Defining accuracy benchmarks for freeway traffic simulations in support of highway operations and planning

 Co esponding au ho : Ayodeji Ajidahun
Copy igh © 2025 Au ho (s) e ain he copy igh o his a icle. This a icle is published unde he e ms o he C ea i e Commons A ibu ion Liscense 4.0.
De ining accu acy benchma ks o eeway a ic simula ions in suppo o highway
ope a ions and planning
Ayodeji Ajidahun 1, * and Mujeeb Abiola Abdul azaq 2
1 Depa men o Ci il Enginee ing, Uni e si y o New Ha en, Wes Ha en, CT, USA.
2 Depa men o Ci il and En i onmen al Enginee ing, Uni e si y o No h Ca olina a Cha lo e.
Wo ld Jou nal o Ad anced Resea ch and Re iews, 2025, 27(02), 790-797
Publica ion his o y: Recei ed on 01 July 2025; e ised on 09 Augus 2025; accep ed on 11 Augus 2025
A icle DOI: h ps://doi.o g/10.30574/wja .2025.27.2.2900
Abs ac
Accu a e calib a ion o a ic simula ion models is essen ial o eplica ing obse ed a ic condi ions, and subsequen
op imiza ion o decision-making p ocesses and a ge ed in es men s in anspo a ion in as uc u e. This s udy
applies a gene ic algo i hm (GA) o op imize key pa ame e s o he ca - ollowing model o a basic eeway segmen in
Cali o nia, aiming o minimize he e o be ween simula ed and obse ed a ic da a. Ou pu s gene a ed du ing GA
i e a ions we e analyzed using pai ed T- es s and Wilcoxon signed- ank es s o compa e simula ed speed and low
agains g ound u h da a. Accu acy o each sample was ma ched o i s co esponding P- alue, e ealing a clea end:
when accu acy le els exceeded 80%, P- alues o bo h speed and low consis en ly ose abo e 0.05. This indica es ha
he simula ed ou pu s became s a is ically indis inguishable om he obse ed ield da a a e 80% accu acy. These
indings demons a e ha combining s a is ical signi icance wi h accu acy me ics can e ec i ely guide calib a ion
p ocesses and es ablish h esholds o accep able simula ion accu acy, con ibu ing o a obus amewo k o a ic
simula ion s udies.
Keywo ds: Ci il enginee ing; Highway enginee ing; T a ic simula ion; T a ic low modeling; Gene ic algo i hm
op imiza ion; T anspo a ion in as uc u e planning
1. In oduc ion
T a ic simula ion has become a cos -e ec i e and indispensable ool o anspo a ion planning, aiding enginee s and
planne s in designing and managing e icien oad sys ems [1, 2]. By modeling a ious scena ios, simula ion p o ides
insigh s in o po en ial a ic condi ions, ope a ional pe o mance, and sa e y ou comes, ul ima ely in o ming c i ical
decisions o in as uc u e in es men and policy-making [3, 4]. Howe e , he accu acy o hese simula ions in
e lec ing eal-wo ld condi ions is pa amoun . A poo ly calib a ed model isks ei he unde es ima ing o o e es ima ing
a ic pe o mance/beha io , leading o un eliable u u e p edic ions and subop imal ou comes o simula ion-based
s udies.
Accu a e eplica ion o eal-wo ld a ic beha io is pa icula ly c ucial in unique o complex scena ios, whe e eliable
p edic ions can ha e signi ican implica ions. Fo ins ance, simula ions may be employed o s udy a ic beha io unde
ex eme wea he condi ions, e alua e he ela i e bene i s o inno a i e oad designs, o analyze he impac o eme ging
echnologies such as connec ed and au onomous ehicles (CAVs) [5] on p e ailing a ic condi ions. Each o hese cases
demands a model ha aligns closely wi h eal-wo ld da a o ensu e alid and ac ionable esul s.
