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Traffic Concepts

CEE 320Anne Goodchild

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Outline

1. Basic Conceptsa. Flow Rateb. Spacingc. Headwayd. Speede. Density

2. Relationships3. 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

tnq

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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

lnu

n

ii

1

1

nnltltltn

t ...12211

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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).

uq

lnk

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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 (m

ph)

kj

Jam Density

uf

Free Flow Speed

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Flow vs. Density

jf k

kkuq2

Density (veh/mile)

FLow

(veh

/hr)

kj

Jam Density

Optimal flow, capacity, qm

km

Optimal densityUncongested Flow

Congested Flow

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Speed vs. Flow

fj u

uukq2

Flow (veh/hr)

Spe

ed (m

ph)

uf

Free Flow Speed

Optimal flow, capacity, qm

Uncongested Flow

Congested Flow

um

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3-D Model

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ExampleI-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

Perc

ent o

f Dai

ly T

raffi

c

Rural CarsBusiness Day TrucksThrough TrucksUrban Cars

From WSDOT 2003 Annual Traffic Report

From WSDOT 2003 Annual Traffic Report

I-405 NE 37th St GP SB

0

500

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 Weekday Volume Profile: GP and HOV Lanes (Nov 98)

GP

HOV

I-5 NE 45th St-SB GP SB

0

500

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)

I-5 S Spokane St GP NB

0

500

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 GP and HOV Volume and Speed Conditions

HOV speed < 45 mph

Saturday, J uly 31, 1999 DataMulticolor = Average GP LaneGray = HOV Lane

I-405 NE 37th St GP NB

0

500

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 PM0

10

20

30

40

50

60

70

80

90

100

Estimated Weekday Volume, Speed, and Reliability Conditions (1999)

GP

HOV

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.