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Garber & Hoel - Traffic & Highway Eng. (SI) 5/e (Homework)

James Finch

Engineering, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 1 / 66

Due : Sunday, January 27, 2030 12:00 EST

Last Saved : n/a Saving...  ()

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1/66 (1.5%)

  • Instructions



    The enhanced edition of Traffic and Highway Engineering (SI Edition) 5th Edition, by Garber and Hoel, provides insights into all facets of traffic and highway engineering. Students initially examine the pivotal role transportation plays today, including creating employment opportunities and its historical impact and influence on daily lives. With this approach, students gain an understanding of the field as well as an appreciation for its challenges. Later chapters focus on specific issues facing contemporary transportation engineers. Effective learning tools such as worked problems, diagrams and tables, reference material and realistic examples and demonstrate how to apply concepts. Available via WebAssign is MindTap Reader, Cengage's next-generation eBook, and other digital resources.

    Question 1 uses space and time to determine the time mean speed, the space mean speed, and the flow at a specific section of a highway.

    Question 2 uses the Greenshields model to determine the mean free speed, the jam density, the capacity, and the speed at maximum flow.

    Question 3 uses Greenberg’s model to determine the optimum speed and optimum density; it uses the Greenshields model to determine the free flow speed, optimum density, and optimum speed.

    Question 4 uses regression analysis to determine the capacity of a highway.

    Question 5 uses the Greenshields model to determine the speeds of the shock waves created by the operation of the school zone and the number of vehicles affected by the school zone during a 30 minute operation.

    Question 6 uses the deterministic approach to determine the maximum queue length, the total delay, and the number of vehicles that will be affected by the closing of one lane of a three lane freeway due to an emergency bridge repair.

    Question 7 uses expected repair time periods to plot a graph of average individual delay versus the repair period due to the closing of one lane of a three lane freeway.

    Question 8 uses expected demand flow percentages of the capacity of a highway to plot a graph of average individual delay vs the expected demand flow.

    Question 9 uses data on accepted and rejected gaps of vehicles on a minor road and a peak hour volume to determine the expected number of accepted gaps that will be available for minor road vehicles during peak hour.

    Question 10 assumes a deterministic analysis of a queue to determine the expected length of queue at a ticket gate, the probability that there are no more than 5 cars at the gate, and the average waiting time of a vehicle. This demo assignment allows many submissions and allows you to try another version of the same question for practice wherever the problem has randomized values.

    The answer key will display after the first submission for demonstration purposes. Instructors can configure these to display after the due date or after a specified number of submissions.

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For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer.

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1. 1/3 points  |  Previous Answers GHTrafficHE5SI 6.1.001. My Notes
Question Part
Points
Submissions Used
1 2 3
0/1 0/1 1/1
4/50 4/50 3/50
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1/3
 
Observers stationed at two sections XX and YY, 210 m apart on a highway, record the arrival times of four vehicles as shown in the accompanying table. If the total time of observation at XX was 15 s, determine the following.
Time of Arrival
Vehicle Section XX Section YY
A
T0
T0 + 7.58 sec
B
T0 + 3 sec
T0 + 9.10 sec
C
T0 + 6 sec
T0 + 12.36 sec
D
T0 + 12 sec
T0 + 22.10 sec
(a)
the time mean speed (in km/h)
Incorrect: Your answer is incorrect. km/h
(b)
the space mean speed (in km/h)
Incorrect: Your answer is incorrect. km/h
(c)
the flow at section XX (in veh/h)
Correct: Your answer is correct. veh/h
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2. –/4 points GHTrafficHE5SI 6.2.007. My Notes
Question Part
Points
Submissions Used
1 2 3 4
–/1 –/1 –/1 –/1
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–/4
 
The data shown below were obtained by time-lapse photography on a highway. Use regression analysis to fit these data to the Greenshields model and determine the following.
Speed (km/h) Density (veh/km)
18.0 84
27.1 69
34.6 54
43.7 40
55.7 19
57.5 14
(a)
the mean free speed (in km/h)
km/h
(b)
the jam density (in veh/km)
veh/km
(c)
the capacity (in veh/h)
(veh/h)
(d)
the speed at maximum flow (in km/h)
km/h
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3. –/5 points GHTrafficHE5SI 6.2.009. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5
–/1 –/1 –/1 –/1 –/1
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–/5
 
