The table below shows data on speeds and corresponding densities on a section of a rural collector road. If it can be assumed that the traffic flow characteristics can be described by the Greenberg model, develop an appropriate relationship between the flow and density. Also determine the capacity of this section of the road.

Question

What will be an ideal response?

Answer 1

A linear regression analysis can be applied to a logarithmic transformation the

given data to estimate parameters in Greenberg’s model of traffic flow.

Greenberg’s model (Equation 6.26) is:



A linear regression model takes the form y = a + bx; therefore, in this case, the

given data us and ln k correspond to y and x respectively, c ln kj is represented by

a, and c is represented by –b. The linear regression analysis can be performed

using Equations 6.28, 6.29, and 6.30, or using a computer software spreadsheet

package. Linear regression analysis yields values of a = 151.2 and b = –30.17.

Therefore, the jam density, kj can be found as follows:

In the regression model, a = c ln kj and b = –c

c ln kj = 151.2

c = 30.17

ln kj = 5.01

kj = 149.9 veh/mi