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Greenberg's Model: (Ce 425) Transportation Engineering

This document discusses Greenberg's model for traffic flow modeling. It presents Greenberg's model, which uses a fluid-flow analogy and the equation vs = C ln(kj/k) to relate speed, flow, and density. The document provides an example problem calculating maximum flow, speed, and density using a given speed-density relationship. It also gives another example problem calculating maximum flow using known jam density and density values. Finally, it presents traffic data to fit into the Greenberg model using regression analysis.

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2K views5 pages

Greenberg's Model: (Ce 425) Transportation Engineering

This document discusses Greenberg's model for traffic flow modeling. It presents Greenberg's model, which uses a fluid-flow analogy and the equation vs = C ln(kj/k) to relate speed, flow, and density. The document provides an example problem calculating maximum flow, speed, and density using a given speed-density relationship. It also gives another example problem calculating maximum flow using known jam density and density values. Finally, it presents traffic data to fit into the Greenberg model using regression analysis.

Uploaded by

guian doman
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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(CE 425) TRANSPORTATION ENGINEERING

J. J. J. Cabanban
University of the Cordilleras
College of Engineering and Architecture

Greenberg’s Model
Greenberg’s Model
• Macroscopic Approach
– Greenberg (1959) developed a model taking
speed, flow, and density measurements in the
Lincoln Tunnel resulting in a speed-density model
– Used a fluid-flow analogy concept, using the
form:
vs  C ln(k j / k )
– Greenberg’s model shows better goodness-of-fit
compared to Greenshield’s model, although it
violates boundary conditions in that zero density
can be attained at an infinitely high speed
J. J. J. Cabanban University of the Cordilleras Transportation Engineering
Example
• Problem
– The speed-density relationship of traffic on a
section of a freeway lane was estimated to be
v x  18.2 ln(220 / k )
– Required:
a. What is the maximum flow, speed, and density at
this flow?
b. What is the jam density?

J. J. J. Cabanban University of the Cordilleras Transportation Engineering


Example
• Problem
– Given kj = 130 veh/mi; and k = 30 veh/mi,
when vs = 30 mph, find qmax.

J. J. J. Cabanban University of the Cordilleras Transportation Engineering


Example
• Problem
– Using regression analysis, fit the data shown
into the Greenberg model.
Speed (mi/h) Density (veh/mi)
14.2 85
24.1 70
30.3 55
40.1 41
50.6 20
55.0 15

J. J. J. Cabanban University of the Cordilleras Transportation Engineering

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