O e he yea s, esea che s ha e de eloped a a ie y o echniques o calib a e simula ion models and adjus d i ing
beha io pa ame e s. Mos calib a ion e o s ha e elied on me aheu is ic op imiza ion algo i hms such as gene ic
Wo ld Jou nal o Ad anced Resea ch and Re iews, 2025, 27(02), 790-797
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algo i hms, pa icle swa m op imiza ion, and simula ed annealing [6, 7], which sys ema ically minimize he di e ences
be ween simula ed and obse ed a ic condi ions. These me hods au oma e he calib a ion p ocess, achie ing high
accu acy and e iciency. On he o he hand, some esea che s ha e aken a mo e manual app oach, employing g id
sea ch me hods o i e a i ely es and adjus pa ame e s [8, 9]. While hese app oaches ha e ad anced he ield o a ic
simula ion calib a ion, hei ocus has been p ima ily on minimizing e o s, wi hou de ining an accep able h eshold
o accu acy in simula ion s udies.
Despi e hese ad ancemen s, no s udy has ye es ablished a s anda d o wha cons i u es an accep able le el o
accu acy in a ic simula ion. This knowledge gap has signi ican implica ions, as simula ions o en se e as he
ounda ion o policy decisions and in as uc u e in es men s. Wi hou a clea s anda d, he e is a isk o o e - eliance
on models ha may no mee he igo equi ed o eliable p edic ions. To add ess his gap, his s udy in es iga es he
use o bo h pa ame ic and non-pa ame ic s a is ical me hods o e alua e calib a ion accu acy. A basic eeway
segmen in Cali o nia is used as a case s udy, p o iding a con olled en i onmen o es ing and analysis.
This pape makes a no el con ibu ion by no only applying me aheu is ic op imiza ion me hods o calib a ion bu also
analyzing he s a is ical signi icance o accu acy le els achie ed. By ma ching accu acy me ics wi h s a is ical
signi icance, his s udy es ablishes a amewo k o de e mining accep able h esholds o simula ion accu acy. These
indings aim o con ibu e o he s anda diza ion o accu acy me ics in a ic simula ion, ensu ing ha u u e models
achie e he eliabili y necessa y o c i ical anspo a ion planning decisions.
2. Me hods
2.1. S udy A ea
The s udy a ea is a segmen o In e s a e I-80, loca ed in Los Angeles, Cali o nia, wi hin Yolo Coun y, as illus a ed in
Figu e 1. This sec ion o he eeway is a ou -lane basic segmen wi h a o al leng h o 5,280 ee . The s udy ocused on
he e ening peak pe iod, speci ically om 4:00 PM o 5:00 PM on Augus 21, 2018. Field a ic da a, including low and
speed, we e collec ed and agg ega ed in o 5-minu e in e als.
Figu e 1 I-80 F eeway Segmen in Yolo Coun y (Google Ea h)
Table 1 summa izes he a ic low obse ed in each lane du ing hese in e als. The able also p esen s he o al a ic
low ac oss all ou lanes and he a e age a ic speed o he segmen .
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Table 1 Collec ed T a ic om Senso s.
Time
Speed (mph)
Flow (Veh/ 5 Minu es)
Lane 1
Lane 2
Lane 3
Speed
Lane 1
Lane 2
Lane 3
Flow
4:05 PM
58.30
56.30
55.60
56.90
172
150
112
434
4:10 PM
57.70
57.70
54.00
56.80
161
160
107
428
4:15 PM
57.50
58.90
53.00
56.80
172
159
119
450
4:20 PM
58.10
58.20
58.70
58.30
171
154
122
447
4:25 PM
56.70
58.30
54.20
56.60
168
138
108
414
4:30 PM
41.00
43.60
43.90
42.80
139
134
128
401
4:35 PM
46.20
46.70
46.00
46.30
160
148
127
435
4:40 PM
53.10
54.30
54.50
53.90
159
145
116
420
4:45 PM
55.70
56.30
56.60
56.20
182
164
130
476
4:50 PM
54.90
57.40
56.80
56.30
167
160
131
458
4:55 PM
36.30
44.40
44.00
41.70
117
132
122
371
5:00 PM
33.30
38.70
37.40
36.40
136
131
126
393
2.2. Ca Following Model
The Wiedemann 99 (W99) model is a psycho-physical ca - ollowing model de elop in 1999, de i ed om he o iginal
Wiedemann model p oposed in 1974 (W74) [10]. I consis s o 10 pa ame e s (CC0, CC1, ..., CC9), which can be
calib a ed (o adjus ed) o ep esen d i ing beha io s o human d i en ehicles (HDVs) on eeways. Among hese,
CC0, CC8, and CC9 a e pa icula ly c ucial in de e mining he model's pe o mance. The equa ion go e ning he model
is gi en by:
𝑣𝑛(𝑡+∆𝑡)=𝑚𝑖𝑛{𝑣𝑛(𝑡)+3.6×(𝐶𝐶8+𝐶𝐶8−𝐶𝐶9
80 ×𝑣𝑛(𝑡))∆𝑡;𝑢𝑓,3.6×𝑆𝑛(𝑡)−𝐶𝐶0−𝐿𝑛−1
𝑣𝑛(𝑡);𝑢𝑓 } (1)
Whe e 𝑣𝑛(𝑡+∆𝑡) ep esen s he speed o he subjec ehicle a e ∆𝑡 seconds ela i e o ime s ep , 𝑆𝑛(𝑡) is he dis ance
be ween he subjec and leading ehicle; 𝐿𝑛−1 deno es he leng h o he leading ehicle; and 𝑢𝑓 is he ee- low speed.
