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7/29/2019 2.1. Traffic Flow Characteristics
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CIVL4660TrafficEngineering
2.1:TrafficFlowCharacteristics
Dr.JeffX.Ban
ra c ng neer ng
Rensselaer
Polytechnic
Institute
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Amacroscopic
view
of
vehicular
traffic
as
flowsvs.amicrosco icviewoftraffic
focusingonindividualvehicles
Understandtrafficflowcharacteristics
Investigatethe
traffic
flow
relationships
in
TrafficEngineeringstudies
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traffic
stream
characteristics
are
based
solely
for example:freewaysegmentsmorethan2miles without fixed interru tions
InterruptedFlow
forexample:signalizedintersections
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Volume
or
flow
rate
density
headway
spacing
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Headwayh (s/veh):time
interval
that
two
consecutivevehicles frontbum ertofront
bumper)passonestationarypoint
stationarypointduringaunittimeinterval
aperiodoftime(temporally)
q
h =5
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highwayduring
aspecific
time
interval
(one
lane,
onedirectionetc);unit:veh
Flowrate:numberofvehicles/hour;themeasurement
duration
could
be
less
than
1hour
Dailyvolume:representannualtrendofvolumeinhighway.
Hourlyvolume:peakhourvolume(directional)
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Average
Annual
Daily
Traffic
(AADT) Average24hourvolumeoverayear
Average24hrvolumeperweekday
AverageDaily
Traffic
(ADT)
SameasAADT, utaverageoverperio esst anayear,say,amonth
AverageWeekdayTraffic(AWT)
Same
as
AAWT,
but
average
over
aperiod
less
than
ayear,
say,
amonth
**Generallynotdirectional
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AADTApplications
Estimationofhighwayuse
Estimationoftrends
Economicfeasibility
evaluation
Planning
Maintenance
pp cat ons Planning
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Dailyvolume
is
useful
for
planning
purposes,
butcannotbeusedalonefordesi nand
operationpurposes
Peakhourvolumegenerallyisdirectional
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DDHV=AADT*K*D
K:
proportion
of
daily
traffic
occurring
in
the
peak
our
D:proportionofpeakhourtraffictravelinginthe
peakdirection
KandDgenerallydecreaseinhighdensityarea
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Themax
#veh passing
apoint
on
ahighway
over
60
consecutiveminutes
= PHV
(0.25
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memeanspee spotor nstantaneousspee Individualvehiclesspeedismeasuredatasingle
Arithmetic averageofallvehiclesthataremeasureddurin a time eriod
i
=N
it vN
u1
1
N: number of vehicles that are measured at a pre-specified time interval13
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Spacemeanspeed(harmonicmean) Individualvehiclesspeedisnotdirectlymeasured
n v ua ve c e s rave meacrossaprespec e distanceismeasured
Obtainavera e
travel
time
Obtainaveragespacemeanspeed
=D
=N
i
avg
i
i
v
D
Nt
v
1
1
==N
i
avg
s
vNt
Du
1
11
1
it 14
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Relationshipbetween
timemeanspeedand
spacemeanspeed
Timemeanspeedisgreaterorequalto spacemean
speed Thetwospeedshavethefollowingrelationship:
s
sst
uuu +=
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44,42,
51,
49,
46
mph.
Assume
each
vehicle
is
,
timemeanspeedandspacemeanspeed?
Answer:ut=46.4mph>us =46.2mph
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Spacing s (ft/veh):distance
(front
bumper
to
frontbumper)betweentwoconsecutivevehicles
Densityk(veh/lane/mile):numberofvehiclesper
laneper
mile,
which
is
defined
on
asegment
of
roa spatia y atagiventime tempora y
s1
=
s 17
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aneoccupancy:measureuse n reewaysurveillance. Ratioofthetimethatvehiclesarepresentatadetection
stationinatrafficlanecomparedtotheobservationtime(0
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InductanceLoopDetector
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Laneoccupancy ei
LCLt =+= Time that the vehicle used to travelL+C:
100
occupiedisdetectorvehicletimetotal
==
ti
ss
sv
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Laneoccupancy Assumekvehiclesareevenlyspreadouton1mile
highwayatspeed (mile/hr)sv Density = k vehicle/mile
Totaltimeneededtohaveallvehiclespassthe
1 mile
detectoris:
(hrs)
Therefore:
svT 1=100
/1
5280100
s
si
v
v
T
t
==
(veh/mile)100
5280
)(
5280
eLCLk
=+
=
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Signal Coordination
Length of acceleration andece era on anes o reeway
on-ramps and off-ramps
Estimation of safe passing
si ht distances
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UsingGPSDatatoConstructTime
SpaceDiagram
4.0
4.5
.
