Crowd simulation software of INCONTROL: Pedestrian Dynamics® supports to increase capacity of any infrastructure to be compliant with physical distance regulations to ensure public health.

Currently governments worldwide have to deal with Covid-19 and developed and implemented lock down policies to protect public health. This has been successful by limiting the spreading of the virus. The number of individuals infected with the coronavirus and the number of corona patients in hospitals have dropped, but these lockdowns have had a major effect on economies.

Social vs Physical Distancing

We use the term physical distancing because social distancing implies that we are no longer socially active. While that might have been the situation during a lockdown or self-quarantine, countries are now opening up again. Both terms describe the same phenomenon that we need to keep a safe distance from each other to limit the risk of spreading the COVID-19 virus.

Governments and consulted virologists have designed sets of guidelines and restrictions to start up economies and open up public areas. In case a vaccine has been found or no more individuals infected with the corona virus there is still a severe threat of second wave. Policy makers have therefore set measures for the reopening of public life and to start up the economy. One very important measure that has helped containing and limiting the spread of the virus is to have non-household individuals keep distance to each other. This distance is often referred to as the physical distance between individuals.

With the reopening of public life individuals are demanded to keep a physical distance. Depending on local government regulations this distance can be 1 meter in Denmark, 1.5 meter in Germany and The Netherlands, 2 meters in the United Kingdom and Canada and 6 feet in the USA. Restaurants, theaters, stadiums and arenas, and other infrastructures are reopening with limited capacities to ensure the required physical distance.

This raises a lot of questions and challenges for everyone, whether you are representing local government, a factory manager, an individual shop holder, a restaurant owner or a sport facility and venue manager. How can we manage that people are able to keep this physical distance from each other? What is the capacity of a restaurant, a shopping area, transport hub, a public parc or a city square if we need to comply to physical distance rules? From a utilization point of view, how can we maximize these capacities? What will be the effects of these rules on the user experience and required staff levels? Is reopening under these conditions economically viable?

Pedestrian Dynamics® is a crowd simulation software that can answer these questions. It can be used to analyze different physical distance management scenarios, finding optimal safety, increase capacity and user experience as much as possible. Simulation can also be used to train staff and guide visitors to comply to the physical distancing rules.

Pedestrian Dynamics® is a tier-one crowd simulation tool that has been used for more than a decade to model large crowds in all kind of infrastructures, from shopping centers, to airports, festivals and city areas. Pedestrian Dynamics® has helped to answer questions about the capacity, considering safety and comfortability that emerge in crowded places.

In Pedestrian Dynamics® every individual is modeled as an agent with its own characteristics such as a radius, preferred walking speed and goals within the infrastructure. It uses a vision-based algorithm with 2 simple heuristics

A collision force is used to make sure agents do not collide and try to keep the physical distance. Agents try to avoid other agents within their view field while moving toward their goal.


The six “closest” agents in the view field of the agent are taken into account in the avoidance behavior. A weight factor makes sure that agents walking towards the agent seem closer than an agent that is at the same distance and moves away from (the) agent(s).

to determine walking direction and speed, making sure that the agent takes the most direct path to its goal and collisions with other agents and obstacles are avoided. In case of overcrowding agents can have unintentional contact with other agents and obstacles. In these cases, a collision force is taken into account.   This type of model is very good at modelling collision avoidance. This makes it therefore very suitable for modelling physical distancing where agents need to keep even more distance from each other.

Implementing physical distancing in society requires crowd management plans such as a well-constructed or prepared layout and design but it also requires that people follow the rules. To be able to model physical distancing in an existing crowd simulation tool and give relevant insight into the capacity, safety, and user experience changes in the walking algorithms are required and new types of simulation outputs need to be added. Another requirement is the ability to model different types of crowd management measures.

To model physical distancing, individuals must be able to keep a local applicable physical distance from each other. In order to respect this distance between people this means that each individual is surrounded with a private circle. In this private circle other individuals are not allowed except members of the same household. In Pedestrian Dynamics® we have introduced a new property of an agent, the “physical distance”. An agent is modeled as a circle. The radius of this circle is referred to as the body radius. The private area is also a circle. Its radius equals the body radius plus half the physical distance.

Assuming a physical distance of 1.50 meter and a body radius of 0.239 meter the private circle of an individual to keep a physical distance has a radius of 0.989 meter which is the body radius + the physical distance divided by 2.

