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Ecole Polytechnique Fédérale de Lausanne

School of Architecture, Civil and

N. GeroliminisFall 2018

Environmental Engineering

Fundamentals of Traffic Operations and Control

Lab 1: Traffic Data from Urban Inductive Loop Detectors and the Macroscopic Fundamental Diagram

Lab Report Due: Monday November 9th, 2018

Required Material:

Matlab and/or Excel software

Data file: dataLab1.mat and/or dataLab1_excel.xlsx (provided)

Function for plotting a directed graph: gplotdc.m (provided)

Introduction:

In this first lab we will do an analysis of traffic data in urban networks. The provided data

is extracted from a micro-simulation environment that replicates the real measurements of

inductive loop detectors in cities. We will be able to estimate some common traffic

characteristics (flow, density, occupancy, speed) and plot relations between them. We will

estimate the Macroscopic Fundamental Diagram of flow vs. density (or production vs.

accumulation) for different spatial scales and identify how this scaling changes the results.

Data description:

The provided .mat file contains 4 matrices with different data that is described below. First

of all, there are 2 matrices (links and nodes) that describe the topology of the network.

Every urban network can be graphically represented with links and nodes. The format of

the matrices is as follows:

links

Link ID Length

(m)

Number of

lanes

Starting

node ID

Ending

node ID Region

512 109.224 3 21109 19069 4 513 129.668 3 19067 21109 4 514 133.572 2 19065 21042 4 516 47.650 2 11 19201 3 ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. …..

72127 12.172 2 46751 46453 4 73054 2.284 2 20620 20620 4 73546 80.754 3 73547 41877 1

Region: the network is partitioned in 4 regions for perimeter control purposes and this index indicates the

region that the link belongs to. You can plot regions with different colors to see how the network looks like.

2

nodes

Node ID x_coordinate y_coordinate

1 429948 4581385 2 431582 4580937 3 432524 4583069 4 432650 4582536

….. ….. ….. ….. ….. ….. ….. ….. …..

55304 429032 4581044 69623 428339 4581708 73547 427855 4581714

Using part of this data (x and y coordinates, link ids, starting node, ending node) and the

provided .m file you can plot a directed graph of the network (city center of Barcelona).

The data file contains also 2 matrices (flow and occupancy) with the measurements of the

inductive loop detectors (for 90-seconds intervals) for two hours of simulation. The loop detectors data is in the form of counts and occupancies per link (i.e., average occupancy

and total flow of all lanes). The format of the data is as follows:

flow

Time

(sec)

First row: Link ID

Next rows: Flow measurements (veh)

0 512 513 514 516 ….. ….. ….. 73054 73546 72127 90 0 2 0 17 ….. ….. ….. 0 16 0 180 0 6 3 10 ….. ….. ….. 1 23 3 270 11 13 8 10 ….. ….. ….. 0 17 0 ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. …..

7020 6 19 2 2 ….. ….. ….. 1 0 0 7110 8 7 12 2 ….. ….. ….. 4 0 0 7200 16 0 5 20 ….. ….. ….. 5 1 0

occupancy

Time

(sec)

First row: Link ID

Next rows: Occupancy measurements (% )

0 512 513 514 516 ….. ….. ….. 73054 73546 72127 90 0.00 0.32 0.00 4.50 ….. ….. ….. 0.00 0.00 1.92 180 0.00 0.95 0.69 2.76 ….. ….. ….. 0.98 0.08 2.82 270 1.47 2.04 1.78 2.65 ….. ….. ….. 0.00 0.00 2.09 ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. ….. …..

7020 0.88 4.37 76.90 99.89 ….. ….. ….. 0.32 34.17 66.67 7110 1.12 42.14 61.50 83.77 ….. ….. ….. 0.93 0.00 66.67 7200 2.59 66.67 99.51 94.76 ….. ….. ….. 1.28 33.78 66.67

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Step 1: Create three snapshots of the network presenting the level of congestion of each link at

time 60min, 90min and 120min of the simulation. Use the provided gplotdc.m file for plotting the network in a gray-scale format in which the color denotes the level of

congestion for each link. Use the occupancy measurements [0, 100] to specify how dark should be the color of each link (i.e., links with occupancy 0 and 100 are shown with white and black color respectively).

