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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.
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