The private circle is used in the vision-based model to make sure that individual agents keep a distance dictated by the physical distance property from each other and avoid this area. The body circle is used for all agents to keep a distance from walls and other obstacles. This means that agents can walk close to a wall but keep the necessary distance from other agents to comply with the physical distance rules. For individuals from the same household the body circle instead of the private circle is used to keep distance. This allows families to walk close together.

The current Pedestrian Dynamics® 3.3 stable release already provides a large number of specific objects that can be used to model all kinds of crowd management techniques such as timeslots, one-way routing and following a mandatory route. Examples are a passageway object that can be used to set the direction to one-directional flow or a connected activity route can be used for mandatory routing.

Agents are able to decide to take a detour if more than a few people are in a certain area. A new routing method has been introduced that can be enabled by setting a property and a weight factor of each agent which determines when an agent decides to take a detour. A routing method already existed with a density delay weight to influence when an agent decides to take a detour. For the physical distancing-based routing method instead of the area of a circle with the body radius, each agent contribution to the density is now based on the area of its private circle.


For global routing an agent will typically take the shortest global route to its goal.

With physical distancing routing even a few agents in a corridor will behave differently. Where, under normal routing, an agent would find a path through the corridor, the agent will now take a detour. A density weight factor determined by the private circle of an agent determines whether or not an agent decides to take this detour.

The above formula is used for the global routing. In physical distancing routing, the individual agent attribution to the density is based on its private circle instead of the body radius.

To be able to estimate the safety of the individuals in different scenarios, new types of simulation output are required that makes it easy to analyze how well the physical distancing rules are met. Examples are a proximity maps of the area indicating locations where the physical distance has not been met and a histogram indicating how often individuals breech the physical distancing rule.


Map showing whether or not the physical distance is respected all the time.



Comparison of different physical distance scenarios.

What can we in general say about the capacity and possible flow?

In many cases the main question is what impact has physical distancing on the capacity and flow of an infrastructure. Given a static infrastructure and by making several simplifying assumptions, estimates can be made relatively easy. In practice however, we have to deal with more complex and dynamic situations. Every individual should have enough space to be able to walk around without immediate violation of the physical distance rules. Individual characteristics of the crowd and the infrastructure should be taken into account as well.

In a static situation, when taking physical distancing into account each agent occupies 3.38 square meter compared to 0.198 square meter in a normal situation. We assume a physical distance of 1.5 meter, an average agent radius of 0.239 meter and an optimal filling of the space while everybody is from a different household.

Explanation static calculations
To be able to keep a physical distance of 1.5 meter and assuming an average agent radius of 0.239 meter, each agent occupies an area of A=πr^2 = 3.073 square meter where r = 0.989 = 0.239 + 1.5/2 is the private radius. Recall that the private radius is equal to the body radius plus the physical distance divided by 2. However, you cannot use the whole area when filling it with circles without creating an overlap. The proportion of the surface covered by the circles is the packing density. The maximum packing density of circles in the plane is known to be 0.9069. This means that a group of agents need 3.073/0.9069 =3.38 square meter.

Optimal usage of space for a standing crowd in case of a physical distance of 1.5 meter. Each agent uses 3.38 square meter.

The amount of space required to comply with physical distance rules in dynamic situations where people walk around is much more difficult to determine. Factors such as the walking speed and specific geometry of the infrastructure have impact too. This makes it more complicated to estimate the amount of space each individual will occupy at any given time and the flow and speed that can be obtained. In these cases, crowd simulation with pedestrians trying to keep this physical distance is required.

Using Pedestrian Dynamics®, we have examined the maximum flow through corridors with different widths, assuming an average preferred walking speed of 1.35 meter per seconds. Without physical distancing the flow through the corridor is approximately 80 agents/ m/min. With physical distancing of 1.5m this is around 12.5 agents/ m/min. This is about 16% of ‘normal’ maximum flow in a one-directional situation! For bi-directional flows it even drops to 8 agents/ m/min. This shows that for practical situations both the infrastructure and the profile of the public, signs and local governmental physical distance instructions needs to be taken into account to work towards an optimal solution.

INCONTROL will continue its research in how to model physical distancing and how to calibrate models for physical distancing. INCONTROL also supports research projects such as the spread of the corona virus in specific types of infrastructures, e.g. city areas, shopping malls, (sport) venue facilities, hospitals, bars and restaurants.

If you need support with implementing physical distancing, are interested in research in this area or if you would like to work with the Pedestrian Dynamics® software including physical distancing do not hesitate to contact us.