cee 320 fall 2008 course logistics hw3 and hw4 returned midterms returned wednesday hw5 assigned...
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Course Logistics
• HW3 and HW4 returned• Midterms returned Wednesday• HW5 assigned today, due next Monday• Project 1 due Friday
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Traffic Concepts
CEE 320Anne Goodchild
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2nd Phase of Class
• Move from infrastructure or hard side of transportation to operations or soft side of transportation
• Consider models of the vehicles moving on the infrastructure and how to analyze or manage them– Traffic flow theory– Queueing theory
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Traffic – Time of Day Patterns
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1 3 5 7 9 11 13 15 17 19 21 23
Hour of Day
Perc
ent o
f Dai
ly T
raff
ic
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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Traffic Flow Theory
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
• Uninterupted flow
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Flow (q)
• The number of vehicles (n) passing some designated roadway point in a given time interval (t)
• Units typically vehicles/hour• Volume typically refers to flow in an hour
t
nq
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Flow
• Text also uses flow rate
• Flow varies over time
• Analysis flow rate is peak 15-minute flow within the hour of interest.
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Spacing
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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.
hh
nq n
ii
1
1
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Headway
From HCM 2000
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Measuring Speed
• Time mean speed– Taken at a specific point– Average of instantaneous speeds
• Space mean speed – Harmonic speed– Look at a segment of roadway– Average speed of all vehicles in that segment
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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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Time Mean Speed
• Arithmetic mean of speeds observed at some point
• Easy to measure
n
uu
n
ii
t
1
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Space Mean Speed
• It is the harmonic mean
• More intuitive as measure of traffic, but harder to measure
t
lus nnltltlt
nt ...
12211
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Example time
• You are in a vehicle traveling a total of 10 miles. – the first 5 miles you travel at 40 mph – the next 5 miles you travel at exactly 60 mph
• What is your average speed over the time you spent traveling that 10 miles?
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Average speed over time and average speed over distance are different
10 miles
40 mph 60 mph
7.5 minutes 5 minutes
12.5 minutes
7.5 minutes 5 minutes
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Example time
• You are in a vehicle traveling a total of 10 miles. – the first 5 miles you travel at 40 mph – the next 5 miles you travel at exactly 60 mph
• What is your average speed over the time you spent traveling that 10 miles?
• 5 miles at 40 mph = 7.5 minutes• 5 miles at 60 mph = 5 minutes• weighted average = (40(7.5) + 60(5))/(7.5 + 5) = 48
mph
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Example - distance
• 5 vehicles over a given 1 mile section take
1.0, 1.2, 1.5, 0.75 and 1.0 minutes respectively
• Average travel time – 5.45/5 = 1.09 minutes = 0.0182 hours
• Therefore, average speed over that distance1 mile/0.0182 hours = 55.05 mph
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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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Density (k)
• Number of vehicles in length of segment
• Inverse of average spacing
ss
nk n
ii
1
1
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Density
u
qk
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Traffic Flow Theory
• A model for the relationship between flow, density, and speed
• Represents idealized behavior and fundamental relationships
• Useful for traffic analysis
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Additional definitions
• Free-flow speed (uf)– The speed at which vehicles will travel
unimpeded
• Jam density (kj)– The density of vehicles in stopped traffic
• Capacity (qm)– The maximum flow a section of roadway can
maintain
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Speed-density relationship
jf k
kuu 1
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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-density relationship
jf k
kkuq
2
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Flow vs. Density
jf k
kkuq
2
Density (veh/mile)
FLo
w (
veh/
hr)
kj
Jam Density
Highest flow, capacity, qm
km
Optimal densityUncongested Flow
Congested Flow
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Speed-flow relationship
fj u
uukq
2
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Speed vs. Flow
fj u
uukq
2
Flow (veh/hr)
Spe
ed (
mph
)
uf
Free Flow Speed
Highest flow, capacity, qm
Uncongested Flow
Congested Flow
um
qm is bottleneck discharge rate
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Measurement
• Density can easily be measured by remote sensing, but has historically been difficult to measure– Use occupancy obtained from loop-detectors
• TMS more easy to measure than SMS– Use correction or approximation– Easy to measure with remote sensing (GPS)
• Flow and headway are easy to measure• Occupancy is measure of density• Only need to measure 2 of 3