Learning Objectives

Learning Objectives

• To define and apply basic measures of traffic flow, including;– Speed– Volume– Density– Spacing and Headway– Lane occupancy– Clearance and gap

Traffic Flow

• Complex: between vehicles and drivers, among vehicles

• Stochastic: variability in outcome, cannot predict with certainty

• Theories and models– Macroscopic: aggregate, steady state – Microscopic: disaggregate, dynamics– Human factor: driver behavior

Speed (v)

• Rate of motion• Individual speed

• Average speed– Time mean speed

Arithmetic mean– Space mean speed

Harmonic mean

T

Lv

T

Lv avg

,

n

vv i

i

t

ii

i

is t

nL

n

tL

v

st vv

Individual Speed

600 700

1 0.0 2.0 50.0

2 4.4 6.7 45.0

3 6.0 8.0 50.0

4 11.4 14.3 35.0

5 15.0 17.5 40.0

6 17.5 20.0 40.0

7 21.1 23.3 45.0

8 23.3 25.0 60.0

Location (ft)

Ve

hic

le

Time of Passing (sec)

Speed (ft/sec)

(1)

Spot Speed

mph) or (mi/hr

ft/sec

09.345280/3600*50

500.00.2

6007001

v

Time Mean Speed

Mile post

Observation Period

(ft/sec) 6.458

6045404035504550

tv

Space Mean Speed

Observation Period

(mi/hr)(ft/sec) 1302447.12.25.25.29.223.22

8*100..vs

Ob

se

rva

tio

n D

ista

nc

e

Volume (q)

• Number of vehicles passing a point during a given time interval

• Typically quantified by Rate of Flow (vehicles per hour)

vph) or (veh/hr 11523600/25

8q

Time-Space Plot

0

100

200

300

400

500

600

700

800

900

1000

0 5 10 15 20 25

Time (sec)

Dis

tan

ce

(ft

)

Volume (q)

Density (k)

• Number of vehicles occupying a given length of roadway

• Typically measured as vehicles per mile (vpm), or vehicles per mile per lane (vpmpl)

Density (k)

Density (k)

(veh/mi)(mi/hr)(veh/hr) kvq *

(veh/mi)

(mi/hr)(veh/hr)

22.381.30/1152

*1.301152

k

k

Spacing (s)

• Front bumper to front bumper distance between successive vehicles

S1-2S2-3

T=3sec

Headway (h)

• Time between successive vehicles passing a fixed point

T=0 sec

h1-2=3sec

Spacing and Headway

spacing

headway

Spacing and Headway

A

What are the individual headways and the average headway measured at location A during the 25 sec period?

Spacing and Headway

A

What are the individual headways and the average headway measured at location A during the 25 sec period?

600 700

1 0.0 2.0

2 4.4 6.7

3 6.0 8.0

4 11.4 14.3

5 15.0 17.5

6 17.5 20.0

7 21.1 23.3

8 23.3 25.0

Location (ft)

Ve

hic

le

Time of Passing (sec)

h1-2

h2-3

Lane Occupancy

• Ratio of roadway occupied by vehicles

L1L2L3

D

D

LLO i

i

Clearance (c) and Gap (g)

• Front bumper to back bumper distance and time

Spacing (ft) or headway (sec)

Clearance (ft) or Gap (sec)

avg

avgavgavg v

Lhg

avgavgavg vgc *