calcula ion o hese a iables only conside s
he e ec gene a ed by ci ies i ha a e wi hin a adius o 15 km om a gi en oad loca ion k; ha is he
ne wo k dis ance om he ci y i o he loca ion k is less o equal han 15 kilome es (dki≤15km). This adius
o in luence has been selec ed aking in o accoun ha he a e age ip dis ance in a wo king day is a ound
15 km (Eu os a 2007). This simpli ica ion is needed o educe he numbe o ci ies conside ed in he
calcula ion o accessibili y indica o s, and i is o ally cohe en wi h he assump ion ha nea es ci ies a e
esponsible o mos o he a ic suppo ed by a gi en oad. Based on his dis ance, none oad loca ion was
isola ed; he e was always a leas one ci y wi hin he adius o in luence o a gi en oad loca ion.
Table 2. Se o a iables based on socioeconomic and o he wo k- ela ed ac i i y cha ac e is ics o loca ion k.
Socioeconomic/wo k- ela ed ac i i y ea u e
Va iable
Popula ion (inhabi an s) o he ci y i (Pi)
()
k i ki
i
AP P F c=

Economic ac i i y index* (pe 100,000) in ci y i (Ei)
()
k i ki
i
AE E F c=

Unemploymen a e (pe 100) in ci y i (Ui)
()
k i ki
i
AU U F c=

G oss loo a ea (me e 2) o ci y i (GFAi),
()
k i ki
i
AGFA GFA F c=

Numbe o indus ial es ablishmen s in ci y i (IEi)
()
k i ki
i
AIE IE F c=

Numbe o manu ac u ing es ablishmen s in ci y i (MEi)
()
k i ki
i
AME ME F c=

Mos -popula ed ci y (inhabi an s) nea loca ion k (MPCk)
()
kk
k MPC kMPC
AMPC P F c=
Nea es ci y(inhabi an s) (NCk)
()
kk
k NC kNC
ANC P F c=
(*) Ra e o economic ac i i y o each ci y in Spain based on he business and p o essional economic ac i i ies ax collec ed. This
index measu es he municipal pa icipa ion (X o 100,000 pa s) ega ding he espec i e o al a na ional le el (100,000 pa s).
Selec ion o explana o y a iables
Once he se o a iables a ailable a e es ablished, he selec ion o explana o y a iables o be used in
eg ession modelling is equi ed. In s a is ics, selec ion p ocedu es exis o objec i ely choose a subse o
explana o y a iables such as s epwise eg ession. In his semi-au oma ed p ocess, he choice o explana o y
a iables is ca ied ou by successi ely adding ( o wa d) o emo ing (backwa d) a iables based on use -
speci ied c i e ia, which usually akes he o m o a sequence o F- es s o - es s, bu o he echniques a e
possible (Blanche e . al 2008). Fo his s udy he o wa d-s epwise eg ession algo i hm is used o analyze
he subse o explana o y a iables o be used in eg ession. The p oposed app oach implemen s wo
di e en eg ession models (one o modeling g oup choice and o he o es ima ing daily a ic) using he
same inpu a iables; he choice is pe o med using a combina ion om bo h s epwise eg ession ou pu s.
The modele ’s judgmen also plays a key ole in selec ing a iables because o collinea i y issues.
