DYNAMIC ASSIGNMENT IN MICROSIMULATIONS
OF PEDESTRIANS
Authors: Tobias Kretz1, Karsten Lehmann1,2, Ingmar Hofsäß1, Axel Leonhardt1
Affiliation1: PTV Group
Address1: Haid-und-Neu-Straße 15, D-76131 Karlsruhe, Germany
Affiliation2: init AG
Address2: Käppelestraße 4-6, D-76131 Karlsruhe, Germany
Email (corresponding author): Tobias.Kretz@ptvgroup.com

ABSTRACT
A generic method for dynamic assignment used with microsimulation of pedestrian dynamics is
introduced. As pedestrians – unlike vehicles – do not move on a network, but on areas they in principle
can choose among an infinite number of routes. To apply assignment algorithms one has to select for each
OD pair a finite (realistically a small) number of relevant representatives from these routes. This
geometric task is the main focus of this contribution. The main task is to find for an OD pair the relevant
routes to be used with common assignment methods. The method is demonstrated for one single OD pair
and exemplified with an example.

INTRODUCTION
Finding and evaluating the user equilibrium network load for road networks (traffic assignment) is one of
the core tasks of traffic planning. Various algorithms to solve this problem have been developed over the
years (Wardrop, 1952) (Beckmann, McGuire, & Winsten, 1956) (LeBlanc, Morlok, & Pierskalla, 1975)
(Bar-Gera, 2002) (Gentile & Nökel, 2009).
For readers who are not familiar with the concept of iterated assignment a short summary: the basic idea
is to simulate (or compute) a scenario multiple times always computing the assignment on the routes
based on the results of one or more or all previous simulations (iteration steps). The aim is to come up
with a user-equilibirum route assignment which is –Wardrop’s principle – that no driver (or pedestrian)
can achieve a smaller travel time by changing the route. This implies that tall travel times of the routes for
an origin destination pair are equal. The efficient computation of the assignment from previous simulation
runs such that the equilibrium is reached with as few iterations as possible, is a demanding task and
progress has been made throughout recent decays since Wardrop stated his principle.
The main hindrance for the application of said algorithms with pedestrian traffic is that all these
algorithms are formulated for application with discrete networks, i.e. they compute flows on a node-edge
graph. Pedestrians on the contrary can and do move continuously in two spatial dimensions. Their
walking area can have holes (obstacles), but this does not change the fact that – even when loops are
excluded – there are infinitely many possible paths for a pedestrian to walk from an origin to a
destination.

Dynamic Assignment in Microsimulations of Pedestrians
There are two ways to face the resulting challenge: either one develops an entirely different assignment
algorithm for pedestrian traffic – this was done for example in (Hoogendoorn & Bovy, 2004, S. a)
(Hoogendoorn & Bovy, 2004, S. b) (van Wageningen-Kessels, Daamen, & Hoogendoorn, 2014)– or one
extracts from the pedestrian walking area in a well-grounded suitable way a graph structure which can be
used with existing assignment methods. This is what is attempted in this contribution.
In the remainder the conditions and restrictions for the application will be discussed and the task that is
attempted to be accomplished in this contribution will be clearly defined. This is followed by the section
which defines the main ideas of the method. Finally an example of application will be given.

PRELUDE: NAVIGATING WITH DISTANCE MAPS
Models of pedestrian dynamics usually rest on the assumption that pedestrians predominantly move into
the direction of the (spatially) shortest path toward their destination. This basic direction then is modified
by other effects of which one has to be the influence of other pedestrians. For the computation of the
direction of the shortest path there are a number of methods of which one is distance maps.
The method of distance maps or static potentials has been particularly popular for modeling pedestrian
dynamics in particular in use with cellular automata models (Burstedde, Klauck, Schadschneider, &
Zittartz, 2001) (Kirchner & Schadschneider, 2002) (Klüpfel, 2003) (Nishinari, Kirchner, Namazi, &
Schadschneider, 2004) (Kretz & Schreckenberg, 2009) (Schadschneider, Klüpfel, Kretz, Rogsch, &
Seyfried, 2009). The reason for this is probably that the data structure of the distance map fits well to the
spatial representation of cellular automata models: a regular usually rectangular grid. FIGURE 1
visualizes an example of a distance map.

