Crowd modelling: Game theory, implementation & validation

Lead Research Organisation: Imperial College London
Department Name: Dept of Mathematics


During the last decade, pedestrian modelling and simulation has become one of the key component of the design cycle in the civil engineering sector. Indeed, the most advanced and complex developments of train stations, airports, office buildings, hospitals or even entire cities involve a people flow study that aim to assess the quality and accessibility of the space from the point of view of its future users. These studies are performed by people flow experts such as the Smartspace team from Buro Happold Engineering and pedestrian simulation represents a key tool of the design process. Despite the fast growing need for always more challenging and complex analysis, state of the art pedestrian simulation software face crying limitations in terms of computational speed and agreement with the real-world. Buro Happold develops its own pedestrian simulation software that relies upon agent based models where pedestrians are modelled as individual particles. For more details about Buro Happold Engineering Smart Space Team, see

Crowd safety and crowd management are important matters in our urban societies. To improve the efficiency of crowd safety and management procedures, reliable numerical models are needed. Numerical models are routinely used to improve the design of public places, such as terminals or walkways. However, the walking behavior of humans in highly crowded environment is still very poorly understood and many existing numerical models, which treat humans like physical particles, fail to provide a reliable and accurate account of pedestrian behavior.

In this project, we propose to improve the modelling of pedestrian flows, analyse this theoretically and in real life problems, implementing it and validating against real data. The three basic pillars of the project are:
- Improvements in Local Navigation modelling: Implementation and Analysis.
- Improvements in Global navigation and planning modelling: Implementation and Analysis.
- Validation with real data.

Local navigation rules in the existing software for pedestrians are typically based on social force models or velocity-based model as in , we will improve these by incorporating rational behaviour in these social force models and by changing completely this paradigm with models based on optimizing the utility for each individual in the crowd. We propose to investigate a hierarchy of models which treat humans as rational agents who try to optimize their walking trajectory among moving obstacles (the other pedestrians) to reach their target.

Global navigation and planning refer to the fact of including the effect of external signals in the control of a crowd or how to include the effect of the observed density in the global decision making of an individual. Optimal control approaches can be used to implement some of these ideas both to include external navigation fields and/or include rational behaviour of the individuals at larger spatial scales.

One of main aims of this PhD project is to develop, validate and implement these new agent based models into Buro Happold existing software with the objective to improve its relevance and performance. The accuracy of the studied models will be assessed against quantitative criteria such as the relationship between the speed and density in a crowd. As a second and more adventurous and rewarding stage, the student would aim to improve upon the studied models and design a new pedestrian dynamic model that is both, more accurate and more efficient than the ones mentioned above.

The research proposed may have direct impact in security and transport included in the EPSRC strategy: Transportation operations and management.


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Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/N509486/1 01/10/2016 31/03/2022
1835367 Studentship EP/N509486/1 01/10/2016 15/04/2020 Rafael Sanchez Bailo
Description The work's outcomes are twofold: in one hand, we have developed new models for pedestrian dynamics which permit the simulation and prediction of the motion of crowds; in the other hand, we have developed improved numerical schemes which correctly solve a family of evolution equations, equations which come from the field of pedestrian dynamics among others.
Exploitation Route The new pedestrian models have drawn interest from the community and already generated some discussion. The new numerical schemes are already being used by others.
Sectors Other