The explana ions o 10 pa ame e s a e desc ibed in Table 2.
Table 2 T a ic Pa ame e s
W99
Pa ame e s
In e p e a ion
De aul
CC0
A e age s ands ill dis ance (m)
1.4
CC1
Headway (s)
1.2
CC2
Longi udinal oscilla ion (m)
8
CC3
S a o decele a ion p ocess (s)
-12
CC4
Minimal closing Δ (m/s)
-1.5
CC5
Minimal opening Δ (m/s)
2.1
CC6
Speed dependency o oscilla ion (10−4 ad/s)
6
CC7
Oscilla ion accele a ion – m/s2
0.25
CC8
Accele a ion a e when s a ing (m/s2)
2
CC9
Accele a ion beha io a 80 km/h (m/s2)
1.5
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2.3. Calib a ion
A gene ic algo i hm (GA) is used o enhance he calib a ion o a mic oscopic a ic simula ion model ( he W99 ca
ollowing model) by app oaching nea -global op imal solu ions [11, 12]. The GA simula es biological e olu ion h ough
selec ion, c osso e , and mu a ion mechanisms. Ini ially, he algo i hm begins wi h a andomly gene a ed popula ion o
solu ions, and in each i e a ion, highe -quali y solu ions ha e a g ea e chance o being selec ed o ep oduc ion,
p oducing new popula ions h ough c osso e and mu a ion. This s udy employs wo di e en GA con igu a ions: he
i s uses a popula ion size o 20, wi h a 20% mu a ion p obabili y o e 20 gene a ions, while he second uses a
popula ion size o 30, wi h a 30% mu a ion p obabili y o e 30 gene a ions. The objec i e is o assess indi idual GA
membe s o ob ain a su icien sample size o gene aliza ion in he s udy.
The calib a ion p ocess is execu ed in Py hon, whe e bina y ch omosomes a e andomly gene a ed o ep esen easible
solu ions. These ch omosomes a e hen decoded in o model pa ame e s, which a e ed in o he SUMO simula ion
so wa e. The objec i e unc ion is e alua ed by compa ing he simula ed a ic low and speed da a wi h obse ed eal-
wo ld alues. The calib a ion con inues un il he maximum numbe o gene a ions is eached o a p ede ined s opping
condi ion is sa is ied. This p ocess is depic ed in Figu e 2 as adop ed om. In his ega d, he op imiza ion amewo k
is o mula ed as ollows:
Figu e 2 GA Calib a ion p ocess
𝑓(𝑉𝑜𝑏𝑠,𝑉𝑠𝑖𝑚)
Subjec o he cons ain s:
𝑙𝑥𝑖≤𝑥𝑖≤𝑢𝑥𝑖,𝑖 =1…𝑛,
Whe e 𝑥𝑖= he model pa ame e s o be calib a ed, 𝑓(𝑜𝑏𝑗)= objec i e unc ion, 𝑉𝑜𝑏𝑠,𝑉𝑠𝑖𝑚= obse ed and simula ed alue
o model pa ame e s, 𝑙𝑥𝑖,𝑢𝑥𝑖= he espec i e lowe and uppe bounds o model pa ame e , n = numbe o a iables. The
objec i e unc ion uses he Mean Absolu e No malized E o (MANE), which is p o ided by he ollowing equa ion. The
calib a ion using he low and speed da a as pe o mance measu es is o mula ed as ollows:
𝑀𝑖𝑛 𝑀𝐴𝑁𝐸(𝑞,𝑣)=1
𝑁∑⬚
𝑁
𝑖=1 (|𝑞𝑜𝑏𝑠,𝑖−𝑞𝑠𝑖𝑚,𝑖|
𝑞𝑜𝑏𝑠,𝑖 +|𝑣𝑜𝑏𝑠,𝑖−𝑣𝑠𝑖𝑚,𝑖|
𝑣𝑜𝑏𝑠,𝑖 ) …….. (2)
Whe e 𝑞𝑜𝑏𝑠,𝑖,𝑞𝑠𝑖𝑚,𝑖= obse ed and simula ed a ic olume o a gi en ime pe iod i, 𝑣𝑜𝑏𝑠,𝑖,𝑣𝑠𝑖𝑚,𝑖= obse ed and
simula ed a ic speed o a gi en ime pe iod i, N = o al numbe o obse a ions.
