Transcript Slide 1

Learning Objectives
• To define and apply basic measures of
traffic flow, including;
–
–
–
–
–
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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
L
L
v
, vavg 
T
T
• Average speed
– Time mean speed
Arithmetic mean
– Space mean speed
Harmonic mean
vt 
v
i
i
n
L
nL
vs 

ti  ti
i n i
vt  vs
Individual Speed
(1)
Time of
Location (ft) Speed
Passing (sec) 600
700 (ft/sec)
700 600
v1 
 50 ft/sec
2.0  0.0
 50* 3600/ 5280 34.09 (mi/hr or mph)
Vehicle
Spot
Speed
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
Time Mean Speed
Mile
post
Observation Period
vt 
50  45  50  35  40  40  45  60
 45.6 (ft/sec)
8
Observation Distance
Space Mean Speed
Observation Period
100* 8
vs 
 44.2(ft/sec)  30.1(mi/hr)
2  2.3  2  2.9  2.5  2.5  2.2  1.7
Volume (q)
• Number of vehicles passing a point during
a given time interval
• Typically quantified by Rate of Flow
(vehicles per hour)
Time-Space Plot
1000
900
800
Distance (ft)
700
q
600
500
400
300
200
100
0
0
5
10
15
Time (sec)
20
25
8
 1152 (veh/hr or vph)
25 / 3600
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)
q(veh/hr)  v(mi/hr) * k(veh/mi)
1152 (veh/hr)  30 .1(mi/hr) * k
k  1152 / 30 .1  38 .22 (veh/mi)
Spacing (s)
• Front bumper to front bumper distance
between successive vehicles
S2-3
S1-2
Headway (h)
• Time between successive vehicles passing
a fixed point
T=3sec
T=0
sec
h1-2=3sec
Spacing and Headway
spacing
headway
Spacing and Headway
What are the individual headways and the average headway measured at
location A during the 25 sec period?
A
Spacing and Headway
What are the individual headways and the average headway measured at
location A during the 25 sec period?
Time of
Location (ft)
Passing (sec) 600
700
Vehicle
A
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
h1-2
h2-3
Lane Occupancy
• Ratio of roadway occupied by vehicles
L2
L3
LO 
L
i
i
D
L1
D
Clearance (c) and Gap (g)
• Front bumper to back bumper distance
and time
Clearance (ft) or Gap (sec)
g avg  havg 
Lavg
vavg
cavg  gavg * vavg
Spacing (ft) or headway (sec)