Click to edit Master subtitle style Urban Mobility: A Data-Driven Approach Anders Johansson casa.ucl.ac.uk –

Simulating pedestrians can been done in various different ways: Discrete Continuous space space Microscopic Macroscopic Cellular- automata models Social-force model Fluid-dynamic models Queuing- network models Fluid-dynamic model: 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:

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:

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:

88 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. Model Videos Brutus cluster at ETH Zurich 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..

1111 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.

1313 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-kinetic pressure as a function of (a) time, and (b) space.

Validation on dense crowds Kaaba, Grand Mosque, Saudi Arabia, 47,000 pedestrians