# Simulations of Pedestrian Dynamics

These animations are examples of the behaviour of the different models of pedestrian evacuation dynamics. These should be read in conjunction with the Report on the project (The interim report can be found here). The model employed is based on the “Social Forces” model proposed by Helbing et al [1]. This project is the MPhys project of Edgar Haener and Paul Vriend under the supervision of Tobias Galla.

### Introduction

There are two main approaches to modeling of pedestrian dynamics. Physicists tend to favor simplistic models that have a small number of parameters allowing detailed analysis and enable analytic solutions to be found. Social scientist tend to use detailed models to describe real-world dynamics as exactly as possible. This results in models with a large number of parameters and calculation intensive simulations. This makes it easier to predict the outcome of real-world situations while incurring the drawback that the complexity of the model makes it difficult to distinguish between cause and effect.

In order to bridge this gap, several scenarios that have been studied using a simple cellular automaton are now investigated using the more detailed “Social forces” model proposed by Helbing et al [1]. The hope of this is to find a way to map the well understood general dynamics of simplistic models to more quantitative statements about real-world situations. The specific focus of this project is the effect of communication on the evacuation behaviour.

### Room Reproduced

When Helbing et al introduced their social forces model [1], one of the scenarios they studied was the escape from a room. To confirme that we implemented the model correctly we tried to reproduce their results. Two examples at 5 m/s and 0.4 m/s of the evacuation of a room are shown below the picture of the same scenario from Helbing et al papers [1]. The rooms is 15x15m with a 1 meter wide door and 200 pedestrians in the room.

### Bridge Scenario

Examples of the “bridge” scenario with a population of 500 pedestrians. All the examples are with 60% of the people communicating. This is based on a paper by Smyrnakis and Galla [2], investigating the effect of agent-to-agent communication on the evacuation of a bridge like structure. We are interested whether the observed behavior in simulations with a cellular automaton will persist when using the social forces model.

An exact replication of Smyrnakis and Galla’s scenario [2] on the left and the adapted simulation with the pedestrians going straight to all 4 exits and a changed utility function on the right.

The three videos below are with 1500 people and the utility function specified by Smyrnakis and Galla’s adapted to use 4 exits. The communication interval is set to 10 seconds (shorter thant in their paper [2]). After 10 seconds the agents start communicating. If they change direction and after 10 seconds are still closer to their old exit than to the new exit, they turn back. The fraction of communicators is (from left to right) 20%, 60% and 100%.

To investigated the effect of a central steering agent, we implemented the “text messaging” model with 500 people. An description of the model is given in the report

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### Corridor Scenario

We also investigated the scenario of two streams of counter flowing pedestrians to see whether the empirically observed lane observation would manifest. While there are cases where lanes form, we later abandoned this avenue to concentrate on the other scenarios.

### T-Junction Scenario

To investigate the exact correspondence between CA models and real-live situations, we aim to gradually move away from the simplicity of the CA model and investigate what behaviours of the CA model are retained. Below is an example of the T-Junction simulated with a CA and the exact replication with the Helbing model based on a paper by Galla [3].

### References

[1] D.Helbing, I. Farkas and T. Vicsek, Nature 407, 487 (2000)

[2] M. Smyrnakis and T. Galla, Eur. Phys. J. B. 85:378 (2012)

[3] T. Galla, J. Stat. Mech. (2011) P09004