Laboratory 6 – Traffic Models and Field Data
1. Learning Objectives/Outcomes
· Be able to relate field data and a model that represents the field data.
· Be able to identify strengths and weaknesses of a model.
· Be able to estimate capacity flow.
· Understand the value of field data.
2. Textbook References
· Section 5.3 – Basic Traffic Stream Models
· Section 6.4 – Introduction (Highway Capacity and Level of Service Analysis)
3. Background
The purpose of this laboratory is to learn more about traffic stream models, how they can help you understand the basic relationships between speed, flow, and density, and appreciate the inherent differences that you will see between field data and a model used to represent these field data.
In chapter 5 of your book, you learned about one traffic stream model, known as Greenshields’ model, which postulates that as the density of traffic increases, the speed that driver’s choose decreases in a linear manner. When the density is zero, drivers select the free flow speed, or the speed that makes sense based only on the geometric constraints of the roadway. When density reaches its maximum value, known as the jam density, speeds approach or are equal to zero. We can represent this model mathematically, as per equation 5.15 in your textbook:
u=uf1-kkj
The model identifies two parameters that must be estimated, free flow speed (uf) and jam density (kj).
Your book also notes (page 146) that field studies have shown that a more realistic representation of the speed-density relationship includes three parts, as illustrated in Figure 1:
· Speed declines slowly, and non-linearly, from free flow speed at low densities.
· Speed declines linearly with density (as per equation 5.15) at medium densities.
· Speed approaches zero asymptotically at high densities.
Figure 1
The data that you will use in this laboratory were collected at a freeway in Canada. The data are 5-minute averages of speed, flow, and density data that were collected at one point (and for one lane) over a 9 hour period. The data cover periods both when the freeway is flowing freely and when the freeway is congested.
You will answer the following questions as part of this lab:
1. What do the data tell you about traffic conditions on the freeway?
2. What are the model parameters assuming a linear relationship between speed and density?
3. Relative to Greenshield’s model , what is a better representation (model) of the data?
4. Assignment
Question 1: What do the data tell you about traffic conditions on the freeway?
Your first task is to get to know the data. You have been given an Excel spreadsheet that includes data averaged over 5 minute periods for speed (in miles per hour), flow rate (in vehicles per hour), and density (in vehicles per mile). The data set includes 108 individual data points that cover both freely flowing (uncongested) and congested periods over 9 hours.
· Prepare x-y (scatter) plots of speed vs. density, speed vs. flow, and flow vs. density. Use maximum values of 80 miles per hour, 2500 vehicles per hour, and 200 vehicles per mile for your chart scales, and minimum values of 0 for each of the three parameters.
· Consider the speed-flow plot. Identify the uncongested (generally free flow) and congested regions of the chart. What basis did you use to make the distinction between these two regions?
· Compare the plot of the speed-flow data with the model plot (as per Figure 5.3, page 148 of your text). Based on your visual inspection of the two plots, discuss whether or not you think that the model fairly approximates the data.
· Consider the flow-density plot. Identify the uncongested or free flow region. Then identify the congested region. How would you characterize the flow-density plot in each of these two regions?
· Compare the plot of the flow-density data with the model plot (as per Figure 5.2, page 147 of your text). Based on your visual inspection of the two plots, discuss whether or not you think that the model fairly approximates the data.
· Next consider the speed-density plot. Again, identify the uncongested and congested regions. How would you characterize the nature of the speed-density relationship based on this plot?
· Compare the plot of the speed-density data with the model plot (as per Figure 5.1, page 146 of your text). Based on your visual inspection of the two plots, discuss whether or not you think that the model fairly approximates the data.
Question 2: What are the model parameters assuming a linear relationship between speed and density?
The Greenshields model assumes a linear speed-density relationship. Making this assumption regarding the data, estimate the free flow speed (uf), the jam density (kj), and the capacity flow rate (qmax).
· Use the regression tool in Excel to estimate a speed-density model of the form y = mx + b.
· Considering the linear model, represent the coefficients m and b in terms of the free flow speed and the jam density. Use these relationships to estimate the free flow speed (uf) and the jam density (kj).
· Using equation 5.20 in your text, estimate the capacity for the traffic conditions that you have been given.
Question 3: Relative to Greenshield’s model , what is a better representation (model) of the data?
We know that the linear model is only a first stage approximation of the speed-flow-density relationship (see discussion on page 146 of your text). An additional study of the freeway shows that:
· The free flow speed is 70 miles per hour.
· The uncongested portion of the flow-density relationship is linear.
· The jam density is 200 vehicles per hour.
Consider the following tasks:
· Prepare a set of sketches of a revised set of relationships overlaying the data based on the three points listed above.
· Based on your sketches, estimate the capacity of this section of freeway.
· How does this estimate compare with the HCM for a basic freeway section?
· Why is there a variation between your estimate and the HCM value?
· How does it compare with page 183 (figure 6.2) (reproduced below as Figure 2).
· Prepare a paragraph summarizing your findings.
Figure 2 Basic freeway segment speed-flow curves and level of service criteria (Figure 6.2, page 183)
5. Report
Prepare a two page report in which you summarize your answers to the questions that you considered during this laboratory. The report should include the following sections:
1. Laboratory title.
2. Names of the authors of the report.
3. Date that the report was completed.
4. Answers to the three questions that were posed during the lab.
5. One paragraph describing the main points that you learned from this laboratory.
Draft #2 (9 March 2009) 4