Learning Objectives
Post on 05-Jan-2016
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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 *
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