The heart of any simulation software is its scientific model. The better the model can map behaviour and movement, the more accurate the results. It takes four steps to get from theory to a validated simulation model.

Theory and experiment

Patterns of movement behavior are identified through observations, experiments, etc. (e.g. Institute for Advanced Simulation Jülich).

Validation and verification

The computer models are validated on the basis of tests and comparison with real data.

Translation of behaviour

These patterns are evaluated and translated into models that describe different levels of movement.

Modeling in the computer

The characteristics of the different levels of behavior are translated into algorithms and the computer models are calibrated.

For crowd simulation, the most common models are derived from various fields. Cellular automata evolved from traffic engineering and are characterized by their chessboard-like construction. Their reduced geometric information results in short computation times. The Social Force Model has its origins in fluid mechanics and is therefore able to represent high densities.

The Optimal Steps Model breaks new ground. Instead of relying on existing models from other disciplines, it focuses on the basic tenet of crowd simulation: human movement. For this, we start with a single step. Each simulated person has a dynamic step length that depends on his walking speed and direction, and his avoidance of obstacles and other people. Thus each simulated step adjusts to current environmental conditions.

However, locomotion alone is not enough. Social psychology provides a deeper understanding of how to model human behaviour. The environment must also be included in the analysis. For this purpose, knowledge from social psychology and techniques to model behavior must be aligned. We must ask: How does a person move? What characteristics does a person possess? And how does a person interact with his environment?

Modellierungsebenen in crowd:it
To represent these aspects in a simulation, we have three modelling levels: 


Locomotion Layer

The locomotion layer models the way in which people move.  That is, how someone walks, uses stairs, runs, moves on escalators etc. For this, attention must be paid to how geometry is mapped: unlike other models, the OSM has continuous geometry. This means every point on a surface can be reached at any time.

Discrete geometry: only specified areas can be accessed / OSM: Continuous geometry: every point can be accessed

Collision avoidance is also considered on the locomotion layer. In reality, people implicitly avoid collisions. Navigation fields can be used to avoid collisions not only with obstacles but also with other people.

In crowd:it the locomotion layer is created as follows:

Continuous geometry

  • Simulated pedestrians (agents) are free to move in any direction.
  • All details of the plan are preserved. For instance, round objects can be modelled. This prevents dangerous artefacts.

Dynamic navigation field

  • At each time step, agents consider which route is best under the given circumstances.
  • They regard other agents as obstacles and, depending on the situation, can decide on a longer but ultimately faster route.

Optimal Steps Model

  • The model imitates a real, human step.
  • The underlying Optimal Steps Model facilitates implicitly realistic pedestrian behaviour. For instance, agents slow down naturally when confronted with dense crowds by taking smaller steps. This means no density-velocity relationship need be input.

Vertical connection objects

Unlike other simulators, crowd:it explicitly models stairs with their indiviual properties like the number of steps or the step depth. In other programs, for example, stairs are modelled as areas where walking speeds reduce. Due to the reduced step size on stairs, however, faster people are more likely to be decelerated more than slower people. A linear scaling is therefore not exact (cf. (10)). The stair model of crowd:it, the Optimal Stair Model, takes this knowledge into account. This means that people are also decelerated by the depth of the staircase and not exclusively depending on their speed on the level.

The Optimal Stair Model of crowd:it also reflects the insight that people tend to walk down on stairs in a straight manner and avoid slant paths on stairs. This is due to the fact that walking down stairs at an angle increases the risk of not hitting the stair step exactly and thus, in the worst case, causing a fall. In conventional models, one often sees agents zigzag. This has an effect on the space occupied by a single person and therefore does not accurately represent the flow on stairs.

In crowd:it, fixed staircases, escalators and elevators can be modelled directly, giving more realistic results.

Modeled stairs vs. zigzag running on deceleration planes

stairs vs scaled velocity in crowd:it

Simulation of walking behaviour on fixed staircases and escalators

escalators and stairs in crowd:it

Individual Layer

The individual or behavioural layer describes the cognition and characteristics of each person, such as space requirements, desired speed, mobility, knowledge of a place and individual plans. Places that are visited can be represented as points of interest.

Individual layer in crowd:it:

  • Each agent has an individual plan and personal characteristics.
  • By applying pre-selected heuristics, the agents interact individually with space and events. This could mean taking the shortest or fastest route across a building; or seeking the area with the most available space, or the queue with the shortest waiting time. This brings flexibility to your simulation–model the relevant simulation with the appropriate heuristic.

