Transcript Traffic Flow Characteristics (2)

Traffic
Flow
Traffic
TrafficFlow
Flow
Characteristics
(2)
Characteristics
Characteristics(2)
(2)
Learning Objectives
• To differentiate between interrupted and
uninterrupted flow facilities
• To define general and linear speed-density
relationships
• To derive, sketch, and apply Greenshield’s
Model of traffic flow
Recap
Spacing
Recap
Clearance
Recap
# vehicles/Distance
Density
Recap…
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Speed (v) – ft/sec or mph
Flow (q) – veh/sec or vph
Density (k) – veh/ft or vpm
Spacing (s) – ft/veh
Headway (h) – sec/veh
Clearance (c) – ft/veh
Gap (g) – sec/veh
Remember, units are critical!
Fundamental Relationships
• q=kv
(veh/hr) = (veh/mi)  (mi/hr)
• h=1/q
(sec/veh) = 1 / (veh/hr)  (3600)
• s=1/k
(ft/veh) = 1 / (veh/mi)  (5280)
Types of Facilities
• Uninterrupted flow
– Freeways
– Multilane highways
– Two-lane highways
Types of Facilities
• Interrupted flow
– Signalized streets
– Un-signalized streets
with stop signs
– Transit lanes
– Pedestrian walkways
General Speed-Density
Relationship
p.130
S
V
Free
normal flow
forced flow
Traffic
Jam
Q
Capacity
K
Density at
Capacity
Jam
Density
General Speed-Density
Relationship
p.137
K
V
Traffic
Jam
Free
forced flow
normal flow
Q
Capacity
K
Density at
Capacity
Jam
Density
General Speed-Density
Relationship
p.137
Q
V
Capacity
Free
Traffic
Jam
V
K
Density at
Capacity
Jam
Density
Greenshield’s Model
• Assume a linear relationship between v
and k:
 vf 
Low Density = High
v  v f   k
Speed
vf
k 
 j
High Density = Low
Speed
kj
Greenshield’s Model
Q
Max flow
vf
v0
qmax
K0
 vf
q  vf k 
k
 j
Kj
K
 2
k


Greenshield’s Model
V
Vf
1/k0=s0
V0
Q
Qmax
Max flow
Example
Assuming a linear v-k relationship, the mean
free speed is 60 mph near zero density, and
the corresponding jam density is 140 vpm.
Assume the average length of vehicles is 20
ft. Find:
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–
–
–
v(k) and q(k)
Sketch v-k, v-q, and q-k diagrams
Compute v and k at q=1000 vph
Compute the average headway, spacings, clearances,
and gaps when the flow is maximum