Collinea i y, o excessi e co ela ion among explana o y a iables, is a common p oblem when es ima ing
eg ession models. High co ela ion be ween a iables migh lead o in la ed s anda d e o s o he es ima o s
(collinea i y e ec s), bu he opposi e is no always ue. Va ious me hods o es ing collinea i y exis in
li e a u e; his s udy has op ed by he Belsley collinea i y diagnos ics (Belsley e al. 1980), examining he
6
a iance in la ion ac o (VIF) and he condi ion numbe (CI) o he co ela ion ma ix among he selec ed
a iables, oge he wi h he coe icien R-squa ed. A common ule o humb equi es ha R-squa ed < 0.8,
VIF < 5, and CI < 10, o conside ing collinea i y as negligible (F iendly and Kwan 2009). Acco ding o he
ou pu s o he o wa d-s epwise eg ession analysis on he se o a iables oge he wi h he collinea i y
diagnos ics, he explana o ies a iables inally selec ed a e:
X1: LANk wi h he numbe o lanes a he loca ion k,
X2: AEk ela ed o economic ac i i y o ci ies wi hin he in luence adius a loca ion k,
X3: AGFAk ela ed o he g oss loo a ea o ci ies wi hin he in luence adius a loca ion k,
X4: AMPCk ela ed o he mos popula ed ci y nea loca ion k,
X5: DCPk wi h he dis ance om he loca ion k o he mean cen e o popula ion.
Fig. 1 exhibi s he collinea i y diagnos ics, in which he la ges condi ion index (CI=6) co esponds o a
nea linea dependency in ol ing X4 and X5, wi h a smalle con ibu ion o X2. Howe e , he alues o VIF,
CI and R-squa ed o hese a iables a e less han he ecommended alues, and i is concluded ha he e is
no se ious p oblem o mul icollinea i y. A summa y o desc ip i e s a is ics o he selec ed a iables is gi en
in Table 3. Howe e , he a iables o be used in he models mus be s anda dized by sub ac ing he mean
and di iding by he s anda d de ia ion. S anda diza ion o a iables is pa icula ly impo an when a iables
a e measu ed on di e en scales/uni s; o he wise, hey do no con ibu e equally o he analysis.
Fig. 1. (a) Co ela ion ma ix wi h R-squa ed. (b) Tableplo o CI, VIF and a iance p opo ions (VP) o he selec ed
explana o y a iables. In column 1, he squa e symbols a e scaled ela i e o a maximum CI o 30. In he emaining
columns, a iance p opo ions (×100) a e shown as ci cles scaled ela i e o a maximum o 100. In he las ow, VIF
alues a e exposed.
Table 3. Mean, s anda d de ia ion, maximum and minimum o selec ed a iables.
Mean
S anda d de ia ion
Max
Min
X1
2.474
0.905
4
1
X2
56481670.225
850892348.833
12848260720.179
0.0000000002
X3
1079531438482.049
16225891817230.148
245008999577218.560
0.0093230397
X4
276.435
3836.297
57942.250
0.00081
X5
5716.187
3159.373
14463.597
732.277
T a ic Da a
Desc ip ion
Use mobili y is closely linked o ac i i ies which end o be ou inized on wo king days. Fo commu ing
ips he epea abili y gi es ise o a s able componen in hou ly a ic olumes. Mos o daily ac i i ies
depend on coun y-speci ic habi s (e.g. s a o wo king hou s, lunch b eaks, e c.) which sugges he
exis ence o a ic dis ibu ion pa e ns by hou o he day. These pa e ns p o ide aluable in o ma ion o
p edic olumes, especially o de ec peak pe iods occu ence.
7
The empi ical a ic da a used h oughou his wo k comes om pe manen au oma ic coun e s ( hese da a
a e collec ed 24 hou s pe day, 365 days pe yea ) loca ed in a b oad geog aphic dis ibu ion ac oss he
Spanish oad ne wo k, p o ided by he Spanish Di ec o a e Gene al o T a ic (DGT 2011). The da a o e a
wide ange o a ic s a is ics including no only measu emen s o AADT (in eh/day), bu also a ic
olume measu ed on hou ly in e als (in eh/hou ). This in o ma ion e e s on an a e age day,
dis inguishing be ween an a e age weekday and weekend. This s udy has aken only weekday da a since his
kind o day is mo e app op ia e o es ima ion pu poses. T a el beha io is epea ed equen ly on weekdays,
while ips on weekends espond o non- ou inized ac i i ies (en e ainmen , shopping o social pu poses).
