TheImpactofNarrowLane
onSafetyoftheArterialRoads
Hyeonsup Lim
WhatdoweknowaboutNarrowLane?
•
AASHTOGreenbook,
lanewidthsmayvaryfrom10to12feet forruralandurbanarterials.
•
NCHRP330(EffectiveUtilizationofStreetWidthonUrbanArterials)
“Narrowerlanewidths(lessthan11ft)canbeused effectivelyinurbanarteri
alstreetimprovementprojectswheretheadditionalspacecanbeusedtorelieve
trafficcongestionoraddressspecificaccidentpatterns”…
•
Ingred B.Potts,etal.,2007
“Asafetyevaluationoflanewidthsforarterialroadwaysegmentsfoundnoindic
ation,exceptinlimitedcases,thattheuseofnarrowerlanesincreasescrashf
requencies”
2
WhatdoweknowaboutNarrowLane?
• HighwaySafetyManual
“Wideninglanesonruraltwo‐laneroadsreducesaspecificsetofrelatedcrashtypes,namelys
ingle‐vehiclerun‐off‐the‐roadcrashesandmultiple‐vehiclehead‐on,opposite‐directionsidesw
ipe,andsame‐directionsideswipecollisions.”
3
NegativeBinomial
Letx1 beVMTandynumberofcrashes
1 1
2 2
1
2 2
Ifx1 =0,then
2 2
indicatesthaty>0,unlessα+ β2x2=‐∞
4
NegativeBinomial
Whatifweusey/x1 (rate)insteadofy(count),wherex1 denotese
xposure?
1
2
2
Thisrestrictsx1>0,whichalsocanbeshownbelow
1
1
2
2
2
2
However,theterm–log(x1),whichiscalledanoffset,meansthaty
isproportionaltox1 withconstantproportionalitydependingont
hevalueoftheexplanatoryvariable
5
NegativeBinomial
Toalleviatethisissue,usex1 (orsimilarvariables)bothinleftand
rightside.
1
1
1
2
2
Whatisthistellingus?(expectation)
6
DescriptiveStatistic
•
4cities(GrandIsland,Lincoln,Omaha,andSouthSioux)ofNebraska.
•
1,956segmentsforyear2003to2012,andtotallengthis773.4miles
Variable
Year
TotalCrash
RelatedCrash
LaneWidth(ft)
SpeedLimit(mph)
NumberofLanes
AADT(veh/lane)
SegmentLength(miles)
RoadClassification* (categorical)
OneWay
BinaryVariable Shoulder
Median
(1=Yes/
On‐StreetParking
0=No)
CBD
N
18,227
18,227
18,227
18,227
18,227
18,227
18,227
18,227
18,227
18,227
18,227
18,227
18,227
18,227
Mean
2007.5
1.2
0.3
11.3
38.3
1.9
5348.1
0.39
15.5
0.0
0.3
0.7
0.1
0.1
StdDev
2.9
1.9
0.6
0.8
6.4
0.6
2460.1
0.33
0.9
0.2
0.4
0.4
0.2
0.3
Minimum Maximum
2003
2012
0
44
0.0
10.0
9.0
12.0
20
60
1
6
100.0
19480.4
0.02
3.88
14
17
0
1
0
1
0
1
0
1
0
1
7
VariableSelection
Whatshouldbey,x1,x2,...?
Fory,TotalCrashesvs CrasheswithSpecificTypes
μ+σ/2
μ
μ‐σ/2
 Relatedcrashtypeincludeshead‐onandsideswipecollisions
(bothsameandoppositedirection)
8
VariableSelection
Lane Width (ft)
Lane Width (ft)
9
ModelSelection
AkaikeInformationCriterion
•
IncludedVariables
OnStre
No.of
Should Media
AADT
etPark CBD
Limit Width Lanes
er
n
ing
Numberof
Model Parmeters Year Speed Lane
Segme Road
One
ntLen Classif
Way
gth
ication
logL
AIC
1
10
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
2
11
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
3
11
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
4
12
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
5
9
Y
Y
Y
Y
Y
Y
Y
Y
Y
6
10
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
‐11103.7 22,227.4
7
10
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
‐11103.8 22,227.5
8
9
Y
Y
Y
Y
Y
Y
Y
Y
Y
9
10
Y
Y
Y
Y
Y
Y
.
.
.