Oak Villa Blvd
3.0
3.5
(m
i) Wooddale
Airline Hwy interchange
2.0
2.5
Distanc
Ardenwood
Donmoor
Bon Marche MallLobdell
0.5
1.0
. Posted speed limit
Actual profile
N Foster
Cloud
0.0
0 100 200 300 400 500 600
Travel time (s)
Acadian Thruway
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7000o(feet)
5000
6000
ucktowardsS
anPabl
2000
3000
4000
from
University:Shatt
7000
Pab
lo(feet)
5.54 5.545 5.55 5.555 5.56 5.565 5.57
x 104
0
1000
time (seconds)distancetraveled
4000
5000
hattucktowardsSa
2000
3000
ledfrom
University:
5.4 5.5 5.6 5.7 5.8 5.9 6 6.1 6.2
x 104
0
1000
time (seconds)dis
tancetrav
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Time Latitude Lon itude S eed(UTC) () () (mph)
16:27:39 30.389885 -91.242426 40.016:27:40 30.390090 -91.242276 40.6
16:27:41 30.390159 -91.242225 40.7
16:27:42 30.390298 -91.242122 41.016:27:43 30.390507 -91.241966 41.8
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RelationshipsamongFlow,speed,and
density
v=S*D(textbook)
q=k*v(commonly
used)
Flow veh hr =S eed mile hr *Densit veh mile
Proof:Considerasegmentoffreeway.
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60
70
80
40
50
ed
(mph)
20
30sp
0
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150
densit veh/mile/lane
Field data Vo=15 mph & Kj=250 veh/mi/ln
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45
55
25
35
ee
d(mph)
5
15S
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140Density (veh/mi/ln)
alpha =1.0 (Vo =5, Vf =35, Kj =75) alpha =1.25 (Vo =5, Vf =37, Kj =90)
alpha =1.67 (Vo =5, Vf =39, Kj =130)
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Speed,Flow,andDensity
Relationship
Wehave
BkAv =2==
( ) vv
AvAvq
2
=
=
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RelationshipsbetweenSpeed,
Densityand
Flow
A:
almost
zero
density,
free
flow
speed,
very
low
volume B:increaseddensity,reducedspeed,increasedvolume
C:increaseddensity,reducedspeed,maxvolume
D:jamdensity,minspeed(crawling),verylowvolume
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GeneralPropertiesforanyTrafficFlow
Model
Needto
satisfy
four
boundary
conditions
Flowiszeroatmaximumdensity
Flowdensitycurvesareconcave(i.e.,thereisapoint
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TheproductofthexycoordinatesofthepointP istheflowassociatedwithP
Maxflowoccursat:B
kBkAk
q
2020 ===
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Theslope ofthelineconnectinganypointonthecurveandtheoriginistheaveragespeed
Fundamental Diagram
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Theslopeofthelineconnectinganypointonthecurve
and
the
origin
is
the
inverse
of
the
density
Maxflowoccurredat:2
0 vv
q==
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Greenshields model Greenbergs model k
=jam
fk
vv 1
=jamk
v n
Modified Greenshields model Underwoods model
=jam
fk
vvvv 100 )(
=m
fk
vv exp
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. ,
200ft/veh.
Calculate
the
average
speed
of
the
.
Flowq=1/h=0.4veh/s=1440veh/h
.
.
Speedv=q/k=1440/26.4=54.5mi/h
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TextbookChapter
5
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