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Urban Mobility: A Data-Driven Approach

Anders Johansson

casa.ucl.ac.uk – www.ajohansson.com

Simulating pedestrians can been done in various different ways:

Discrete Continuous space space

Microscopic

Macroscopic

Cellular-automata models

Social-force model

Fluid-dynamic modelsQueuing-

network models

Fluid-dynamic model: www.matyka.pl

Simulating pedestrians can been done in various different ways:

The social force model (Helbing et al., 1990, 1995, 2000):

Each pedestrian is influenced by a number of forces:

Repulsive forces from other pedestrians.

Repulsive forces from borders. Driving force towards the desired direction of

motion. Force into the desired direction

of motion

Forces from boundaries

Forces from other pedestrians

Resulting force

The social force model (Helbing et al., 1990, 1995, 2000):

Each pedestrian is influenced by a number of forces:

Repulsive forces from other pedestrians.

Repulsive forces from borders. Driving force towards the desired direction of motion.

The Social force model is specified via the equation of motion:

Where the force is composed by:

The Social force model is specified via the equation of motion:

Where the force is composed by:

The Social force model is specified via the equation of motion:

Where the force is composed by:

Acceleration time

Desired velocity

Actual velocity

Forces from all other pedestrians β

Forces from all boundaries i

Noise term

The Social force model is specified via the equation of motion:

Where the force is composed by:

Everything put together: Social interaction forces, obstacle forces, and a driving force towards the destination:

Everything put together: Social interaction forces, obstacle forces, and a driving force towards the destination:

To be able to calibrate and validate the model, data from different locations have been gathered:

Budapest, Hungary Budapest, Hungary Dresden, Germany

To be able to calibrate and validate the model, data from different locations have been gathered:

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Even more detailed data have been obtained from a walking experiment carried out together with Guy Théraulaz and Mehdi Moussaïd at Paul Sabatier University. Markers were put on the feet and knees and were tracked with an accuracy of a few mm, and with a time frequency of 100 measurements per second.

Even more detailed data have been obtained from a walking experiment carried out together with Guy Théraulaz and Mehdi Moussaïd at Paul Sabatier University. Markers were put on the feet and knees and were tracked with an accuracy of a few mm, and with a time frequency of 100 measurements per second.

A large collection of video material of pedestrian crowds have been used as a test bed for evaluating and calibrating pedestrian models.

)/exp()( Bdd

dAtf

Model

Videos

Brutus cluster at ETHZurich

Evaluation and calibration results

A large collection of video material of pedestrian crowds have been used as a test bed for evaluating and calibrating pedestrian models.

.Substitution: A pedestrian from the empirical trajectory data is replaced by a simulated pedestrian.

Error: The deviation of the simulated position to the position in the data gives an error measure.

Optimization: This error measure is used by an optimization procedure in order to find model parameters that minimize the error.

.

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Calibration results

Validation on dense crowds

In this chart of density as function of time and space we can clearly see the

emerging stop-and-go waves.

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Validation on dense crowds

In this chart of density as function of time and space we can clearly see the emerging stop-and-go waves.

Gas-kineticpressure

as a function of (a) time, and (b) space.

)(Var)()( VttP t

Validation on dense crowds

Kaaba, Grand Mosque, Saudi

Arabia, 47,000 pedestrians