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Workshop Week 2

Courses: CVEN 2401/2402/3401/3402

(11 March 2015)

Introduction to traffic flow theory

Part 1. Understanding a stream of vehicles.

Objective: become familiar with the basics of traffic flow.

The town of Congestington (pop. 5400) has recently received an influx of complaints about the

driving behaviour of its populace. Congestington has only a single road, 5 km in distance, that

connects the sides of town. Congestington is not a wealthy town, and so they’ve hired you (an

independent contractor) to evaluate their traffic situation. Unfortunately, due to the presence of

endangered bears (see Figure 1), there is no way for Congestington to take measurements on the

road itself.

Figure 1. The Congestington Road Network

Being very poor indeed, the town of Congestington has managed to provide you with only the

following data for the entire 5km length of the only road into the town:

Vehicle Entrance time

(s) Exit time (s)

1 0 290

2 22 233

3 60 190

4 80 300

5 100 439

6 150 384

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Help Congestington understand their traffic situation by performing the following series of steps.

1. Begin by visualising your data. Create a time-space diagram. Do you need to make any

important assumptions?

2. Calculate headways, time-mean, and space-mean speeds when 𝑥 = 1000,4000 and 𝑡 =

150,300.

3. Consider how you would represent other situations, such as encountering a bear in the road.

Consider and discuss safety implications of this dataset. Is this analysis micro- or macro-scopic?

Part 2. Understanding the fundamental properties of traffic and how they are related.

Objective: review fundamental theories of traffic flow.

The following figures depict the Greenshields diagrams, which can be used to evaluate the state of

the traffic stream according to three variables: the mean speed, the density and the flow.

4. Draw a diagram showing the relationship between speed - density.

Figure 2. Speed - density diagram

a. What does 𝑣𝑚𝑎𝑥 corresponds to?

b. In what state is the traffic if the mean speed is equal to 𝑣𝑚𝑎𝑥 ?

5. Draw a diagram showing the relationship between flow - density.

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Figure 3. Flow - density diagram

a. In what dimension is the traffic flow expressed?

b. Describe the state of the traffic at point A.

6. Draw a diagram showing the relationship between speed - flow.

Figure 4. Speed - flow diagram

a. Describe the state of the traffic at point B.

b. Describe the state of the traffic at point C, what can we do to improve it?

Part 3. Follow up numerical questions.

Objective: apply the fundamental theory to numerical problems.

7. You go back to the town of Congestington and request further data. Congestington decides to

implement a novel technique to gather traffic data based on satellite images, so the bears are

undisturbed.

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Vehicle time headways and spacings were measured at a point along the Congestington expressway,

from a single lane, over the course of an hour. The average values were calculated as 2.5 s/veh for

headway and 61 m/veh for spacing. Calculate the average speed of the traffic.

8. Finally, Congestington conducts a study of freeway flow at a site along the expressway and after

analysis, resulted in calibrated speed-density relationship as follows:

𝑆 = 57.5(1 − 0.008𝐷)

For this relationship, determine: (a) the free flow speed, (b) jam density, (c) the speed-flow

relationship, (d) the flow-density relationship, and (e) capacity

Assumptions of units: Speed (S) = km/hr,

Density/Density (D) =vehicles/km/lane

Flow (Q) = vehicles/hr/lane

Part 4. Level of service analysis.

Objective: consider the concept of level of service.

9. The town of Congestington is so pleased with your previous work that they’ve asked for you to

perform another analysis. More people have been moving to Congestington lately and now the

town council wants to know about the level of service on their expressway. Using their novel

technology, the town provides you with a traffic count in two locations, a and b.

The recorded speed for the same time period at a and b was 85 kph and 35 kph. Estimate the

level of service in each location and describe any necessary assumptions.