Tutorial 1 Worksheet Solutions PDF

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THE UNIVERSITY OF NEWCASTLE CIVL2720: TRANSPORTATION ENGINEERING DESIGN

Tutorial 1

1. 2. 3. 4. 5. 6. 7. 8. 9.

What is the physical limit to spacing on a road? What is the relationship between speed and rate of travel? What is the headway? What is the difference with time gap? What is the storage? How can you estimate it from the density? What is the continuity expression for traffic flow? In queuing theory, what are  and ? Can D(t) be greater than the capacity of the system? What happens if A(t) > D(t)? A freeway has a flow-density relationship approximated by v = 70 D for 0 < D < 40 and a jam density of 120 veh/km where D is in vehicles/lane/kilometer. Flow on a particular day is approximately 2,100 veh/lane/h. At 10:00 a.m. an incident occurs which reduces capacity to 1,600 veh/lane/h. The incident is cleared 45 min later and the flow returns to the normal. Assuming there are no ramps upstream, what are the speeds of the forming and clearing shock waves of the queue upstream of the incident? (-11.28 km/h , -34.98 km/h) When and where do they intersect? (at 12.48 km after 1.1 hours) Solve this exercise analytically and graphically in a space-time diagram. 10. Same road than in exercise 9 and same initial traffic flow. Consider a traffic light for a pedestrian crossing (it is not a traffic intersection) that goes red for 2 minutes. Plot on a space time diagram the different zones of traffic, the boundaries between these zones and the trajectory of vehicles. 11. Consider a single track 90 km long from west to east. There is one double track section from 60 km to 67.5 km from west end. A train leaves west at 1.00 pm doing 45 km/h. If another train leaves east at 1.30 pm and can travel at a speed up to 90 km/hr, what is the earliest time this train can arrive at the west end and how should it travel? Train B arrives at 60 km at 2.20 pm and reaches the W end at 3 pm travelling at 90 km/h 12. In question 11, the fast train (probably a passenger train) as to travel slow or wait for about 0.5 hour. How can the double track be modified to optimize passenger travel? Consider that the passenger train and slow train can be 15 and 10 minutes late, respectively. 13. Consider a single track 50 km long. A coal train 2 km long leaves one end at 1.00 pm and travels at 40 km/h. A passenger train leaves from the same end at 1.30 pm and travels at 80 km/h. How long and where has to be the siding to allow the passenger train to overtake the coal train without having it stopping? Siding from km 40 to km 44. 14. Because of a minor collision, one of the two lanes of a freeway is blocked at 9.30 am. The normal capacity of the freeway of 3000 veh/h is then reduced to 1200 veh/h. The flow on the freeway at this time of the day is 2500 veh/h. The incident is cleared after 30 minutes. a. Does a queue form? Yes b. What is the longest time a vehicle is in the queue? 15.6 min c. At what time does the queue clear? 11h18 am d. What is the total delay? 585 veh·h e. If a driver enters into the queue at 9.50 am, how many vehicles would be ahead of him? How long would he have to wait in the queue? (433 veh, 14.7 min) 15. Same exercise with a changing traffic flow: 1300 veh/h before 9.45 am and 2800 veh/h after. The accident is cleared after 45 minutes. (yes, 17.7 min, cleared after 4.875 hours, 1917.18 veh·h, 105 veh, 5.25 min )

16. A post office has 5 counters and opens at 9 am. People are arriving 15 minutes before the opening of the post office at a rate of 12 persons/hr. A counter can accommodate a client in 6 minute. The number of counters opened and the arrival rate of clients are given in the table below. What is the earliest time at which you can come to the post office without having to wait? (at 10h52 am) Time 9.00 - 9.30

Number of counters opened 1

Arrival rate [pers/h] 18

9.30 -10.00

2

24

10.00 -10.30

2

14

10.30 -11.00

3

12

11.00 -11.30

3

18

11.30 -12.00

5

30...