FIGURE 1: The left figure shows a distance map with the brightness of a spot directly proportional to the value of the
grid point, i.e. the distance of that spot to the destination area. The destination area is shown as a green-black
checkerboard, the obstacle is marked with diagonal red lines on white ground. In the central figure the brightness is
computed modulo to some distance value d. The figure on the right side shows an excerpt of the geometry: shown is the
area around the upper left corner of the obstacle with the field of negative gradients (white) of the distance field. It is a
general mathematical property of gradients that they are orthogonal to lines of equal value (equi-potential lines) of the
field from which they are derived. Therefore the negative gradients give the direction which for a given step distance most
reduces the distance to destination. Following the negative gradients pedestrians are also guided around the obstacle.

In cellular automata models the distance maps are usually used such that pedestrians move with higher
probability to a cell which is closer to the destination. In other modeling approaches which do not directly
operate with space, but rather with velocity or acceleration as for example the force-based models do,

Kretz, Lehmann, Hofsäss, Leonhardt

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pedestrians follow the negative gradient of the distance map at their current position. ``Follow'' here
means that this direction is used as preferred or desired or base direction and may be subject to
modifications as consequence of influence of for example other pedestrians or limited acceleration ability.
A standard method for the computation of the distance maps is the Fast Marching Method (Kimmel &
Sethian, 1998). For other methods see (Kretz, Bönisch, & Vortisch, Comparison of Various Methods for
the Calculation of the Distance Potential Field, 2010), (Schultz, Kretz, & Fricke, 2010).

PROBLEM ILLUSTRATION
Imagine a walking geometry as shown in FIGURE 2. A pedestrian following the above mentioned
principle of walking into the direction of the shortest path would pass the obstacle on the left side
(reader’s perspective) as it is shown in the left figure. In this case it is easy to make pedestrians pass the
obstacle on either side by introducing on each side of the obstacle an intermediate destination area. With
the intermediate areas and the routes which include them, it is possible to route pedestrians locally into
the direction of the shortest path, but still make a given fraction of pedestrians detour: first the pedestrians
would head toward one of the two intermediate destinations and as soon as it is reached proceed to the
final destination.

FIGURE 2: Walking area (black), obstacle (diagonal red lines on white ground), origin area at the upper sides (red and
black diagonal checkerboard pattern) and destination at the lower ends (green and black checkerboard pattern). Left
figure: The yellow line shows the path a pedestrian (set into the simulation at some arbitrary coordinate on the origin
area) would follow if a distance map is used to determine his basic direction. The route data simply would be some
information (e.g. an area ID) identifying the destination area. Right figure: Compared to the left side figure the blackblue areas mark intermediate destination areas. There are two routes, one leading over each of the intermediate
destination areas. (The intermediate destination is not necessary along the shorter (left) path, it has been added for
illustration.)

In FIGURE 2 the intermediate destination area on the left side was not necessary. Having a route directly
leading from the origin to the destination area would have the same effect. However, it is important to
note that the lower intermediate destination area does not change the path of the pedestrians on that route
compared to the case without any intermediate destination area. This is not in general the case. In general

Dynamic Assignment in Microsimulations of Pedestrians
it is difficult to shape the intermediate destinations such that the path on the principally shortest route is
not distorted compared to the case without intermediate destination. FIGURE 3 shows such a case. It is
concluded that the intermediate destination areas cannot be of trivial shape (rectangles) in general.

FIGURE 3: Example with necessarily non-trivial geometry for the intermediate destination areas. Walking area (black),
obstacle (diagonal red stripes on white ground), two origin areas to the left (red-black diagonal checkerboard),
destination area to the right (green-black checkerboard), and shortest paths (yellow and orange). Compare FIGURE 4.

The basic idea is now that the intermediate destination areas need to be shaped along the equi-distance
(equi-potential) lines of the destination area distance map (static potential). This is shown in FIGURE 5.

FIGURE 4: For the example of FIGURE 3 simple rectangular areas are used as intermediate destination areas (light and
dark blue checkerboard pattern). With none of the three variants the shortest paths as shown in FIGURE 3 are
reproduced.