Step 2:

Traffic volume V in traffic engineering is typically expressed in terms of vehicles per hour. Convert all the flow measurements in the data file to an equivalent expressed in vehicles

per hour. Pick one link of the network and produce a scatter plot of volume vs. occupancy for the 90-seconds intervals. Do the same scatter plot for the average volume vs. average occupancy of two links. Finally, produce the scatter plot of average volume vs. average

occupancy for all network links. Do the same plot for each of the 4 regions of the network. Is there any pattern to the relationship between average volume and average occupancy?

Comment on the partitioning of the network.

Step 3:

Estimate the density of each link using the following equation:

Density 𝑘 =

𝑜𝑐𝑐𝑢𝑝𝑎𝑛𝑐𝑦100

∙ 𝜇

𝐿 + 𝐿 𝐷

(𝑣𝑒ℎ/𝑘𝑚)

where occupancy is the given average measurement across all link lanes, μ defines the

number of lanes of the link, LD = 2m is the detector length and L = 5m the averagevehicle length.

The average speed of each link can be computed using the formula:

Link speed (𝑘𝑚/ℎ) =Volume 𝑉 (𝑣𝑒ℎ/ℎ)

Density 𝑘 (𝑣𝑒ℎ/𝑘𝑚)

The space-mean speed of a region for each time interval can be computed by weighting the volumes and densities with the link lengths (for all links belonging to this region),

according to:

Μean Speed 𝑢 (𝑘𝑚/ℎ) =∑ 𝑉∀𝑙𝑖𝑛𝑘 ∙ 𝑙𝑒𝑛𝑔𝑡ℎ

∑ 𝑘∀𝑙𝑖𝑛𝑘 ∙ 𝑙𝑒𝑛𝑔𝑡ℎ

Produce a scatter plot for each region with mean speed as a function of average density of

the region. Is there any pattern to the relationship? Plot also the time-series of the region mean speed for the two hours of simulation. Does the range of values of the mean speed

make sense for an urban network? What do the time series reveal for the congestion of the network?

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Step 4:

The number of vehicles in each link can be calculated by multiplying the density with the

length of the link (in km). Also, another metric of the performance of each region is the

production. The production of each link may be calculated as follows:

Production 𝑃 = 𝑣𝑜𝑙𝑢𝑚𝑒 ∙ 𝑙𝑒𝑛𝑔𝑡ℎ (𝑣𝑒ℎ ∙ 𝑘𝑚/ℎ)

Produce a scatter plot of production vs. accumulation for one random link. Do the same

plot for the summation of the variables for two links. Finally, produce scatter plots for all

the regions displaying the total production of the region vs. the accumulation (total number

of vehicles in the region). What is the difference between these MFDs and the ones

generated in Step 2?

Step 5:

For each region, first estimate a polynomial that fits the MFD found in Step 4. Then

choose 50% of the links in each region according to the following three strategies: i) highest number of lanes; ii) longest link length; iii) maximum average flow. Produce

production vs. accumulation plots and estimate the MFD of each region according to

the proposed strategies (Note: scale both axes of the MFD by the ratio [total link length

of the region/total link length of the selected sample]). Finally, compute and compare

the fitting errors of the MFDs obtained in this step with the ones found in step 4.

Step 6 (bonus):In the provided data file you have the measurements for all the links of the network.

Assume now that for each region you want to select only 50% of the links and produce the

production vs. accumulation MFD, similarly to Step 5. This time, you multiply all your

measurements by a factor of 2 and then compare the resulting MFD with the one produced

in Step 4 (that uses all the network links). Can you propose a methodology to select the

50% of the links so that the difference between the two MFDs is minimized?

Step 7 (bonus):Heterogeneity in the spatial distribution of density can influence the shape and the noise of

the MFD. Plot the spatial distribution of occupancy for the 4 different clusters and the

whole network for times 60min and 90min (use the Matlab command histogram to produce

the plots). Can you identify any quantitative metric of heterogeneity that shows that the

clustering helps to divide the network in homogeneous regions?

Note: The final two steps (i.e., steps 6 and 7) are optional. The groups that do these two steps correctly will get an extra 10% added to their final lab 1 grade.