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Traffic Concepts
CEE 320Steve Muench
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Outline
1. Basic Conceptsa. Flow Rate
b. Spacing
c. Headway
d. Speed
e. Density
2. Relationships
3. Example
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Concepts
• Definitions• Volume, Speed, Density relationships
• Speed– Space mean speed– Time mean speed
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Flow Rate (q)
• The number of vehicles (n) passing some designated roadway point in a given time interval (t)
• Units are typically vehicles/hour
• Flow rate is different than volume
t
nq =
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Spacing
• The distance (ft) between successive vehicles in a traffic stream, as measured from front bumper to front bumper
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Headway (h)
• The time (in seconds) between successive vehicles, as their front bumpers pass a given point.
∑=
=n
iiht
1 hh
nq n
ii
1
1
==∑
=
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Headway
From HCM 2000
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Speed
• Time mean speed (spot speed)– Arithmetic mean of all instantaneous vehicle
speeds at a given “spot” on a roadway section
• Space mean speed (u)– The mean travel speed of vehicles traversing a
roadway segment of a known distance (d)– More useful for traffic applications
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Space Mean Speed
• It is the harmonic mean (1/H = 1/a + 1/b + …)
• Space mean speed is always less than time mean speed
t
ln
u
n
ii∑
== 1
1
( )nnltltltn
t +++= ...1
2211
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Time Mean vs. Space Mean Speed
From HCM 2000
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Density (k)
• The number of vehicles (n) occupying a given length (l) of a lane or roadway at a particular instant
• Unit of density is vehicles per mile (vpm).
u
q
l
nk ==
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Other Concepts
• Free-flow speed (uf)
• Jam density (kj)
• Capacity (qm)
( ) ( )vehftspacingmivehDensity
/
280,5/ =
( ) ( )( )sftspeed
vehftspacingvehsHeadway
/
// =
( ) ( )vehsheadwayhrvehrateFlow
/
600,3/ =
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Speed vs. Density
−=
jf k
kuu 1
Density (veh/mile)
Spe
ed (
mph
)
kj
Jam Density
uf
Free Flow Speed
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Flow vs. Density
−=
jf k
kkuq
2
Density (veh/mile)
FLo
w (
veh/
hr)
kj
Jam Density
Optimal flow, capacity, qm
km
Optimal densityUncongested Flow
Congested Flow
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Speed vs. Flow
−=
fj u
uukq
2
Flow (veh/hr)
Spe
ed (
mph
)
uf
Free Flow Speed
Optimal flow, capacity, qm
Uncongested Flow
Congested Flow
um
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3-D Model
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Example
I-5 over the ship canal bridge has 4 lanes in each direction. The northbound capacity is 8200 veh/hr/lane and the free-flow speed is 65 mph. What is the maximum flow rate, maximum density, jam density? If a one-hour vehicle count in the northbound direction for the outside lane gives 7034 vehicles in a non-congested condition, what is the estimated space mean speed of these 7034 vehicles?
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Traffic – Time of Day Patterns
0.00%
1.00%
2.00%
3.00%
4.00%
5.00%
6.00%
7.00%
8.00%
9.00%
1 3 5 7 9 11 13 15 17 19 21 23
Hour of Day
Per
cent
of D
aily
Tra
ffic
Rural Cars
Business Day Trucks
Through Trucks
Urban Cars
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From WSDOT 2003 Annual Traffic Report
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From WSDOT 2003 Annual Traffic Report
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I-405 NE 37th St GP SB
0
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2500
12 AM 2 AM 4 AM 6 AM 8 AM 10 AM 12 PM 2 PM 4 PM 6 PM 8 PM 10 PM
Estimated Weekday Volume Profile: GP and HOV Lanes (Nov 98)
GP
HOV
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I-5 NE 45th St-SB GP SB
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1000
1500
2000
2500
12 AM 2 AM 4 AM 6 AM 8 AM 10 AM 12 PM 2 PM 4 PM 6 PM 8 PM 10 PM
Estimated Volume and Speed Conditions (2/17/00)
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I-5 S Spokane St GP NB
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1000
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2500
12 AM 2 AM 4 AM 6 AM 8 AM 10 AM 12 PM 2 PM 4 PM 6 PM 8 PM 10 PM
Estimated GP and HOV Volume and Speed Conditions
HOV speed < 45 mph
Saturday, July 31, 1999 DataMulticolor = Average GP LaneGray = HOV Lane
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I-405 NE 37th St GP NB
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2500
12 AM 2 AM 4 AM 6 AM 8 AM 10 AM 12 PM 2 PM 4 PM 6 PM 8 PM 10 PM
0
10
20
30
40
50
60
70
80
90
100
Estimated Weekday Volume, Speed, and Reliability Conditions (1999)
GP
HOV
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Time PMAM0 2 4 6 8 10 12 2 4 6 8 10 12
Time PMAM0 2 4 6 8 10 12 2 4 6 8 10 12
405
5
Montlake Blvd.
520
Arboretum
92nd Ave.
B’vue. Way
148th Ave.
NE 60th St.
84th Ave.
Lk. Wash.
Uncongested, near speed limit
Restricted movement but near speed limit
More heavily congested, 45 - 55 mph
Extremely congested, unstable flow
Westbound
SR 520 Traffic Profile General Purpose Lanes 1997 Weekday Average East bound
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Primary References
• Mannering, F.L.; Kilareski, W.P. and Washburn, S.S. (2005). Principles of Highway Engineering and Traffic Analysis, Third Edition. Chapter 5
• Transportation Research Board. (2000). Highway Capacity Manual 2000. National Research Council, Washington, D.C.