FIGURE 5: The left side shows the distance map of the destination area. Brighter pixels show larger distance. However,
about at half the maximum distance the brightness is set back to zero to better display one distinct equi-distance line. The
right side shows the geometry with two intermediate destination areas added which are shaped along that particular equidistance line with their left side. The exact shape of the right side is not relevant. With these intermediate destination

Kretz, Lehmann, Hofsäss, Leonhardt

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areas the shortest paths of FIGURE 3 are reproduced necessarily and exactly up to the limited precision in the numerical
definition of the intermediate destination areas.}

METHOD FORMULATION
In this section a method will be formulated that computes the geometry of intermediate destination areas
for routes which represent the main routing alternatives for pedestrians.
A note in advance: the method will be proposed here only insofar it is necessary for the concluding
example of application. The complete method includes two more elements to deal with certain more
difficult geometries. As a consequence of the strictly limited extent of this publication we have omitted
these parts. The publication of the full method is currently in preparation (Kretz, Lehmann, & Hofsäss,
2014). The method will be defined and explained visually and not in a mathematical language.
The first step is to compute a distance map for the destination (respectively for all destinations; this option
is implied in the following) for which alternative routes ought to be computed. Next the modulo variant of
this potential as it is displayed in the middle of FIGURE 1 is computed. This is not only a useful
visualization to see the properties of the distance map clearly, but its structure is also an important
element of the method. FIGURE 6 shows for a simple example geometry the same potential for various
modulo values d.
FIGURE 7 shows a modification of FIGURE 6. The gradual color change from black to white has been
omitted. Instead one range from black to white is shown in one and the same color and the next range in a
different one. In this way areas which are within a range of distances to destination are grouped.
The coloring of FIGURE 7 (left and center figure) is the key for the further steps in the method. To be
precise: all regions which share the property of the magenta colored region have to be identified. These
are regions, which are unique for their range of distances to destination, but which have two unconnected
regions directly neighbored which are closer to the destination than they are.
Relevant origin positions of a pedestrian in a simulation of the scenario of FIGURE 7 are the light and
dark orange and the magenta regions as well as the light and dark cyan regions which are further away
from the destination than the magenta area. If a pedestrian's origin position is on a cyan area which is
closer to the destination than the closest orange area no route alternatives are generated.

Dynamic Assignment in Microsimulations of Pedestrians
FIGURE 6: One potential displayed with three different modulo values d. The ratio of the modulo values of the middle
and the left display is 2, the one of the right vs. the left one is 8. The destination is colored as black and green
checkerboard, diagonal red lines on white ground depict an obstacle.

FIGURE 7: The destination is shown as green and black checkerboard, an obstacle is colored with diagonal red lines on
white ground. Light and dark cyan mark regions which are simply connected and which lie within a range of distances to
destination and which have exactly one simply connected area as direct neighbor which is closer to destination. Light and
dark orange mark regions where there is more than one (here: exactly two) unconnected (split by an obstacle) regions
which are within a range of distances to destination. The magenta region is simply connected and has more than one
(here: exactly two) directly neighboring areas which are closer to destination than the magenta region is itself.

In almost all simulation models of pedestrian dynamics the base direction is set into the direction of the
shortest path. This implies that it is determined by the origin position if a pedestrian passes the (red)
obstacle to the right or to the left side. If we want to choose freely if a pedestrian passes the obstacle
either to the left or the right side, the magenta region in FIGURE 7 is the critical one. Once a pedestrian
has passed it, the shortest path paradigm will take the pedestrian to the destination.
Therefore the route choice if the obstacle is passed to the left or to the right side is modeled by making the
two light orange regions immediately neighbored to the magenta region intermediate destination areas.
Each of the two is assigned to one route, generating a route choice.
Obviously not only the shape of the additional intermediate destination areas depends on parameter d, but
first and foremost if it exists at all. The right figure of FIGURE 7 shows no additional intermediate
destination areas because the value of parameter d has been chosen too large
The choice of the value of parameter d at first might appear to be arbitrary and its existence therefore as a
major downside of the method. However, simulation models of pedestrian dynamics usually contain
elements to deal with obstacles. These elements work the better -- i.e. they capture a larger share of the
effect of the obstacle -- the smaller the obstacle is. Therefore it is not desired to have a litter box create a
route alternative, but one wants such small obstacles be handled by the operational pedestrian dynamics
model and the value of d should be chosen at least that large that such small objects do not create route
alternatives. Second, for the purpose of computational efficiency and limited computation resources, in
large simulation projects it can be desirable to not consider every existing routing alternative, but only the
major ones. Then one may set the value of parameter d to even larger values to maintain a feasible
simulation project size.

