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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

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

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