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Traffic in Paris

or The heartbeat of Paris

Visualization of the traffic (#cars/hour) in Paris from data published by the OpenData-Paris project. The data covers the period from the 21.01.2016 till 05.2017.

Traffic in paris per month and per hour

Map: Stamen Toner -- Data: comptages routiers permanents -- Code: traffic-movie.ipynb -- Movie: link -- Interactive: link

The heartbeat depicted

We distinguish (statistically, see below) the periferique (essentially a 1D membrane) from the city (essentially a 2D cell :D). In the figure below we plot how many cars are counted per hour and per month among all checkpoints (normed by the average over months). Each line is a month, and the numbers indicate the months from August (8) till December (12).

The two give similar pdf for the number of car passes, shifted by a lag of ~1h: the periferique wakes up earlier than the city?

The second figure is a plot of the relative variation of number of car counts. Again, each line corresponds to a different month, and numbers enumerate months from August to December. Are fluctuations repressed during peak hours because the network reaches maximum throughput?

Traffic cycle

Illusions

You may think the number of cars in the periferique to be bigger than that in the city. Wrong. We can't measure it, you can't too. By measuring passages via the checkpoints (or measuring stations) with the time resolution of 1h[^] we can't measure which cars are repeatedly counted during the same hour in different contiguous checkpoints.

[^] 1h is the minimum time scale reported in the raw data).

How it is done

  1. Downloaded the full csv (1.2Gb, 31e6 records)

  2. We aggregated the data averaging over business days (Monday to Friday) [code].

  3. Checkpoints with fixed counts among the dataset or 0/nan readings are removed (I guess that they are broken).

  4. Paris is discretized on a coarse-graining grid of 25x25 cells. Per each measurement station inside a cell we sum the # of passages and average the position [code]

  5. To achieve a good visualization:

    1. the maximum number of counted car passes per hour is capped at 15e3 per counter
    2. we compute intermediate points on a 100x100 grid with linear interpolation [code]. This yield the smoothly varying colormap.

The data files are not stored in this repo because they will get outdated in weeks. The final dataframe after pre-processing is about 60Mb, totally manageable.

Daily traffic cycle

The code is [here].

We can easily distinguish checkpoints on the periferique by the others because those in the periferique are less, but with a high maximum rate of cars passing through:

Histogram of max counted cars

Thus, we can plot the number of cars in the periferique versus those in the inner city each hour per month:

Traffic cycle

Principal Components

All modes versus all modes but first mode

Map: Stamen Toner -- Data: comptages routiers permanents -- Code: traffic-pca.ipynb -- Movie: link

Principal components analysis allow to isolate the dominant behavior in a signal from the rest. It computes a set of empirical eigenvectors, directions along which the data is statistically uncorrelated. The associated eigenvalues give a measure of the importance of the mode in the dataset. I chose to study the fluctuations of the counters with respect to the mean at each hour. In this case the data is a 2D map C(i,t), where i is the i-th counter, and t the measurement time. The dataset looks like

Dataset for PCA

And the first 4 modes are

PCA modes

and time modulation and relative importance of the modes are

PCA modes

An academic use of this technique is on the paper: Human sperm steer with second harmonics of the flagellar beat (arxiv,Nature Communications/2017)

We can now reconstruct the data filtering out the 0th mode which brings in 92% of the signal but shadows other small yet correlated parts of the signal. In the opening animation, on the left there is a reconstruction with all modes, on the right with all but the 0th; a red big dot indicates more car passes than average, and a blue small dot indicate less car passes than average.

Missing further data to validate possible models, I leave the interpretation to the reader ;)

License

The movies, animation, plots, and texts (said the content) of this project are licensed under the Creative Commons Attribution Share Alike 4.0 license, and the underlying source code used to analyze, format, render, and display that content is licensed under the GNU GPLv3 license.

Nothing of this would have been possible without:

python, numpy, pandas, sqlite, matplotlib, jupyter, bookeh, holoviews, conda, imagemagick, ffmpeg and the effort of those releasing and maintaining FOSS.