Homework 3 (HW 3) / Due: Mon. 17 September 2007
CE361 HW 3 Fall 2006 - 2 -
HIGHWAY DESIGN FOR PERFORMANCE
· You will be permitted to submit this HW with as many as three other CE361 students. If the HW is submitted by more than one student, the signatures of all students in the group must appear (along with printed names) at the top of the front page of the materials submitted.
· For every problem, identify the problem by its number and name, be clear, be concise, cite your sources, attach documentation (if appropriate), and let your methodology be known.
· “FTE” = Fundamentals of Transportation Engineering, the textbook for CE361.
1. Poisson models. When the Mythaca County Engineer isn’t thinking about transportation, he is thinking about soccer. The frequency distribution for the number of goals his daughter’s travel team (The Mythaca Scorch) gave up during each game in the Spring 2007 season is given in Table 1.A. (10 points) Assuming that opponents’ goals per match is a Poisson process, calculate P(0), …, P(5), and P(n5) for the team’s Spring season.
B. (10 points) Using the format of FTE Figure 2.25, show the Observed and Poisson frequencies. Using your judgment, state whether the Poisson assumption in Part A was justified.
2. (10 points) Time between events. If The Scorch play matches consisting of two 35-minute halves, what is the probability that the team will give up a goal in the first two minutes of a match? Assume the Poisson assumptions hold. / Table 1
Goals / Freq
0 / 3
1 / 3
2 / 0
3 / 4
4 / 1
5 / 3
6 / 0
7 / 0
8 / 1
12 / 1
3. LOS on Two-Lane Highways. A segment of State Road 361 goes through rolling terrain. Over the 6.7-mile-long segment, SR361 has 79 access points, 12-foot lanes, and shoulders with an average width of 4.5 feet. During the peak hour of interest, 6 percent of the 950 vehicles are trucks and buses, and 1 percent are recreational vehicles. The peak hour factor is 0.85, the major direction has 55 percent of the two-way volume, and there are no-passing zones for 50 percent of the segment.
A. (10 points) Adjusted flow rate for Average Travel Speed. Find vp after one iteration. Is a second iteration needed? Explain. If a second iteration is needed, what is the new vp value?
B. (5 points) An early morning field measurement of speeds results in an average of 54.5 mph. Eleven of the 175 vehicles observed were trucks and buses. What is the free-flow speed?
C. (5 points) Average Travel Speed. Explain how you determined the value of fnp that you extract from Exhibit 20-11. What is the ATS value? What is the corresponding LOS?
D. (10 points) Adjusted flow rate for Percent Time Spent Following. Find vp after one iteration. Is a second iteration needed? Explain. If a second iteration is needed, what is the new vp value?
E. (5 points) Percent Time Spent Following. Explain how you determined the value of BPTSF and of fd/np that you extracted from Exhibit 20-12. What is the PTSF value? What is the corresponding LOS?
F. (5 points) Two-Way Two-Lane Highway Segment Worksheet. What is the LOS for the segment of State Road 361 analyzed? Include a copy of the worksheet with the HW you submit.
4. I-96 Incident and Queueing Analysis. FTE Exercise 3.19. 10 points each part, a-c.
5. Analyzing a Stable Queue. A traffic signal is timed with a constant cycle, so that 960 vph can enter the intersection. Normally, 400 vph approach the intersection during the morning peak period.
A. (10 points) What type of queueing system (x/y/z) is the signalized approach? Explain your decision.
B. Assuming that a non-persistent queue situation exists, answer the following questions.
a. (5 points) To the nearest 0.01 vehicles, what is the average queue length?
b. (5 points) To the nearest 0.1 second, what is the average time spent waiting in a queue?