Traffic Flow Data

TRAFFIC FLOW DATA

CE361 08HW2 Solutions- 1 -Fall 2008

• 1-3 CE361 students. If 2-3, signatures required.
• ID each problem by its number and name. State your methodology.

1. (10 points) Mr. Posey’s letter. The largest standard deviation in FTE Table 6.15 is S = 4.378. Use z = 1.96 unless otherwise told. In FTE Table 2.7, U = 1.04 for the 85th percentile speed.

FTE (2.4) == 113.45 = 114 vehicles.

1. Occupancy and density from loop detectors. Effective length of 7.0 feet, actuated for 4.8 percent of one-hour. 632 vehicles detected, mean speed 63.2 mph, mean length 18.24 feet.

A. (10 points) Convert the apparent occupancy rate to the actual occupancy rate.

(2.6) = 0.2732 second

(2.7) = 0.1977 second

(2.8) Actual Occupancy Oact = q * t’(P) = (632 * 0.1977)/3600 = 0.035 or 3.5%.

B. (10 points) What was the density (vpm) on the roadway during the occupancy measurements?

Use any one of three equations:

(2.9) = 9.99 veh/mi

Calculate Oapp as in FTE Example 2.10A, then use (2.10) = 10.03 veh/mi

(2.12) = 10.00 veh/mi

1. Speed-Flow-Density relationships. Do FTE Exercise 2.40, using the data emailed to you.
2. (15 points) Speed-density plot.

• Using Equation 2.12, calculate D = q/S values for the Density column. Figure 3A is the plot of 30 data points of S vs. D.

• Fit a straight line through the data points.

• The fitted line is consistent with the plotted data points.

1. (15 points) Flow-density plot.
2. See Figure 3B.
3. Use Equation 2.19 to convert D = 0, 5, 10, …, 95, 100, 102.45 veh/km into corresponding “model” values of q.
4. Sample calculation for D = 30 veh/km:

• Plot the model values as a smooth parabolic curve.
• The smooth curve is not inconsistent with the plotted points.

1. (15 points) Speed-flow plot.
2. See Figure 3C.
3. Use Equation 2.18 to convert S = 0, 10, 20, …, 70, 73.36 kph into corresponding “model” values of q.
4. Sample calculation for S = 30 km/hr:

• The smooth curve is not inconsistent with the plotted points.

1. The road to Shreveport. 343 miles = 552 km) from New Orleans to Shreveport. Normally 5 hours and 21 minutes; before Hurricane Gustav, 25 hours. 2 lanes each direction on a 10-kilometer segment. Metric distances.

(2.13) ; (2.19) ; (2.18)

A. (10 points) Normal mean speed of the trip to Shreveport? What is the corresponding traffic density and flow rate on the 10-kilometer segment, according to the Greenshields equations?

= 103.18 km/hr.

FTE (2.13) ;; D = 15.56 veh/km.

FTE (2.18) = 1606 veh/hr

B. (10 points) Mean speed of the pre-Gustav trip to Shreveport? Corresponding traffic density and flow rate on the 10-kilometer segment, according to the Greenshields equations?

= 22.1 km/hr.

FTE (2.13) ;; D = 68.0 veh/km.

FTE (2.18) = 1503 veh/hr

C. (5 points) Do all the values you calculated make sense? (Are any suspicious?)

• 103.18 km/hr = 64.11 mph, which is a little low for an Interstate segment under normal conditions, but it is not unreasonable.
• A density 68.0 veh/km. equates to a vehicle every 1000 m/68 = 14.7 meters or 48.2 feet. If an average vehicle is about 15 feet long, the D=68 veh/km value represents a situation in which each vehicle (on the average) has a little more than two vehicle lengths behind it until the next vehicle. This is possible in an evacuation situation.
• The flow rates of 1606 veh/hr and 1503 veh/hr are reasonable.