## Selected Applications of a Dynamic Assignment Method for Microscopic Simulation of Pedestrians

### Authors

Tobias Kretz, PTV Group, Karsten Lehmann, PTV Group, Thomas Friderich, PTV Group

### Description

In micro-simulation models of pedestrian dynamics where pedestrians move freely in two spatial dimensions (i.e. they are not restricted to links as vehicles are) it has so far not been possible to apply methods of iterated (dynamic) assignment which were developed for application with simulations of vehicular traffic. The obvious reason is that the network structure of the infrastructure of vehicular traffic a priori allows only a limited number of routes (provided loops are excluded), while the areas of pedestrian dynamics in principle allow an unlimited (even uncountable) number of routes.

If one wants to apply assignment methods which have been developed for vehicular simulation to pedestrian simulation one therefore has to find a limited subset out of the infinitely many routes a pedestrian can walk between origin and destination. The subset needs to be meaningful in the sense that it should represent route choices which are actually perceived as such.

In this conference contribution such a general method will be summarized. Rather than the details of the method its application will be in the focus of this contribution.

### Abstract

In micro-simulation models of pedestrian dynamics where pedestrians move freely in two spatial dimensions (i.e. they are not restricted to links as vehicles are) it has so far not been possible to apply methods of iterated (dynamic) assignment which were developed for application with simulations of vehicular traffic. The obvious reason is that the network structure of the infrastructure of vehicular traffic a priori allows only a limited number of routes (provided loops are excluded), while the areas of pedestrian dynamics in principle allow an unlimited (even uncountable) number of routes.

So it appears that formulating a dynamic assignment method for microscopic pedestrian simulation is more difficult than formulating it for a simulation of vehicles. Another reason why there is not yet such a method might be that it appears that there is no need for such a method as the identification of the need for such a method rests on the assumption of an actually realized (near) equilibrium distribution of demand. For pedestrians this might have been the case only rarely in the past. However this situation has changed and will change even more so in the coming decades as both the number and the size of cities (and also their population density) have been and are growing dramatically. Ever more complex infrastructures are being built to accommodate for the demand that results in various aspects of life. Particularly in public transport infrastructure, but also on the roadside in city centers a major share of people walks between identical origins and destinations on many days of a year in moderate to high density situations. Thus the conditions are fulfilled that individuals walk spatial detours to arrive earlier and contribute to the establishment of an equilibrium. On smaller spatial scales where one can oversee a situation immediately repeated movement is not even required to assume that a group of people would distribute in a near equilibrium way instead of having everyone insist to pass an obstacle on that side which includes the shortest path.

If one wants to apply assignment methods which have been developed for vehicular simulation to pedestrian simulation one therefore has to find a limited subset out of the infinitely many routes a pedestrian can walk between origin and destination. The subset needs to be meaningful in the sense that it should represent route choices which are actually perceived as such. First: no route which a real pedestrian would actually consider should be skipped, second: as few routes as possible should be included twice or more in the set, and third: no route should be included in the set which is hypothetically possible, but can obviously not have demand assigned in an equilibrium situation (e.g. a route leading into a dead-end and back). Finally the method to find the subset should be generally applicable and not be limited to certain scenarios with specific properties.

For simple scenarios (e.g. two doors between two rooms) choosing the set of relevant routes is intuitive and obvious. This remains like this even in more complex geometries, as long as the geometry can be described as “a set of rooms which are connected by doors or corridors”; it changes if one would rather describe it as “one room or area with various obstacles of different size”.

In this conference contribution such a general method will be introduced in a summarized way while the detailed definition will be published elsewhere as it would clearly exceed the extent of both the oral and the written conference contribution. Rather than the details of the method its application will be in the focus of this contribution.

#### Publisher

Association for European Transport