Traffic and Highway Engineering
5th Edition
ISBN: 9781305156241
Author: Garber, Nicholas J.
Publisher: Cengage Learning
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Chapter 6, Problem 12P
To determine
Capacity of the highway from the given data using regression analysis, and the flow conditions for the given model to be valid.
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For the following speed-density
relationship of a highway,
determine 1) mean free-flow
speed, 2) jam density, and 3)
capacity from the given data
shown in table. The regression
model is following Eq.1. Also,
assess when this model could
be used?
U = U; * e
kj)
Eq.1
K (vpm)
U (mph)
43
38.4
50
33.8
8
53.2
31
42.3
Assuming that the expression:
u = ue k,
%3D
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/mi)
u, (mi/h)
43
38.4
33.8
50
53.2
42.3
8
31
Under what flow conditions is the above model valid?
The data shown below were obtained on a highway. Use regression
analysis to fit these data to the Greenshields & Greenberg model and
determine the capacity AND R-SQUARE.
Speed (km/h)| Density (veh/km)
50
18
45
25
40
41
34
58
22
71
13
88
12
99
Chapter 6 Solutions
Traffic and Highway Engineering
Ch. 6 - Prob. 1PCh. 6 - Prob. 2PCh. 6 - Prob. 3PCh. 6 - Prob. 4PCh. 6 - Prob. 5PCh. 6 - Prob. 6PCh. 6 - Prob. 7PCh. 6 - Prob. 8PCh. 6 - Prob. 9PCh. 6 - Prob. 10P
Ch. 6 - Prob. 11PCh. 6 - Prob. 12PCh. 6 - Prob. 13PCh. 6 - Prob. 14PCh. 6 - Prob. 15PCh. 6 - Prob. 16PCh. 6 - Prob. 17PCh. 6 - Prob. 18PCh. 6 - Prob. 19PCh. 6 - Prob. 20PCh. 6 - Prob. 21PCh. 6 - Prob. 22PCh. 6 - Prob. 23PCh. 6 - Prob. 24PCh. 6 - Prob. 25PCh. 6 - The arrival times of vehicles at the ticket gate...Ch. 6 - Prob. 27P
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- Assuming that the expression: u = ue i, 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/mi) u, (mi/h) 43 50 38.4 33.8 53.2 42.3 31 Under what flow conditions is the above model valid?arrow_forwardGiven a freeway flow study at a certain highway. The speed- density relationship is described in the givenequation or relationship: V s = 58- 0.40k Determine the following:a. Free-flow speed and jam densityb. Derive the equation describing flow and speed.c. Derive the equation describing flow and density.d. Determine the capacity of highwayarrow_forwardThe traffic volume for a section of a highway can be estimated using the following equation: q = 15.1k[ln (195) - In(k)] Where q is the traffic flow measured in veh/hr and k is the traffic density measured in veh/mi. Based on the provided information, estimate the following (Show all your calculation steps): Maximum flow a. b. Jam density C. Maximum densityarrow_forward
- SITUATION The data presented in the table illustrates traffic density-speed information gathered from a segment of a highway. If we assume the Greenberg model describes this data, employ linear regression analysis to ascertain the following: Density, k (vpm) 100 92 84 75 70 64 60 54 42 35 28 22 Speed, u, (mph) 20 21 25 27 29 33 35 38 41 46 53 61 determine: Density at maximum flow in veh/mi. Express answer into two decimal places. Do not type the unit. veh/miarrow_forward7) In studying of traffic flow at a highway toll booth over a course of 60 minutes, it is determined that the arrival and departure rates are deterministic, but not uniform. The arrival rate is found to vary according to the function A(t) = 1.8+0.25t - 0.00312. The departure rate function is u(t) = 1.4 +0 .1lt. In both of these functions, t is in minutes after the beginning of the observation and (t) and „u(t) are in vehicles per minute. At what time does the maximum queue length occur? a) 49.4 min, b) 2.7 min ,c) 19.4 min, d) 60.0 minarrow_forward6-9 Assuming that the expression: - k/k, us = Ufe 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/mi) u, (mi/h) 43 38.4 50 33.8 8. 53.2 31 42.3arrow_forward
- The table below shows data on speed and corresponding densities on a section of a collector road. It can be assumed that the traffic flow characteristics can be described by the greenberge model, develop an appropriate relationship between flow and density. Also deyerdete the capacity of this section of the road Speed kph density veh/km 60 20 46 32 40.8 38 39.3 40 35.7 45 32.6 50 30.8 53 28.4 57 24.7 65 18.5 80arrow_forwardGiven a freeway flow study at a certain highway. The speed- density relationship is described in thegiven equation or relationship:V s = 60- 0.48kDetermine the following:a. Free-flow speed and jam densityb. Derive the equation describing flow and speed.c. Derive the equation describing flow and density.d. Determine the capacity of highwayarrow_forwardQuestion 2 If the model in us = In uf - k/kj is applicable to depict the correlation between speed (mi/h) and density (veh/mi) on a highway segment, and employing regression analysis provides the model constants Y = A + BX (where Y = In u, X =k) as A = 3.9 and B = -0.018, then calculate the: Jam density in veh/km. Express answer into two decimal places. Do not type the unit. veh/km.arrow_forward
- 1. Assume you are observing traffic in a single lane of a highway at a specific location. You measure the average headway and average spacing of passing vehicles as 3 seconds and 150ft, respectively. What is the average speed of the traffic stream? Note: you can use two methods to conduct the calculation. 2. Assume the speed and density at a freeway location follows a linear relationship. You observe traffic flow rate of 2250 vehicles/hour at 45 mph and 3000 vehicles/hour at 30 mph. What are the jam density, free flow speed (max speed), and capacity of this freeway location? How about the density and speed (i.e., the critical density and the critical speed) at the capacity?arrow_forwardQuestion 2 If the model In us= ln uf - k/kj is applicable to depict the correlation between speed (mi/h) and density (veh/mi) on a highway segment, and employing regression analysis provides the model constants Y = A + BX (where Y = In u, X = k) as A = 3.9 and B = -0.018, then calculate the: Jam density in veh/km. Express answer into two decimal places. Do not type the unit. veh/km.arrow_forward1. Data on density and speed were obtained from a four-lane, two-way rural highway (in one direction only): Fitting the recorded data using linear regression, determine: a.the speed-density relationshipb.the correlation coefficientc.The capacity of the road.arrow_forward
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