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2.4. S a is ical Tes ing
Du ing he calib a ion p ocess, each candida e solu ion p oduced by he GA i e a ions was e alua ed o s a is ical
signi icance using bo h pa ame ic and non-pa ame ic me hods o compa e he simula ed and obse ed a ic da a.
The wo es s employed a e desc ibed below:
2.4.1. The Pai ed T- es
The pai ed T- es is a pa ame ic es used o compa e he means o wo ela ed g oups [13, 14], in his case, he
simula ed a ic da a and he obse ed a ic da a. This es e alua es whe he he e is a s a is ically signi ican
di e ence be ween he wo se s o da a [15 ,16]. I assumes ha he di e ences be ween he pai ed alues a e no mally
dis ibu ed. The null hypo hesis o his es is ha he e is no signi ican di e ence be ween he simula ed and obse ed
a ic low and speed da a, and a p- alue less han 0.05 indica es a signi ican di e ence.
2.4.2. The Wilcoxon Signed-Rank Tes
The Wilcoxon signed- ank es , a non-pa ame ic es , is used when he assump ion o no mali y is no me and he da a
a e pai ed [17, 18, 19]. This es compa es he dis ibu ions o wo ela ed samples (simula ed and obse ed da a),
anking he absolu e di e ences be ween he pai s and hen es ing whe he he anks o hese di e ences signi ican ly
de ia e om ze o. I does no equi e he da a o ollow a no mal dis ibu ion, making i sui able o cases whe e he
da a may be skewed o con ain ou lie s. A p- alue less han 0.05 indica es ha he di e ence be ween he simula ed
and obse ed da a is s a is ically signi ican .
Bo h es s we e u ilized o assess he obus ness and accu acy o he a ic simula ion model in eplica ing eal-wo ld
condi ions. The pai ed T- es p o ides a di ec compa ison o means, while he Wilcoxon signed- ank es o e s a mo e
lexible app oach when he da a dis ibu ion does no mee pa ame ic assump ions.
3. Resul s
3.1. Calib a ion Resul s
As p e iously discussed, his s udy in ol ed wo dis inc calib a ions o analyze he impac o di e en pa ame e
con igu a ions on model pe o mance. The i s scena io employed a popula ion size o 20, a mu a ion a e o 20%, and
20 gene a ions, while he second scena io used a popula ion size o 30, a mu a ion a e o 30%, and 30 gene a ions.
Toge he , hese wo scena ios p oduced a o al o 1,300 samples (400 om he i s con igu a ion and 900 om he
second). The p ima y aim o hese analyses was o gene a e a su icien ly la ge sample size o ensu e ha he indings
a e obus and gene alizable.
Table 3 Calib a ion Resul s
W99
Pa ame e s
Pa ame e s
In e p e a ion
De aul
Calib a ion 1
Calib a ion 2
CC0
A e age s ands ill dis ance (m)
1.40
0.50
1.54
CC1
Headway (s)
1.20
1.18
1.03
CC2
Longi udinal oscilla ion (m)
8.00
7.14
8.93
CC3
S a o decele a ion p ocess (s)
-12.00
10.72
12.60
CC4
Minimal closing Δ (m/s)
-1.50
-0.23
-0.35
CC5
Minimal opening Δ (m/s)
2.10
0.25
0.44
CC6
Speed dependency o oscilla ion (10−4 ad/s)
6.00
5.06
5.69
CC7
Oscilla ion accele a ion – m/s2
0.25
0.21
0.31
CC8
Accele a ion a e when s a ing (m/s2)
2.00
2.30
2.69
CC9
Accele a ion beha io a 80 km/h (m/s2)
1.50
2.98
3.04
Me ic
Accu acy
72%
85%
83%

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The esul s e eal a end o diminishing e u ns wi h inc eased compu a ional e o . Speci ically, he i s con igu a ion
(20 gene a ions) achie ed an accu acy o 85%, while he second con igu a ion (30 gene a ions) esul ed in a sligh ly
lowe accu acy o 83%.