Y
Y
Y
‐11100.8 22,221.5
Y
‐11100 22,222.1
‐11100.5 22,222.9
Y
‐11099.9 22,223.7
‐11104 22,225.9
‐11104.8 22,227.6
Y
Y
‐11104 22,227.9
10
SummaryResult1
11
SummaryResult2
Comparedto12ftlane…
CMF9ft =exp(0.2833)=1.33
CMF10ft =exp(0.2990)=1.35
CMF11ft =exp(0.1617)=1.18
12
FinalModel
Parameter
DF
Estimate
Standard
Wald
Wald
Pr>ChiSq
Error 95%ConfidenceLimits Chi‐Square
Intercept
1
0.8851
0.1552
0.5809
1.1893
32.53
<.0001
Year_2003
1
‐0.0339
0.0069
‐0.0473
‐0.0204
24.3
<.0001
SpeedLimit
1
‐0.0481
0.0043
‐0.0566
‐0.0397
124.83
<.0001
NumberOfLanes
AADTK*LaneWidth
(11or12ft)
AADTK*LaneWidth
(9or10ft)
Shoulder*LaneWidth
(11or12ft)
Shoulder*LaneWidth
(9or10ft)
Median
OnStreetP*LaneWidth
(11or12ft)
OnStreetP*LaneWidth
(9or10ft)
SegmentLength
1
0.3192
0.0347
0.2512
0.3873
84.58
<.0001
1
‐0.0372
1
0.0263
1
‐0.1686
1
‐0.5252
1
‐0.3849
1
0.2131
1
0.2989
1
‐1.3371
0.0964
‐1.526
‐1.1483
Dispersion
1
2.8866
0.0987
2.6995
3.0867
AsAADTincreases,sodoestheimpactofLaneWidth.
0.0093
‐0.0554
‐0.0191
16.16
<.0001
AsAADTincreases,thenarrowlaneincreasestherela
0.0129
0.001
0.0517
4.16
0.0414
tedcrashratewhilethewidelanereducesit
0.0574
‐0.281
‐0.0562
8.64
0.0033
‐40%byshoulderwherethelanewidthis9or10ft,
while‐16%wherethelanewidthis11or12ft.
0.1285
‐0.7771
‐0.2732
16.69
<.0001
0.0499
‐0.4827
‐0.2871
59.5
<.0001
0.0964
0.0243
0.402
4.89
0.027
+35%byon‐streetP
wherethelanewidthis9or10ft,
while+24%wherethelanewidthis11or12ft.
0.1055
0.0921
0.5057
8.03
0.0046
192.54
<.0001
13
Conclusion&Limitation
•
Thenarrowlanedoesnotnecessarilyalwaysincrease(ordecrease)crashes
•
CarefullyconsidertheimplementationofnarrowinglanesdependingonAAD
T,andpresenceofshoulderandon‐streetparking
(e.g.,wemightconsiderthenarrowlaneprimarilyontheroadwaywhereAA
DTisnottoohigh,andthereisshoulder,buton‐streetparking)
•
Difficulttoprovideageneralconclusion
•
Modelissensitivetovariableselection
•
Findinginherentimpactofnarrowinglanemightbeveryimportant
14
APropertyofHarmonicMean:
APropertyofSMSthatYouShouldConsider
Hyeonsup Lim
Quiz
• Supposethatwehaveadataset…
1,2,3,…18,19,20
• (A)Calculatetheharmonicmeanofpopulation
• (B)Now,youpickthreeofthem,calculateagain
• Choosethebestanswerfromthefollowings:
1)E(A)>E(B),2)E(A)<E(B),3)E(A)=E(B)
16
Hint
• Exampleof(A)and(B)
.
⋯
.
• Thereare20C3=1,140 casesof(B).
17
Answer
• E(A)=5.56
⋯
• E(B)=
,
=7.82
• 1)E(A)>E(B),2)E(A)<E(B),3)E(A)=E(B)
18
Herearemore
19
Simulationusingafielddata
20
Why?
···
,
,
,
,
,
1
1
2
,
1
1
1
···
,
1
4
···
···
,
2
,
2
1
1
1
1
21
Whatdoesitmean?
• It means that we overestimate SMS of population,
when we have a data set which of sample size is
smaller than the entire population.
,
22
Whyisitsoimportant?
A
Vehicle 2
Collected
Collected
Collected
Collected
Collected
Vehicle 3
...
Collected
Vehicle N-1
Vehicle N
Collected
Collected
The Number of Vehicles
Vehicle 1
B
The Segment Length
23
Whatdoweneedtodo?
• Thisstudyonlyidentifies thattheexpectedvalu
eofSMSisrelatedtosamplesize.
• Itremainsthefollowingquestions:
 Howmuchdifferent?
 Relationshipwithavariationofdata?
 Ifso,canweestimateSMSforanysamplesize?
24
Thankyou
[email protected]
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