Kretz, Lehmann, Hofsäss, Leonhardt

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The left figure of FIGURE 7 suggests that there is some arbitrariness in selecting the regions which are
directly neighbored to the magenta region as intermediate destination areas. Why not two of the dark
orange or the other two light orange regions? The answer can be found by considering pedestrians who
have an origin position somewhere on the dark orange or light orange regions. It is desired to be able to
also assign such pedestrians a route which leads over an intermediate destination area on the opposite side
of the obstacle. If that intermediate destination area was moved toward the destination, some pedestrians
would approach the intermediate destination from the back side. This implies an unrealistic trajectory and
is therefore not desired. In fact because any intermediate destination area has a finite depth, there can be a
small area where this occurs although the region closest to the magenta region has been made an
intermediate destination area. This problematic region is the larger, the larger the value of parameter d is.
Realizing this it is important to realize as well that only the shape of the front side of an intermediate
destination is relevant. The depth can be reduced to the point that it is still guaranteed that any pedestrian
heading to the intermediate destination does not have to slow down to step on it for at least one time step.
Nevertheless for the remainder of this contribution we will not modify the shape of intermediate
destination areas in this way. The unmodified shape simply gives a clearer impression of the idea.

Multiple Obstacles
If there is more than one obstacle in a scenario the idea presented so far has to be applied recursively.
This is shown in FIGURE 8. The left and middle figure show the initial computation step for and with the
potential. The dark orange regions are identified as intermediate destinations to pass the downstream
obstacle, the light orange regions have the same role for the upstream obstacle. However, the shape of the
upstream regions is computed with respect to the destination. If we want to be able to send pedestrians
without artifacts in their trajectories on routes which lead from an upstream intermediate destination area
to that downstream intermediate area which is more remote respectively, we have to calculate the shape
of the upstream intermediate destination areas with respect to the downstream intermediate destination
areas. For one of the two downstream intermediate destination areas this is demonstrated in the figure on
the right side of FIGURE 8.
The brown region in FIGURE 8 (right side figure) -- the region which is closer to the destination than the
downstream intermediate destination area -- does not only mark the region where pedestrians' origin
positions do not generate routing alternatives. When the map of distances -- the potential -- is computed
beginning at the downstream intermediate destination area, the brown region must not be intruded. It is
therefore treated as if it was an obstacle -- for the computation of routing alternatives, not later in the
simulation. If the brown region was intruded during the computation of the potential short cut paths could
result which would lead to unrealistic movement and thus spoil the intended effect of the method.
FIGURE 9 finally shows all resulting intermediate destination areas and resulting routes. One can see
there that the original route without intermediate destinations is preserved -- it is the route which ends at
the central of the nine destination dots which are depicted in green. Of the nine routes the one to the first
green destination point from bottom, third from bottom and fifth from bottom basically are identical as
they either have no intermediate destination point or if they have they are along the globally shortest path.
Does this imply a problem or an inefficiency for the usage of these routes in an assignment method? It is
surely not a serious problem. Most assignment methods can deal with multiple identical routes. In
realistic networks there are always routes which overlap. Assignment methods have to cope with this.
Identical routes are simply routes which overlap by 100%. Second, we have to note that the answer on the

Dynamic Assignment in Microsimulations of Pedestrians
question which routes are identical depends on the location of the starting area. If the starting area in
FIGURE 9 were in the top corner the route without intermediate destinations were identical to different
routes. It may even happen that this property is different for different sections of a starting area. This
makes clear that only an additional a posteriori analysis under consideration of the starting area can show
which routes could be dropped.

FIGURE 8: Compared to the previous example a second obstacle has been added. Right side figure: Computation of the
upstream intermediate destination areas with respect to one of the downstream intermediate destination areas. The
region where pedestrians' origin positions do not generate route alternatives is shown brown. It is a virtual obstacle into
which in the further recursions of the algorithm not anymore a potential will spread.

FIGURE 9: Shown here are the edge of the destination area (green), the edges of the obstacles (red), the edge of some
origin area (gray), the edges of the downstream intermediate destination areas (cyan and yellow) and the upstream
intermediate destination areas (cyan, yellow, magenta). Upstream and downstream intermediate destination areas which
follow in a sequence on one route are shown in the same color (cyan or yellow). Furthermore this figure shows the routes

Kretz, Lehmann, Hofsäss, Leonhardt

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in blue. The origin area is marked with a gray dot, the destination area with green dots. All intermediate destination
areas are marked with the color that corresponds to the color of the edge of the area where they are attached. The dots
only mark the area which is an intermediate destination area. Their position on the area has no impact on the movement
of pedestrians in the simulation.