Case One
Case Two
Figu e 3 Op imiza ion Resul s.
These indings sugges ha inc easing he popula ion size, mu a ion a e, and numbe o gene a ions beyond a ce ain
poin may no yield p opo ional imp o emen s in model accu acy. Despi e his, bo h con igu a ions signi ican ly
ou pe o med he de aul pa ame e se ings, which p oduced an accu acy o 72%. These esul s highligh he alue o
pa ame e op imiza ion while emphasizing he need o balance compu a ional esou ces wi h expec ed gains. The nex
sec ion del es deepe in o he s a is ical es s conduc ed o e alua e hese ou comes and examines he ends obse ed.
3.2. S a is ical Tes ing
Figu e 4 Pai ed T- es o bo h Speed and Flow
Du ing he calib a ion p ocess, candida e solu ions om bo h simula ions unde wen igo ous s a is ical es ing o
assess hei signi icance o speed and low. Non-pa ame ic and pa ame ic me hods, including he pai ed - es and
Wilcoxon signed- ank es , we e applied o ensu e consis ency ac oss he esul s. Following hese es s, a sca e plo
was gene a ed o explo e he ela ionship be ween accu acy le els and s a is ical signi icance (p- alues).
The obse ed ends, as depic ed in he igu es below, highligh a key dis inc ion: while lowe accu acy le els achie ed
accep able s a is ical signi icance o speed, hey ailed o mee he s a is ical signi icance equi emen s o low in bo h
es s. This indica es ha lowe accu acy may sa is y he speed c i e ion bu alls sho o low equi emen s.
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Con e sely, a highe accu acy le els, pa icula ly hose exceeding he 80% h eshold, he p- alues consis en ly
su passed he ejec ion egion o bo h speed and low ac oss all es s. These indings sugges ha an accu acy le el o
80% o highe is gene ally su icien o p oduce esul s ha a e s a is ically indis inguishable om he g ound u h
da a. This unde sco es he impo ance o achie ing highe accu acy le els o ensu e obus and eliable ou comes.
Figu e 5 Wilcoxon Signed Ranked Tes o bo h Speed and Flow
4. Conclusion
This s udy demons a es he e ec i eness o using a gene ic algo i hm (GA) o calib a e a ca - ollowing model o
simula ing a ic beha io . By op imizing key pa ame e s in he Wiedemann 99 (W99) model, we signi ican ly
imp o ed i s accu acy in eplica ing obse ed a ic condi ions on a Cali o nia eeway segmen . The key akeaway is
he es ablishmen o a benchma k o simula ion accu acy. The esul s show ha achie ing an accu acy le el o 80% o
highe ensu es ha simula ed a ic speeds and lows a e s a is ically indis inguishable om eal-wo ld da a, alida ed
h ough pai ed T- es s and Wilcoxon signed- ank es s. This inding p o ides a clea h eshold o model eliabili y,
essen ial o making sound decisions in anspo a ion planning.
Addi ionally, he s udy highligh s he impo ance o balancing op imiza ion e o s wi h compu a ional e iciency, as
u he inc eases in accu acy yield diminishing e u ns. These esul s con ibu e o he g owing body o knowledge on
a ic simula ion calib a ion and se a ounda ion o u u e s udies o e ine and apply hese me hods in b oade
con ex s, such as he in eg a ion o connec ed and au onomous ehicles.
Ul ima ely, his esea ch p o ides a amewo k o es ablishing accep able le els o accu acy in a ic simula ions,
ensu ing hei eliabili y o policy-making and in as uc u e planning.
Compliance wi h e hical s anda ds
Disclosu e o con lic o in e es
No con lic o in e es o be disclosed.
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