traffic flow characteristics (2). learning objectives to differentiate between interrupted and...
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Traffic Flow Characteristics (2)
Traffic Flow Characteristics (2)
Traffic Flow Characteristics (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
Density
# vehicles/Distance
Recap…
• 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
Free
V
KJam
DensityDensity at Capacity
S
QTraffic
JamCapacity
normal flow
forced flow
p.130
General Speed-Density Relationship
Free
V
KJam
DensityDensity at Capacity
K
Q
Traffic Jam
Capacity
normal flow
forced flow
p.137
General Speed-Density Relationship
Free
V
KJam
DensityDensity at Capacity
Q
VTraffic Jam
Capacity
p.137
Greenshield’s Model
• Assume a linear relationship between v and k:
High Density = Low Speed
Low Density = High Speedvf
kj
kk
vvv
j
ff
Greenshield’s Model
K
QMax flow
qmax
K0Kj
vf v0 2kk
vkvq
j
ff
Greenshield’s Model
Q
V
Max flowQmax
Vf
V0
1/k0=s0
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:
– 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