Nested route choices
FIGURE 9 raises the question, if the intermediate destination areas whose edges are colored magenta
could be dropped together with their routes. Obviously the two routes do not actually add an alternative
path choice. So is it sufficient to always just consider that routing alternative which is currently closest to
destination (in FIGURE 8 marked by the dark orange areas in the lower figure) for further process and
omit any more remote one (the light orange areas in FIGURE 8)?
The answer is``no'' and the reason for this is that there are cases where route alternatives are nested; or in
other words: it cannot necessarily be decided what is ``upstream'' and what ``downstream''. FIGURE 10
demonstrates this with an example. It can -- of course -- always be decided which of two points is
spatially closer to a destination. However, in terms of travel time this is different. One can easily imagine
in the third and fourth figure of FIGURE 10 where there has to be a jamming crowd of pedestrians to
make the indicated path the quickest to destination although it implies and includes a spatial detour.

FIGURE 10: In this example the route choices are nested. The destination is on the right side. The first computation of
the potential (upper left figure) brings up two route alternatives, respectively two local maxima of distance to destination.
These are manifest by the existence of the two regions marked with magenta in the upper right figure. lower figures show
two different possible trajectories (black; from red to green) of pedestrians where the two magenta regions are passed in
different sequence.

EXAMPLE APPLICATION
The geometry of FIGURE 10 but with two additional bottlenecks on the straight connection between
origin and destination is used for a demonstration, see FIGURE 11 for details. With this geometry, these
routes and a demand of 5.000 pedestrians per hour an iterated assignment is carried out using PTV
Viswalk (Kretz, Hengst, & Vortisch, 2008) for all operational aspects. This is by no means required as the
method is very generic and can be combined with various operational models of pedestrian dynamics.

Dynamic Assignment in Microsimulations of Pedestrians
The geometry of this example is comparatively close to a node-link network. Therefore the route choices
can relatively easy be determined “by hand” without the help of the proposed algorithm. Therefore the
choice of this geometry may appear to be not a good coice. However, if one is able to reproduce the
results of the algorithm without any tool, one can confirm that these results make sense. Other examples
with a different focus are published elsewhere (Kretz, Lehmann, & Friderich, 2013) (Kretz, Lehmann, &
Hofsäss, 2013).

FIGURE 11: Example geometry with calculated intermediate destinations (blue) and routes with their IDs (yellow). Note
the bottlenecks along the straight connection between origin (red) and destination (green). From left to right the model
extends over 106 m. The corridors are 4 m wide, respectively 2 m at the two bottlenecks. Note that there are two different
intermediate destinations on the upper arc because one is computed based on the final destination and one based on the
intermediate destination on the lower arc.

As initial distribution we’ve set for once a heavy load on the routes along the globally shortest connection
(routes 1, 3, and 4) and in a second run an equal distribution on all routes. After each iteration step, the
routes with the maximum and the minimum average travel time are selected. Based on the number of
possible routes and the time difference between the maximum and minimum average travel time the load
(i.e. the probability for a pedestrian to choose a route) on the routes with maximum travel time is
decreased and the load on routes with the minimum travel time is increased by the same amount, which is
calculated as
(

)

where δ is a free parameter, which has been set to δ=1.0 for this example. To avoid oscillations a further
reduction factor has been applied if from one iteration to the other the route with smallest travel time has
become the route with longest and the route with longest travel time has become the route with the
smallest travel time. We do not elaborate on these details because the geometric aspects are in the focus
of this paper. For the same reason we have chosen this simple assignment algorithm which only makes
use of the results of the immediately previous iteration’s results instead of making use of all results.
As a side note: in reality pedestrians do not choose their route exclusively based on travel time. One
would rather apply a generalized cost approach. With generalized costs it is possible – at least in principle

Kretz, Lehmann, Hofsäss, Leonhardt

11

– to consider other aspects as ground surface, light conditions, social aspects or landmarks which
presumably lead to observed route choice behavior which obviously are not travel time based, at least not
exclusively (Graessle & Kretz, 2011).We stick here with the simpler idea to base route choice purely on
travel time as the geometrical aspects are the focus of the facing work and a discussion on the details of
the generalized costs would clearly exceed the scope and available extent of this contribution. It needs
furthermore be clear that the results of an iterated assignment approach are not connected to local
conditions at spots and times when pedestrians in reality can and do choose about a route or a part of a
route.
Routes with a value of zero get a small load during simulation to take them into account if they get
effective again in later iteration steps. The average travel time of these routes is only taken into account if
it is the minimum average travel time. The iteration is continued until either only one route remains, the
average travel time on all routes differ only by a predefined value from each other or the number of
iterations exceeds a predetermined value, which was set here to half a second.