To ind such pa e ns, a ic da a obse ed a a la ge numbe o si es a e equi ed. In pa icula , he da a
used in his s udy come om 455 oad loca ions wi h di e en a ic backg ounds (highways, seconda y
oads and so on) and cha ac e is ics ( om a single lane o a mul ilane, single o dual ca iageway). All hese
loca ions a e placed on in e ci y oads; u ban en i onmen s a e no conside ed a his s age o he wo k.
Then, hese oad loca ions ha e been andomly spli in o wo subse s, one used o model calib a ion and he
o he o model alida ion. The e o e, 345 oad loca ions (~¾ o al sample) ha e been used as he calib a ion
da ase , and he emaining 110 loca ions (~¼ o al sample) ha e examined he p edic i e accu acy o he
p oposed app oach. Fig. 2 shows he oad loca ions colou ed by he co esponding se ( ed and g een
iangles o calib a ing o es ing se , espec i ely), oge he wi h he cen oids ep esen ing ci ies.
Fig. 2. Map o oad loca ions as well as he cen oids ep esen ing he ci ies and he oad ne wo k (only ci ies wi h
g ea e han 1000 inhabi an s).
Clus e ing
Clus e analysis is a s a is ical p ocedu e o de ine g oups ha sha e simila cha ac e is ics. I s goal is o
o ganise objec s in o di e en g oups o clus e s, such ha a g oup is a collec ion o objec s “simila ” o each
o he and a e “dissimila ” o he objec s belonging o o he g oups. The e a e many ways o combine cases
in o g oups, o e iews o clus e ing p ocedu es can be ound in he li e a u e. The mos commonly used is
he hie a chical clus e ing me hod, which basically o ms g oups by clus e ing cases in o la ge g oups un il
all he cases a e membe s o a single g oup. The c i e ia o deciding g oups a e based on ei he a di e ence
o simila i y ma ix, whe e he simila i y measu es he closeness o cases. Among he common me hods o
doing his (single linkage, a e age be ween-g oups linkage, Wa d's me hod...), his esea ch has selec ed he
a e age wi hin-g oups linkage. Using his me hod, he dis ance is de ined as he a e age o he dis ances
8
be ween all pai s o cases in he g oup ha would esul i hey we e combined. This minimises in a-g oup
dis ances and hus ends o p oduce igh g oups. The e o e i is app op ia e when he pu pose o he
clus e ing is he homogenei y wi hin he g oups. Accu a e clus e ing equi es a p ecise de ini ion o he
closeness be ween a pai o objec s in mul i-dimensional space, in e ms o ei he he pai -wise simila i y o
dis ance. Fo he sake o simplici y, he p oposed app oach has aken Euclidean dis ance o gi e a nume ical
alue o he amoun o simila i y be ween wo objec s, bu se e al simila i y o dis ance measu es has been
p oposed and widely applied in li e a u e (Rui and Wunsch 2005).
The aim is o disco e a se o mobili y pa e ns o e a egion om obse ed a ic da a. Expe ience
shows ha al hough a ic olumes may change o e ime, he ela i e a ia ions o a ic a ce ain hou s
o he day a e o en qui e consis en . The e o e, his s udy has employed he hou ly dis ibu ion in e ms o
he pe cen age o he daily a ic wi hin each hou o he day as objec o be classi ied, o e he calib a ing
se o oad loca ions. One o he main di icul ies o clus e analysis lies in he de e mina ion o he op imal
numbe o g oups p esen in a da ase . A a ie y o indices ha e been de ined in li e a u e o e alua e he
i ness be ween a da ase and clus e ing esul whe e he op imal numbe o clus e s p oduces bes i
(Milligan and Coope 1985). Acco ding o hei wo k, Calinski and Ha abasz’s (CH) index is he mos
e ec i e one in iden i ying he numbe o clus e s. The CH index e alua es he clus e alidi y based on he
a e age be ween- and wi hin- clus e sum o squa es (Calinski and Ha abasz, 1974), so a la ge CH index
indica es homogenous clus e ing. Fig. 3 exposes ha en clus e s is he solu ion wi h he highes CH index
alue.