In a freeway traffic stream, the capacity flow was observed to be 2,110 veh/h/ln, and the jam density at this location had been observed to be 130 veh/ln/km.
If the traffic stream is modeled using Greenberg's model, determine the optimum speed (in km/h) and optimum density (in veh/ln/km).
optimum speed km/h optimum density veh/ln/km
If the traffic stream is modeled using Greenshields' model, determine the free flow speed (in km/h), optimum density (in veh/ln/km), and optimum speed (in km/h).
free flow speed km/h optimum density veh/ln/km optimum speed km/h
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4. 0/4 points  |  Previous Answers GHTrafficHE5SI 6.2.012. My Notes
Question Part
Points
Submissions Used
1 2 3 4
0/1 0/1 0/1 0/1
1/50 1/50 1/50 1/50
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0/4
 
Assuming that the expression
us = uf e−k/kj
can be used to describe the speed-density relationship of a highway, determine the capacity of the highway from the data below using regression analysis.
k (veh/km)
us (km/h)
43 38.7
50 33.8
6 53
29 42.3
Calculate the mean free flow speed uf (in km/h), the jam density kj (in veh/km), and the capacity qmax (in veh/h).
uf = Incorrect: Your answer is incorrect. km/h kj = Incorrect: Your answer is incorrect. veh/km qmax = Incorrect: Your answer is incorrect. veh/h
Under what flow conditions is the above model valid?
     Incorrect: Your answer is incorrect.
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5. 0/2 points  |  Previous Answers GHTrafficHE5SI 6.3.016. My Notes
Question Part
Points
Submissions Used
1 2
0/1 0/1
1/50 1/50
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0/2
 
Studies have shown that the traffic flow on a two-lane road adjacent to a school can be described by the Greenshields model. A length of 0.8 km adjacent to a school is described as a school zone (see the figure) and operates for a period of 30 min just before the start of school and just after the close of school. The posted speed limit for the school zone during its operation is 24 km/h. Data collected at the site when the school zone is not in operation show that the jam density and mean free speed for each lane are 120 veh/km and 97 km/h. If the demand flow on the highway at the times of operation of the school zone is 90% of the capacity of the highway, determine the following.
A diagram of a long, horizontal two-lane road is viewed from above, where traffic goes to the right in the bottom lane and to the left in the top lane. The middle section of this stretch of road is labeled "0.8 km School Zone" and is bounded by two vertical lines.
(a)
the velocity of the shock wave created by the operation of the school zone (Enter the velocity of the backward forming shock wave in km/h. Indicate the direction with the sign of your answer.)
Incorrect: Your answer is incorrect. km/h
(b)
the number of vehicles affected by the school zone during this 30-minute operation
Incorrect: Your answer is incorrect. vehicles
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6. –/4 points GHTrafficHE5SI 6.5.018. My Notes
Question Part
Points
Submissions Used
1 2 3 4
–/1 –/1 –/1 –/1
0/50 0/50 0/50 0/50
Total
–/4
 
Traffic flow on a three-lane (one direction) freeway can be described by the Greenshields model. One lane of the three lanes on a section of this freeway will have to be closed to undertake an emergency bridge repair that is expected to take 2 hours. It is estimated that the capacity at the work zone will be reduced by 35 percent of that of the section just upstream of the work zone. The mean free flow speed of the highway is 110 km/h and the jam density is 140 veh/km/ln. If it is estimated that the demand flow on the highway during the emergency repairs is 85 percent of the capacity, using the deterministic approach, determine the following.
(a)
the maximum queue length (in veh) that will be formed
veh
(b)
the total delay (in h)
h
(c)
the number of vehicles that will be affected by the incident
veh
(d)
the average individual delay (in min)
min
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7. –/22 points GHTrafficHE5SI 6.5.019. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
–/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1
0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50
Total
–/22
 
