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/mi

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/mi

Traffic and Highway Engineering

5th Edition

ISBN:9781305156241

Author:Garber, Nicholas J.

Publisher:Garber, Nicholas J.

Chapter6: Fundamental Principles Of Traffic Flow

Section: Chapter Questions

Problem 12P

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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 80
The traffic shows data on speeds and corresponding densities on a section of a rural collector road. If it can assumed that the traffic flow characteristics can be described by the Greenberg's model, develop an appropriate relationship between the speed and flow and their modelled plotted points to be shown in the Q-u diagram. How strong the correlation of the two are? Also determine the capacity of this section of the road. Traffic Data Speed (kph) 60 Density (Veh/km) 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 80
Consider the following spot speed data, which were collected from the location of expressways operating under free flow conditions: a. Draw the frequency curve and cumulative frequency for this data. b. Find and identify on the curve: average speed, modud speed, pace, percent of vehicles in pace. c. Calculate the mean and standard deviation of the velocity distribution. d. What are the confidence bounds in the true mean velocity estimate of the underlying distribution with a 95% confidence level? With a 99.7% confidence level? e. Based on the results of this study, a second study should be conducted to achieve a tolerance of ±1.5 mi/hour with a 95% confidence level. What is the required sample size? f. Can this data deserve to be declared as normal?
7) 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 min
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 (mi/h) Density (veh/mi) 16.7 84 25.7 69 35.2 54 43.1 40 54.4 19 56.1 14 (a) the mean free speed (in mi/h) mi/h (b) the jam density (in veh/mi) veh/mi (c) the capacity (in veh/h) veh/h (d) the speed at maximum flow (in mi/h) mi/h
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 (mi/h) Density (veh/mi) 19.7 28.8 35.2 43.1 53.8 57.0 (a) the mean free speed (in mi/h) 67.24 mi/h 86 71 56 42 21 16 (b) the jam density (in veh/mi) 105.06 X Your response differs from the correct answer by more than 10%. Double check your calculations. veh/mi (c) the capacity (in veh/h) 52.53 X Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. veh/h (d) the speed at maximum flow (in mi/h) 33.61 mi/h
3 During a traffic speed survey, the following observations were recorded when a vehicle passes a 50 m long road section XY. Vehicle Time of Passing X (seconds) Time of Passing Y (seconds) 1 4.5 5.8 6.1 6.3 7.5 23 4 5 2.0 3.5 4.0 4.5 5.5 Determine the following: (i) Average time mean speed (ii) Average space mean speed using the above data (iii) Also verify the results obtained in (ii) above using relationship between the time mean speed and space mean speed.
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
INSTRUCTIONS: >Solve the given problems on a bond paper as neat and as clean as possible, present complete solutions. PROBLEM: The data shown below were obtained on a highway determine the maximum flow and R-square using Greenshield's and Greenberg Model. X Y 50 18 45 25 40 41 34 58 22 71 13 88 12 99 10 105 9 110 8 124 5 132
SAMPLE PROBLEM |In a particular transportation study, the following traffic data were recorded as shown below. Find the required equations and fit the modeled points in the curve using u-k, Q-k and Q-u relationship in the GREENBERG’S logarithmic traffic model FLOW (veh/hr) SPEED (kph) DENSITY (Veh/km) 1600 80 20 3705 39 95 3900 65 60 2400 20 120 1000 15 66.67 4000 50 80
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?
Question 1 a) The spot speeds and headways of vehicles are measured by two loop detectors on a single lane at location Y on a freeway. A sample of the observations is given below: Vehicle no. ii. 1 2 345 Travel time between loops (seconds) 0.90 0.81 0.92 0.75 1.03 nex nyt q Headway between vehicles (seconds) 3.60 3.14 4.00 3.50 3.72 9 = = =/=/30 S= i. If the loop detectors are spaced 20 meters apart, estimate the space mean speed and flow of the traffic stream. If it is known that the jam density (k;) on this section is 105 vehicles/km per lane, and that a linear speed-density relationship holds, what would you estimate the free-flow speed of the section to be? -110 Ehi n