Fig. 3. Calinski and Ha abasz index as a unc ion o numbe o clus e s.
Hou ly pa e ns
Once he clus e ing s age is pe o med, he oad loca ions included in he calib a ing da ase a e ca ego ized
in o en clus e s o g oups. Each g oup is ep esen ed by he co esponding hou ly pa e n (Fig. 4) wi h he
dis ibu ion o a ic by hou -o -day (in pe cen age) in a wo king day. The i le o each plo indica es he
numbe o loca ions wi hin each g oup, Nj, and he clus e compac ness (CCj) measu e based on a iance in
o de o quan i y how closely ela ed he objec s in a g oup a e. Lowe a iance indica es be e compac ness
(o in o he wo ds, membe s ha e high mu ual simila i y). Mos o g oups ha e high homogenei y and
compac ness, excep G10. A isual analysis o hese pa e ns e eals ha , in gene al, he pe cen age ha
akes place be ween midnigh and 4:00 AM, when he majo i y o people a e es ing, is educed o all
pa e ns. T a ic usually s a s inc easing in ea ly mo ning, be ween 5:00 and 6:00 AM, and d ops in he
e ening, be ween 7:00 and 8:00 PM. The e o e, mos o he a ic is usually concen a ed be ween 7:00 AM
and 8:00 PM, hough he beha iou du ing such hou s a ies om g oup o g oup. Some o hem (G1, G3,
G4, G5 and G6) exhibi dis inguishable peaks associa ed wi h commu e ips. These a e he mo ning-peak
pe iod ela ed o home- o-wo k ips (07:00–09:00 AM) and he e ening-peak pe iod o wo k- o-home
e u n ips (5:00–8:00 PM). I is wo h no ing ha in Spain school ime is concen a ed in hal -day;
mo eo e many people a e employed in spli shi s o e en in pa - ime jobs. These ac s cause a hi d peak
pe iod a ound 1:00–3:00 PM ha can ake some load om he e ening-peak, and usually makes he
mo ning-peak pe iod he mos in ense ime o he day. The e ening-peak pe iod ends o be sp ead o e a
longe du a ion because wo k- o-home e u n ips a e usually linked wi h some o he ip pu poses. The e
a e also g oups in which a ic begins o inc ease a ea ly mo ning and con inues h oughou he es o he
mo ning and in o he a e noon, being he e ening-peak sligh ly highe (G2, G7, G8 and G9). The las g oup
(G10) exhibi s a pa e n o ally di e en , wi h a ema kable e ening-peak in he dis ibu ion o daily a ic.
This g oup is he leas compac based on i s CC measu e, being i s pa e n p obably he leas ep esen a i e
among i s membe s.
15
Fig. 8. (a) Hou ly olumes obse ed and es ima ed (using ADT de i ed by Model 3) o es ing loca ions du ing he
hou pe iods wi hin 7AM-8PM; and (b) Pe cen age o hou ly es ima es wi h APE≤20% in such pe iods.
Table 8. E o le els ob ained o each g oup be ween 7:00 AM and 8:00 PM (using ADT es ima ed by Model 3).
G oup
G1
G2
G3
G4
G5
G6
G7
G8
G9
G10
MAPE o hou ly es ima es
14%
23%
27%
24%
24%
26%
46%
22%
26%
91%
P opo ion o hou ly es ima es wi h
APE≤20%
72%
63%
57%
57%
48%
52%
57%
50%
55%
30%
Nex , he esul s a e applying he o ecas p ocedu e a wo loca ions a e p esen ed and compa ed wi h
obse ed da a. A daily le el (Fig. 9a), he es ima es each educed pe cen age e o le els. Fig. 9b displays
he es ima ed olumes by hou -o -day (b oken line) and he olume p o ile obse ed a each loca ion (solid
line), e ealing ha he es ima es ollow he peaks and alleys o he obse ed cu e o mos hou pe iods.