How can you create individual plans in crowd:it?

crowd:it agents use a list of Points of Interest (PoIs). As soon as an agent reaches a PoI and completes her task there (e.g. used the stairs or waited a while), she can consider the next PoI. Heuristics determine the order in which the PoIs are selected. This simple and flexible architecture allows you to model many use cases in a personalised manner.

Furthermore, the architecture allows us to model other factors, such as an agent’s knowledge of the location by assigning the heuristic "fastest way" for knowledgeable agents and "shortest way" for ignorant agents.

Which properties do agents have and which ones can I adjust?

crowd:it agents are automatically assigned default values for basic parameters like walking speed, size or space requirements. These are derived from studies (e.g. (12)) that form the basis of our pedestrian flow analyses (see literature list below). These standard values have been sufficiently validated (cf. (11), (17)). However, if you have a specific population that deviates from these standard values, such as a school of children, these values can be adjusted.


Points of Interest in crowd:it

Interaction Layer

The interaction layer models social and environment interactions. This includes: queuing, waiting areas, group behaviour. In addition, the interaction layer can enforce site-specific conditions such as timetables and safety-relevant processes.

  • Any number of agents, routes and characteristics can be combined.
  • Our agents reflect real human behaviour, avoid collisions and obstacles and look for the easiest way to their destination. Overcrowding, lane formation and inefficient pedestrian guidance are thus realistically represented.

Queueing in crowd:it


Selected publications on the simulation model

(1)M. J. Seitz and G. Köster, Natural discretization of pedestrian movement in continuous space, American Physical Society, PHYSICAL REVIEW E 2012, 86, 046108

(2)Kneidl, A.; Hartmann, D.; Borrmann, A. (2013): A hybrid multi-scale approach for simulation of pedestrian dynamics. In: Transportation Research Part C, in press.

(3)Kneidl, A. (2013). Methoden zur Abbildung menschlichen Navigationsverhaltens bei der Modellierung von Fußgängerströmen, PhD Thesis, Technische Universität München

(4)I. v. Sivers, G. Köster (2014): How stride adaption in pedestrian models improves navigation

(5)G. Köster, F. Treml, M. Seitz & W. Klein (2014) Validation of Crowd Models Including Social Groups, in Pedestrian and Evacuation Dynamics 2012, Springer.

(6)Angelika Kneidl (2015): How Do People Queue - A Study Of Different Queuing Models, TGF '15, Delft, Netherlands.

(7)M. J. Seitz, „Simulating pedestrian dynamics: Towards natural locomotion and psychological decision making“, PhD Thesis, 2016, Technische Universität München

(8)G. Köster, D. Lehmberg, F. Dietrich: „Is Slowing Down Enough To Model Movement On Stairs?“, TGF '15, Delft, Netherlands.

(9)A. Kneidl, “Simulation of the Neuschwanstein Castle: Egress of a fairy castle”, PED '16, Hefei, China, 2016.

(10) G. Köster; D. Lehmberg; A. Kneidl(2019): Walking on stairs: Experiment and model. In: Physical Review E, Vol. 100, Iss. 2 — August 2019.


Literature studies on setting parameters for the simulation model

(11)Richtlinie für Mikroskopische Entfluchtungsanalysen, Version 3.0, 10. März 2016,

(12)Weidmann, U. (1993): Transporttechnik der Fussgänger: Transporttechnische Eigenschaften des Fussgängerverkehrs (Literaturauswertung)

(13)Forell, B., Klüpfel H., Schneider, V., Schelter S. (2011) Vergleichende Betrachtung zu Evakuierungsberechnungen

(14)Schneider, B., Seyfried, A.: Methods for measuring pedestrian density, flow, speed and direction with minimal scatter, Physica A, vol. 389, no. 9, pp. 1902–1910, 2010.

(15)Oberhagemann, D.: Statische und dynamische Personendichten bei Großveranstaltungen, vfdb Technischer Bericht, März 2012

(16)Lam, Yuen et al. 2014 - Experimental study on upward movement in a high-rise building, Safety Science 70:397–405

(17) Leitfaden Ingenieurmethoden des Brandschutzes, Technischer Bericht vfdb TB 04-01, 3. Auflage November 2013, Hrsg.: Vereinigung zur Förderung des Deutschen Brandschutzes e. V. (vfdb), Technisch-Wissenschaftlicher Beirat (TWB), Referat 4, Prof. Dietmar Hosser