Transportation Engineering Module Exam
Transportation Engineering Module Exam
Transportation Engineering Module Exam
SITUATION 1. After observing arrivals and departures at a highway toll booth over a 60-minute
time period, an observer notes that the arrival and departure rates (or service rates) are
deterministic, but instead of being uniform, they change over time according to a known function.
The arrival rate is given by the function λ(t) = 2.2 + 0.17t − 0.0032t2, and the departure rate is
given by μ(t) = 1.2 + 0.07t, where t is in minutes after the beginning of the observation period and
λ(t) and μ(t) are in vehicles per minute. Assuming D/D/1 queuing.
4. Determine the total vehicle delay in veh-min.
5. Determine the time at which the maximum queue length occurs.
6. Determine the longest queue length.
SITUATION 2. 40 vehicles pass a given point in 1 minute and traverse a length of 1 kilometer
7. Evaluate the flow, in vehicles per hour.
8. Evaluate the density in vehicles per kilometer
9. Evaluate the time headway in seconds. (Hint: headway = 1/density)
10. If 2340 vehicles per hour passes a certain highway, with average speed of 52kph,
determine the appropriate spacing of these vehicles.
11. The number of accidents for 6 years recorded in a certain section of a roadway is 5892.
If the average daily traffic is 476, what is the accident rate per million entering vehicles?
12. Given five observed velocities in kph: 60, 35, 45, 20, 50, determine the time mean
speed.
13. Given five observed velocities in kph: 60, 35, 45, 20, 50, determine the space mean
speed.
SITUATION 3. A simple curve have tangents AB and BC intersecting at a common point B. AB
has an azimuth of 180 and BC has an azimuth of 230. The stationing of PC is 10+140.26. If the
degree of curve is 4-degrees.
14. Compute the length of the long chord from A.
15. Compute the tangent distance AB of the curve.
16. Compute the stationing of point x on the curve which a line passing through the center of
the curve makes an angle of 58 with the line AB, intersects the curve at x
SIUTATION 4. Two tangents converge at an angle of 30-degrees. The direction of the second
tangent is due east. The distance of the PC from the second tangent is 116.50m. The bearing of
the common tangent is S40E.
17. Compute the central angle of the first curve.
18. If a reversed curve is to connect these two tangents, determine the common radius of
the curve.
19. Compute the stationing of the PT if PC is at station 10+620.
SITUATION 5. A symmetrical parabolic summit curve connects two tangents of 6% and -4%. It
is to pass through point P on the curve at station 25+140 having an elevation of 98.134m. If the
elevation of the grade intersection is 100m, with a stationing of 25+160
20. Compute the length of the curve.
21. Compute the stationing of the highest point of the curve
22. Compute the elevation of station 25+120 on the curve.
SITUATION 6. A spiral 80m long connects tangents with a 6.5-degree circular curve. If the
stationing of the T.S. is 10+000,
23. Determine the spiral angle at the first quarter point.