Then, he app oach can p o ide an app oxima ion o he hou ly e olu ion o a ic du ing a day a a
pa icula oad loca ion, e y use ul when no in o ma ion is a ailable. In his ega d, o he impo an
cha ac e is ic o he p oposed app oach is he high accu acy o ecas o he main peak pe iod o oad
loca ions. A he wo loca ions showed in Fig. 9a, he p edic ed pe iod o he main peak (6h-pe iod o E-
288-0 ASC, and 17h-pe iod o E-22-0 DESC) nea ly ma ches wi h he obse ed one (7-hou pe iod o E-
288-0 ASC, and 17-hou pe iod o E-22-0 DESC). The analysis o such de ia ion o all es ing loca ions
(Fig. 10) exposes ha he di e ences be ween p edic ed pe iod o he main peak and he eal one a e less o
equal han one hou o he 80% o oad loca ions.

16
Fig. 9. Obse ed and es ima ed olumes o each hou pe iod (a) and he o al day (b) a wo loca ions.
Fig. 10. De ia ion in hou s be ween he p edic ed pe iod o main peak and he obse ed one.
Conclusions
T a ic olume da a a e key inpu s app ecia ed by Road Adminis a o s in a ic planning and ope a ions.
Bu hese da a a e a ailable in only a limi ed numbe o oad loca ions due o he cos in ol ed o deploying
senso s. The app oach p esen ed in his pape aims o es ima e a ic olumes a anywhe e else in he oad
ne wo k. Fo his pu pose, he app oach combines clus e ing echniques o in e coun y-speci ic mobili y
pa e ns, oge he wi h eg ession modelling using oadway a ibu es and socioeconomic and o he wo k-
ela ed ac i i y s a is ics o ci ies su ounding a gi en oad loca ion. This s udy has been applied on a se o
oad loca ions, dis ibu ed ac oss he Spanish oad ne wo k, whe e also exis pe manen coun s a ions o
calib a ing and alida ing pu poses. Tes esul s show ha he p oposed app oach signi ican ly p oduces
accu a e es ima es o daily olumes o mos loca ions. The accu acy a hou ly le el is a bi mo e educed
bu , o pe iods when a ic is signi ican , mo e han hal o he es ima es a e wi hin 20% o absolu e
pe cen age e o , which is he allowed limi o ul illing s anda ds o loop de ec o s (Lehnho 2004).
Mo eo e , o mos cases, he main peak pe iod is app oxima ely iden i ied. The di e ences be ween he
p edic ed pe iod and he eal one a e less o equal han one hou o he 80% o oad loca ions. This
in o ma ion is also a signi ican inpu o design and planning pu poses ha ake in o accoun p esen and
u u e uses o he conside ed oad. The p oposed app oach allows Road Adminis a o s o build hou ly a ic
olume p edic ions a a pa icula oad loca ion when no in o ma ion is a ailable and an es ima e is help ul.
These indings make his app oach a ac i e o p ac ical applica ions ha do no equi e a high le el o
accu acy. The main ad an age o he p ocedu e is i s applicabili y since he p ocedu e can be applied o any
in e ci y oad loca ion.
The design o oadways is also a ield o which he knowledge o hou ly and daily a ic olumes
plays a key ole. Wi h espec o highways, design c i e ia consis o a de ailed lis o conside a ions in
which a ic equi emen s in ela ion o use as well as changes o e ime should be e alua ed. Fu he
esea ch based on his app oach can p o ide a be e unde s anding o a ic loading ha will be suppo ed
by new in e ci y oads. As a u u e s udy, he complex u ban en i onmen should be also in es iga ed by
explo ing ci y-based ea u es (e.g. he p esence o schools, bus s ops, shopping a eas, and so on) o he
17
in e ence o a ic olumes on u ban oads.
Acknowledgemen s One o he au ho s, N. Cace es, hanks he Minis y o Economy and Compe i i eness o he
Spanish Go e nmen o he unds p o ided h ough he To es Que edo P og amme (PTQ-13-06428).
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