Transportation and Traffic Engineering – Speed – Volume and Density Data – Engineering Assignment Help

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Assignment Task :

Question 1: Speed, volume and density data were collected from westbound lanes of the Fred Gardiner Expressway in Toronto. The data are stored in the tab “Question 1” of “Assignment 1_data.xlsx”. The data contains the average speed in km/hour, total volume in veh/hour and the average density in veh/km for every 15 minutes in one day. (please refer the excel data in Example_1) 

(a) Plot the observed (i) density (x-axis) vs. speed (y-axis),

(ii) speed (y-axis) vs. volume (x- axis), and

(iii) density (x-axis) vs. volume (y-axis).

(b) Estimate the free-flow speed (uf), the jam density (kj), the capacity (qm), the critical speed (uc) and the critical density (kc) from the plots (Note: Estimate approximate values based on your own judgment. Do not calculate the values). 

(c) Calculate the critical speed, the critical density and the capacity (if uf is 110 km/h and kj is 70 veh/kr) using the Greenshields’ model. Compare these calculated values with your estimated values in part

(b). Assuming that your estimated values in part (b) are actual values, does the Greenshelds’ model underestimate or overestimate the parameters? 

(d) Derive the equations of speed-density, volume-speed and volume-density using the Greenshields’ models. Use the calculated values of uf and kj in part (c) in the models. (e) Plot the Greenshields’ models in part (d) in the graphs in part (a). Do the models fit the observed data well? 

 

Question 2: Use the CTM to model the westbound 15km 2-lanes of the Fred Gardiner Expressway in Toronto. The simulation value and excel format (You need build equations) are stored in the tab “Sim Value” and “Question 2” of “Assignment 1_data.xlsx”. Assume that there is an incident (any location where you can see the backward propagation would be fine) that the capacity is reduced to a half (2 minutes later, the capacity is recovered). Show the congestion propagates to backward (using the excel). 

 

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