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a5_cee3604_2011_sol

a5_cee3604_2011_sol - CEE 3604 Introduction to...

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CEE 3604: Introduction to Transportation Engineering Fall 2011 Assignment 5: Traffic and Mass Transit Modeling Solution Instructor: Trani Problem 1 The Greenberg model is known to be: u = c ln k j k where: u is the space mean speed (km/hr), k j is the jam density (veh/la-km), k is the density of the flow (veh/la-km) and c is a model parameter (km/hr). Data collected in a highway in the U.S. is presented in the file called a5_2011_Highway_Data. The file contains two columns: Column 1 = speed (km/hr) Column 2 = density (veh/la-km) a) Plot the three key traffic flow variables (speed vs density, density vs. flow and speed vs. flow). Figure 1. Plot of Density vs. Speed. b) Transform the data to linearize the data, perform regression analysis and estimate the parameters c and k j of the Greenberg model. To transform the data we take the natural logarithm of the Density values and obtain a regression equation of the form, CEE 3604 A5 Trani Page 1 of 6

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u = A B ln( k ) where ; A = c ln( k j ) B = c Running a regression model in Matlab we obtain the results shown in Figure 2. A simple script in Matlab to read the data and transform the density is shown below. load a5_2001_HighwayData % loads the data file % File contains % Column 1 = speed (km/hr) % Column 2 = density (veh/la-km) % Declare the two variables of interest speed =a5_2001_HighwayData(:,1);
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a5_cee3604_2011_sol - CEE 3604 Introduction to...

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