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Know about Traffic Flow Characteristics (2)


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Traffic Flow Characteristics 2

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Traffic Flow Characteristics (2)

Traffic Flow Characteristics (2)

Traffic Flow Characteristics (2)


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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


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Recap

Spacing


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Recap

Clearance


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Recap

# vehicles/Distance

Density


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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!


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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)


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Types of Facilities

  • Uninterrupted flow

    • Freeways

    • Multilane highways

    • Two-lane highways


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Types of Facilities

  • Interrupted flow

    • Signalized streets

    • Un-signalized streets with stop signs

    • Transit lanes

    • Pedestrian walkways


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General Speed-Density Relationship

p.130

S

V

Free

normal flow

forced flow

Traffic

Jam

Q

Capacity

K

Density at Capacity

Jam Density


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General Speed-Density Relationship

p.137

K

V

Traffic

Jam

Free

forced flow

normal flow

Q

Capacity

K

Density at Capacity

Jam Density


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General Speed-Density Relationship

p.137

Q

V

Capacity

Free

Traffic

Jam

V

K

Density at Capacity

Jam Density


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Greenshield’s Model

  • Assume a linear relationship between v and k:

Low Density = High Speed

vf

High Density = Low Speed

kj


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vf

v0

Greenshield’s Model

Q

Max flow

qmax

K

Kj

K0


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Greenshield’s Model

V

Vf

1/k0=s0

V0

Q

Qmax

Max flow


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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