Consider the problem of traffic flow on a three-lane (one direction) freeway which can be described by the Greenshields model. One lane of the three lanes on a section of this freeway will have to be closed to undertake an emergency bridge repair that is expected to take several hours. It is estimated that the capacity at the work zone will be reduced by 28 percent of that of the section just upstream of the work zone. The mean free flow speed of the highway is 110 km/h and the jam density is 120 veh/km/ln. It is estimated that the demand flow on the highway during the emergency repairs is 84 percent of the capacity.
Using the deterministic approach, determine the following for the expected repair periods of 1 h, 1.5 h, 2.5 h, 2.75 h, and 3 h.
(a)
the maximum queue length (in veh) that will be formed
1 h     veh 1.5 h     veh 2.5 h     veh 2.75 h     veh 3 h     veh
(b)
the total delay (in h)
1 h     h 1.5 h     h 2.5 h     h 2.75 h     h 3 h     h
(c)
the number of vehicles that will be affected by the incident
1 h     veh 1.5 h     veh 2.5 h     veh 2.75 h     veh 3 h     veh
(d)
the average individual delay (in min)
1 h     min 1.5 h     min 2.5 h     min 2.75 h     min 3 h     min
(e)
Plot a graph of average individual delay versus the repair period.

(f)
Use this graph to discuss the effect of the expected repair time on the average delay.
    
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8. –/18 points GHTrafficHE5SI 6.5.020. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
–/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1
0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50
Total
–/18
 
Consider the problem of traffic flow on a three-lane (one direction) freeway which can be described by the Greenshields model. One lane of the three lanes on a section of this freeway will have to be closed to undertake an emergency bridge repair that is expected to take 2 hours. It is estimated that the capacity at the work zone will be reduced by 30 percent of that of the section just upstream of the work zone. The mean free flow speed of the highway is 110 km/h and the jam density is 135 veh/km/ln.
Using the deterministic approach, determine the following for the expected demand flows of 70 percent, 75 percent, 80 percent, and 85 percent of the capacity of the highway.
(a)
the maximum queue length (in veh) that will be formed
70 percent     veh 75 percent     veh 80 percent     veh 85 percent     veh
(b)
the total delay (in h)
70 percent     h 75 percent     h 80 percent     h 85 percent     h
(c)
the number of vehicles that will be affected by the incident
70 percent     veh 75 percent     veh 80 percent     veh 85 percent     veh
(d)
the average individual delay (in min)
70 percent     min 75 percent     min 80 percent     min 85 percent     min
(e)
Plot a graph of average individual delay vs the expected demand flow.

(f)
Use this graph to discuss the effect of the expected demand flow on the average delay.
    
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9. 0/1 points  |  Previous Answers GHTrafficHE5SI 6.4.023. My Notes
Question Part
Points
Submissions Used
1
0/1
1/50
Total
0/1
 
The table below gives data on accepted and rejected gaps of vehicles on the minor road of an unsignalized intersection. If the arrival of major road vehicles can be described by the Poisson distribution, and the peak hour volume is 1,264 veh/h, determine the expected number of accepted gaps that will be available for minor road vehicles during the peak hour.
Gap (t) (s) Number of Rejected Gaps > t Number of Accepted Gaps < t
1.5 92 3
2.5 52 18
3.5 30 35
4.5 10 62
5.5 2 100
Incorrect: Your answer is incorrect. gaps
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10. –/3 points GHTrafficHE5SI 6.5.026. My Notes
Question Part
Points
Submissions Used
1 2 3
–/1 –/1 –/1
0/50 0/50 0/50
Total
–/3
 
The arrival times of vehicles at the ticket gate of a sports stadium may be assumed to be Poisson with a mean of 27 veh/h. It takes an average of 1.6 min for the necessary tickets to be bought for occupants of each car.
(a)
What is the expected length of queue at the ticket gate, not including the vehicle being served? (Enter your answer as the number of vehicles.)
vehicles
(b)
What is the probability that there are no more than 4 cars at the gate, including the vehicle being served? (Enter a number as a fraction or decimal.)
(c)
What will be the average waiting time of a vehicle (in minutes, including queue and service)?
min
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