Dynamic Assignment in Microsimulations of Pedestrians
FIGURE 12: The upper figure shows the weighted average travel time and the lower figure the weighted standard
deviations of travel times evolve in the course of iterations. The blue line shows the evolution when the initial distribution
is mainly on the globally shortest path and only one percent is assigned to each of the three detouring routes. The red line
shows the evolution when the initial distribution is equal on all routes.

FIGURE 13: The upper figure shows the evolution of route choice ratios for each route and for both cases of initial
distribution (lines for equal distribution are marked with a cross). The figure on the lower right shows the evolution of
travel times for each route over the course of iterations.

FIGURE 13 and FIGURE 13: The upper figure shows the evolution of route choice ratios for each route
and for both cases of initial distribution (lines for equal distribution are marked with a cross). The figure
on the lower right shows the evolution of travel times for each route over the course of iterations.show the
results for an iterated assignment in the geometry of FIGURE 11 with a demand of 16,000 pedestrians per
hour. Travel times for all pedestrians arriving at the destination in the time interval 300..900 sec were
considered. It can be seen that the total average travel time at equilibrium is the same (88.3 sec)

Kretz, Lehmann, Hofsäss, Leonhardt

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independent of the route choice ratios at the first iteration. Similar holds for the route choice ratios of the
three detouring routes 2 (9.9% resp. 10.3%), 5 (14.2% resp. 14.4%) and 6 (0%). However the three routes
1, 3, and 4, which all lead along the globally shortest path, end up with largely different route choice
ratios for different ratios in the initial iteration. However, in sum the route choice ratios do not depend on
the initial ratios. This is shown in FIGURE 14 where the sum of route choice ratios and the average of
travel times of route 1, 3, and 4 are shown next to the ones of routes 2, 5, and 6.
That the route choice ratios on routes 1, 3 and 4 end up differently for different initial values while the
sum is the same is a clear indication that the introduction of the intermediate destination does not have a
significant effect on local movement behavior. Because if it had, the travel times on these three routes
actually would be different and the route choice ratios for the three routes should be mutually different,
but each of them should be identical for different initial ratios. For only if the travel times are identical the
route choice ratios cannot be determined uniquely.

FIGURE 14: Route choice ratio (top) and travel times (bottom) with routes 1, 3, and 4 averaged or added, respectively.

Dynamic Assignment in Microsimulations of Pedestrians

CONCLUSIONS
We have sketched the core of an algorithm that produces routes with intermediate destination areas to be
applied with pedestrian simulation. The routes which are computed mark the most relevant routing
alternatives in any given walking geometry. Having reduced the infinitely many trajectories by which a
pedestrian can move from origin to destination to a small set of routes it is possible to apply iterated
assignment methods to compute the user equilibrium of any given scenario (walking geometry and OD
matrix). We have demonstrated the capability of the approach with an example.
In our opinion it is less questionable that the method can produce good results in arbitrary scenarios in
principle but it rather remains to be shown that the method is computationally feasible also for large scale,
real life planning work.
The proposed method of iterated assignment is not meant to replace earlier one-shot assignment methods
(Pettré, Grillon, & Thalmann, 2007) (Kirik, Yurgel'yan, & Krouglov, 2009) (Kretz, Pedestrian Traffic: on
the Quickest Path, 2009) (Guy, et al., 2010), (Kretz, et al., 2011), (Kemloh Wagoum, Seyfried, & Holl,
2012). One-shot assignment has to build on current information, be it global or local (only what a
pedestrian can perceive in his environment) and instantaneous or with a delay or extrapolation into the
near future. Iterated assignment and the idea of a dynamic equilibrium on the other hand rest on the
assumption that pedestrians have information of the load of the walking geometry (or road network)
throughout the full time of their presence in the system. This includes – for the early phase of their trip –
knowledge of a relatively far future. This can only be justified in situations which repeat similarly on a
regular base. Obviously both modeling approaches have their justification for shares of all possible
planning problems. The question is how to handle scenarios which are a combination of both. One can
easily imagine that scenarios are repeating only approximately and therefore one has to imagine the
system to be near equilibrium but with large shares of pedestrians actively and continuously searching for
better options based on what they perceive currently. The problem is that one-shot and iterated
assignment are not easily compatible. Thus this remains a puzzle for the future. However, we can very
well imagine that the geometric part of this contribution can be combined with a one-shot assignment
approach.

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