People flow simulation

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Evacuation simulation of a grandstand .

A pedestrian flow simulation is the computer simulation of the sequence of foot traffic on the basis of a mathematical model . People flow simulations are mainly used when calculating evacuation , but also when planning traffic capacities , visitor management or for commercial purposes.

Classification of models

Simulations are the reproduction of reality with the help of mathematical models and the calculation (generally with computers) of predictions based on these models. Simulations do not initially represent optimization tools. In order to be able to carry out an optimization , a result function that is minimized and one or more variables to be varied must be defined. Models can be classified using the following categories:

Macroscopic and microscopic

Microscopic and macroscopic models for evacuation simulation differ in that macroscopic models map superordinate, aggregated parameters of entire moving crowds and microscopic models include the individual decision-making options of individual people.

Typical macroscopic models are the so-called network flow models . Here the geometry is mapped on a graph and the flows of people are viewed as flows on this graph. With the help of network flow algorithms, lower bounds for the evacuation time can be determined.

Microscopic models include the interaction of individual individuals. So people behave differently depending on the currently possible and perceptible directions of movement, the current information situation and personal experience. Microscopic models can also map phenomena such as path formation as people follow others, congestion and shock waves.

If these are autonomous and interact, they are called agents and the models are called multi-agent systems . Stochastic parameters (usually the software agents ) are used to record influences that are not specified or quantifiable in more detail (e.g. difficulties in spatial orientation ). These phenomenological parameters can neither be derived from other directly measurable quantities nor measured directly in experiments . Therefore, they have to be calibrated using empirical studies.

Analytical results are usually not possible for calculating social systems. General models allow the simulation of the evacuation of buildings, aircraft and ships alike.

Discreet and continuous

Discreet and continuous availability

Discrete models either divide the space to be simulated into small, uniform, square or hexagonal cells, or divide the simulation time into calculable sections. They mainly differ in terms of their granularity. Computer-aided simulation models absolutely require a temporal discretization. Models based on cellular automata naturally use discrete spaces.

Continuous models, on the other hand, assume that every point in space can be reached continuously . Continuous models enable a high level of accuracy, but after each individual step they need to rule out collisions so that two people are not standing in the same place. Continuous rooms are usually more computationally intensive and are often used for agent-based models.

The distinction between discrete and continuous only applies to microscopic models.

Agent-based and rule-based

Simulation models can also be categorized according to the way the individuals are modeled:

  • With rule-based models , every pedestrian moves based on a global set of rules.
  • Agent-based models give each pedestrian an individual plan of action and personal characteristics.

While in rule-based models properties are often linked to the geometry and the behavior of people is determined by stepping on a certain area, properties in agent-based models are linked to the person and thus the behavior is decoupled from the geometry.

Potential based and differential equation based

There are two basic approaches to modeling people's movements. Both approaches assume that the mass of people is subject to certain "social" forces. Every person feels an attraction to the goal as well as repulsive forces from other people and obstacles on their way to the goal.

Forces that act on the person on their way to the goal

In potential-based models , these forces are superimposed in a gradient field along which people walk. The minimum of the potential field lies in their target, and the people walk along the gradient of the field

Resulting potential field

Models based on differential equations superimpose the individual forces in force fields . The respective force fields are superimposed in a common force field along which the pedestrians walk towards the destination.

This controls the pedestrian's next step based on the forces acting on him. The underlying differential equation must be fulfilled at all times. It is not possible to stop a person spontaneously.

Application: evacuation simulation

The distinction between the simulation of pedestrians in buildings, on ships and vehicles on the one hand and settlements or areas on the other hand plays an essential role for the simulation of evacuation processes.

Evacuation exercise in the Euerwangtunnel on the new Ingolstadt – Nuremberg line

Buildings or vehicles

Buildings (stations, stadiums, etc.), ships, planes and trains have in common with regard to their evacuation that people move primarily on foot. In addition, there is movement on emergency slides or the like or, in the case of ships, the launching of occupied boats with the help of davits . These are collectively referred to as the evacuation system.

Passenger ships

The evacuation of ships is characterized by three special aspects:

  • the ratio of the number of passengers to the number of crew members,
  • the ship's movement,
  • the operation and use of the life-saving appliances .

The movement of the ship affects the mobility of the people on board. There are a number of investigations for this, which can be taken into account in a simulation using appropriate speed reduction factors.

The same applies to the role of the crew in an evacuation . However, this influence is more difficult to quantify, so that this factor is usually taken into account by the behavior of the passengers (faster orientation or reaction to the alarm ). This relationship, in turn, requires calibration through empirical studies. If only quantitative results are available, the influence of the crew in the sense of an "assumption of the worst case" (worst case analysis) can be completely neglected.

Evacuating a ship consists of two separate phases: the collection phase and the embarkation phase . This is also reflected in the simulation. The times for getting ready and boarding the life-saving appliances (boats or life rafts or liferafts , which can be reached via slides) and for launching are included in the simulation as additional parameters. This means that the entire evacuation process is simulated. The lifeboats do not represent a final "safe place". Nevertheless, the evacuation of a ship is considered to be complete once the boats (or rafts or islands) have been removed from the danger zone. The resettlement of people on other ships is considered a separate process.

Planes

A regulation of the International Civil Aviation Organization (ICAO) prescribes an upper limit of 90 seconds for the evacuation time of aircraft. This must be proven before the approval of an aircraft type. This happens either with the help of a model or on the basis of analogies to already approved aircraft types.

When simulating the evacuation of aircraft - as with ships - the duration for the provision of the rescue slides and the capacity of the doors or emergency slide (individual slide duration) must be taken into account. A distinction between the collecting and sliding phases is not necessary, however, as the people go straight to the emergency exit and immediately climb the emergency slide. The crew plays a crucial role here, as they are responsible for providing the life-saving equipment and actively supporting the passengers (e.g. pushing them onto the slide).

Areas (settlements)

There is a smooth transition from office complexes, stadiums and apartment blocks to entire city districts. One possibility of differentiation in connection with simulations is the transport mode: moving on foot on the one hand and using means of transport (vehicles or helicopters) on the other. Due to their size and heterogeneity, such processes are usually simulated with queue models.

The second phase in the evacuation of areas (the transport of people with vehicles) can e.g. B. be simulated with the help of queue models. Since these are large-scale simulations, no microscopic models have been used to date.

credentials

  • Hubert Klüpfel: A Cellular Automaton Model for Crowd Movement and Egress Simulation. Dissertation, University of Duisburg-Essen, 2003. [1]
  • Tobias Kretz: Pedestrian Traffic - Simulation and Experiments. University of Duisburg-Essen, 2007. [2]

literature

  • Schadschneider et al. "Evacuation Dynamics: Empirical Results, Modeling and Applications" in RA Meyers (editor) Springer Encyclopedia of Complexity and System Science Springer PDF

Individual evidence

  1. ^ Gershenfeld, Neil: Mathematical Modeling. OUP, Oxford, 1999.
  2. ↑ a b c d Angelika Kneidl: Methods for mapping human navigational behavior when modeling pedestrian flows

Web links