Microscopic pedestrian models are frequently used in traffic engineering and safety engineering to simulate crowd behaviors in different scenarios. The Social Force Model (SFM) is a second-order model based on a superposition of exponential repulsions with the neighbors (the social forces). Despite its simplicity, SFM can describe realistic dynamics and self-organized phenomena (lane formation, alternance at bottlenecks, etc.) for fine tunings of the parameter. However, inertia mechanisms can also provide undesired overlapping effects of the pedestrians (“tunneling”  or penetration of particles), oscillating behaviors, as well as additional numerical complexity inherent to second order models. In contrast, the velocity in first-order models is instantaneously adjusted to the neighborhood and the environment. Such a modelling approach is largely inspired by motion planning in robotics. Constraints on the velocity in case of contact allow to model hard-core body exclusion (volume exclusion) and describe collision-free pedestrian dynamics with no overlapping including different self-organization such as jamming and clogging at bottlenecks, lane formation, freezing by heating effect, or intermittent counter flow at bottlenecks (see the videos #1, #2, #3, #4 and this presentation).

Pedestrians also exhibit many intelligent tactical behaviors. For instance, experiments show that load in complex geometries, load balancing occurs across different possible exits, optimising the global leaving time. In the literature, basic tactical models for the exit choice depend only on the distance to the exits. They do not reproduce load balancing when the pedestrians are initially inhomogeneously distributed. More sophisticated models based on simulation prediction of the travel time over the possible exits allow to describe the balancing, but they are numerically very expensive. However, the pedestrian speed is strongly correlated with pedestrian density. This relationship allows to derive the choice of the exit as a combination of the distance and the density at the exit, and to recover the load balancing without complex computations.

In a city, the street network is heterogeneous in terms of composition but also in terms of infrastructure, as the layout is adapted to more and more different users. Current urban traffic flows in European city centers are composed of road vehicles, pedestrians, bicycles, scooters, and other motorized or not personal mobility devices (PMD). The conception of intelligent transportation systems is generally based on simulation analysis. Numerous models exist for the different types of users, such as car-following models for traffic flow or force-based models for pedestrian crowds. However, only few studies address the interactions between different types of users (e.g., pedestrians and cyclists).

In a static heterogeneity model, constant parameter settings are applied to the different agent types. The objective is to model different types of agents (e.g., pedestrians and bicyclists) with specific characteristics in terms of desired speed, agent size, etc. This kind of heterogeneity is usually referred to as quenched disorder in solid-state physics and generally results in the formation of horizontal lanes for counterflow. In the dynamic heterogeneity model, the parameter setting depends on the type of the agent in front, with a specific parameter setting  when interacting with another type of user. Such a mechanism may be realized in mixed urban traffic where cyclists or electric scooter drivers adapt their behaviour, e.g., increasing the time gap or reducing their desired speed, when following a group of pedestrians. The heterogeneity features depend on the interaction and are time-dependent. They are usually called annealed disorder in the literature. Interestingly, such a mechanism generally leads to the formation of vertical bands.