Course Logistics
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•
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Course grading scheme correct
Team assignments posted
HW 1 posted
Note-taker needed
Website and Transportation wiki
CEE 320
Fall 2008
• Traffic Concepts
Traffic questions
CEE 320
Fall 2008
• Have you ever driven out of a traffic jam
only to find that nothing was apparently
causing it?
• Why does stop and go traffic happen?
• Why does traffic slow down as it gets
heavier?
• How do we predict congestion?
CEE 320
Fall 2008
Traffic Concepts
CEE 320
Anne Goodchild
Traffic – Time of Day Patterns
9.00%
8.00%
Percent of Daily Traffic
7.00%
6.00%
5.00%
4.00%
Rural Cars
Business Day Trucks
Through Trucks
Urban Cars
3.00%
2.00%
1.00%
CEE 320
Fall 2008
0.00%
1
3
5
7
9
11
13
15
Hour of Day
17
19
21
23
CEE 320
Fall 2008
How can we describe traffic?
How can we describe traffic?
CEE 320
Fall 2008
• Consider one lane of traffic
• Traffic is constantly changing
CEE 320
Fall 2008
From WSDOT 2003 Annual Traffic Report
CEE 320
Fall 2008
From WSDOT 2003 Annual Traffic Report
How would you model traffic flow?
CEE 320
Fall 2008
•
•
•
•
As a liquid?
As a glacier?
Discrete event simulation?
…
Concepts
CEE 320
Fall 2008
• Flow
• Speed
• Density
Flow (q)
• The number of vehicles (n) passing some
designated roadway point in a given time interval
(t)
n
q
t
CEE 320
Fall 2008
• Units typically vehicles/hour
• Volume typically refers to flow in an hour
Flow
• Text also uses flow rate
• Flow is constantly varying!
CEE 320
Fall 2008
• Analysis flow rate is peak 15-minute flow
within the hour of interest.
CEE 320
Fall 2008
Spacing
How much space do you leave
between vehicles?
CEE 320
Fall 2008
• 2 chevrons!
• Depends on speed
• Varies for each person
Spacing
CEE 320
Fall 2008
• The distance (ft) between successive
vehicles in a traffic stream, as measured
from front bumper to front bumper
Spacing
• Density
– the number of vehicles over a length of
freeway
• Occupancy
CEE 320
Fall 2008
– Measured by loop detectors
– The percent of time the loop is covered by a
vehicle
Headway (h)
• The time (in seconds) between successive
vehicles, as their front bumpers pass a
given point.
q
n
n
h
CEE 320
Fall 2008
i 1
i
1

h
CEE 320
Fall 2008
Headway
From HCM 2000
How do we measure average
speed?
• The average speed of vehicles that pass
by a specific point in space over a specific
time period (TMS).
CEE 320
Fall 2008
• Time necessary for a vehicle to travel a
length of roadway (SMS).
Measuring Speed
• Time mean speed
– Taken at a specific point
– Average of instantaneous speeds
• Space mean speed (u)
CEE 320
Fall 2008
– Harmonic speed
– Look at a segment of roadway
– Average speed of all vehicles in that segment
Time Mean Speed
• Arithmetic mean of speeds observed at some
point
• Easy to measure
radar
n
CEE 320
Fall 2008
ut 
u
i 1
n
i
Space Mean Speed
• It is the harmonic mean
us 
n
n
1

i 1 ui

nl
n
t
i 1
i
1
t  t1l1  t 2l2  ...  t nln 
n
CEE 320
Fall 2008
• Used in traffic models, but harder to measure
Example
• 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?
CEE 320
Fall 2008
• What is your average speed over that distance?
Average speed over time and average
speed over distance are different
10 miles
40 mph
60 mph
7.5 minutes
5 minutes
CEE 320
Fall 2008
12.5 minutes
7.5 minutes
5 minutes
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?
CEE 320
Fall 2008
•
•
•
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
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 distance
CEE 320
Fall 2008
1 mile/0.0182 hours = 55.05 mph
Density (k - konzentration)
• 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).
CEE 320
Fall 2008
n q
k 
l u
Density (k)
• Number of vehicles in
length of segment
• Inverse of average spacing
k
n
n
s
CEE 320
Fall 2008
i 1
i

1
s
CEE 320
Fall 2008
Density
q
k
u
Traffic Flow Theory
• A model for the relationship
between flow, density, and
speed
• Represents idealized
behavior and fundamental
relationships
CEE 320
Fall 2008
• Useful for traffic analysis
flow
speed
Complete the charts
CEE 320
Fall 2008
density
density
speed
Complete the charts
CEE 320
Fall 2008
flow
Speed vs. Density

k
u  u f 1 
 k
j

CEE 320
Fall 2008
Speed (mph)
uf
Free Flow Speed
Density (veh/mile)
kj
Jam Density




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)
CEE 320
Fall 2008
– The maximum flow a section of roadway can
maintain
Flow vs. Density
2 

k
q  uf k  


k
j 

Congested Flow
CEE 320
Fall 2008
FLow (veh/hr)
Highest flow,
capacity, qm
Uncongested Flow
km
Optimal density
Density (veh/mile)
kj
Jam Density
Speed vs. Flow
Speed (mph)
uf
Free Flow Speed




Uncongested Flow
um
Congested Flow
CEE 320
Fall 2008
2

u
q  k j u 

u
f

Highest flow,
Flow (veh/hr) capacity, qm
qm is bottleneck discharge rate
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)
CEE 320
Fall 2008
• Flow is easy to measure
• Occupancy is measure of density
• Only need to measure 2 of 3
CEE 320
Fall 2008
Loop Detector
Freeway Monitoring
CEE 320
Fall 2008
Loop Detector Signatures
Inductance Loop Detectors
Loop inductance decreases when a car is on top of it.
T = ton
ton
0
Inductance
Time
CEE 320
Fall 2008
toff
T = toff
Inductance Loop Detectors
Inductance
High
low
Tn Single
tn1 loop measurements?
tn2
tn3
Tn+1
Time
• Single loops can measure:
CEE 320
Fall 2008
– Occupancy (O): % of time loop is occupied per interval
– Volume (N): vehicles per interval
How do you estimate speed from a
single loop detector?
• You know how long it took the object to
pass over the detector
• You know the percent of time (in a short
interval) the loop was covered by a vehicle
CEE 320
Fall 2008
• What else do you need to know?
Can We Get Speed from a Single Loop?
EVL
s
to
s = speed (ft/sec)
EVL = effective vehicle length (ft)
to = occupancy time (s)
CEE 320
Fall 2008
EVL ~ vehicle length + detector length (24 feet)
Estimating Speed from a Single Loop?
• Using typical traffic data
N
sec
s
 3600
T O g
hr
s = speed (miles/hr)
N = number of vehicles in the observation interval
T = observation interval (s)
O = percentage of time the loop is occupied by vehicles
during the observation interval (occupancy)
CEE 320
Fall 2008
g = speed estimation parameter
g
5280 ft mile
EVL  100
100 converts percent to decimal
What speed is this?
CEE 320
Fall 2008
• TMS