Presentation about modelling pedestrian flows, given during the symposium "50 years of traffic flow theory" in Portland.

1. Challenges in Pedestrian Flow Modelling
Macroscopic Modeling of Crowds capturing Self-Organisation
Serge Hoogendoorn, Winnie Daamen, Femke van Wageningen-Kessels, and others…

2. Societal Urgency
Examples showing increasing importance of crowd modeling & management
Religious or social gathersings, events, (re-)urbanisaiton, increase use of transit and rail…
• Situations where large crowds gather are
frequent (sports events, religious events,
festivals, etc.); occurrence of
‘spontaneous events’ due to social media
• Transit (in particular train) is becoming
more important leading to overcrowding
of train stations under normal and
exceptional situations (e.g. renovation of
Utrecht Central Station)
• Walking (and cycling) are becoming
more important due to (re-)urbanisation
(strong reduction car-mobility in Dutch
cities)
• When things go wrong, societal impacts
are huge!

3. How can models be used to
support planning, organisation,
design, and control?
• Testing (new) designs of stations,
buildings, stadions, etc.
• Testing evacuation plans for buildings
• Testing crowd management and
control measures and strategies
• Training of crowd managers
• On-line crowd management systems
as part of state estimation and
prediction
Development of valid models
requires good data!!!
Courtesy of Prof. H. Mahmassani
Engineering challenges
Societal urgencies leads to demand for engineering solutions
Importance of Theory and Models for Pedestrian and Crowd Dynamics

4. Understanding Pedestrian Flows
Field observations, controlled experiments, virtual laboratories
Data collection remains a challenge, but many new opportunities arise!

5. Empirical characteristics and relations
• Experimental research capacity values:
• Strong influence of composition of flow
• Importance of geometric factors
Fundamental diagram pedestrian flows
• Relation between density and flow / speed
• Big influence of context!
• Example shows regular FD and FD
determined from Jamarat Bridge
Traffic flow characteristics for pedestrians…
Capacity, fundamental diagram, and influence of context

6. Phenomena in pedestrian flow operations
Fascinating world of pedestrian flow dynamics!
Examples self-organisation
• Self-organisation of dynamic lanes in
bi-directional flow
• Formation of diagonal stripes in
crossing flows
• Viscous fingering in multi-directional
flows
Characteristics:
• Self-organisation yields moderate
reduction of flow efficiency
• Chaotic features, e.g. multiple
‘stable’ patterns may result
• Limits of self-organisation

7. Limits to efficient self-organisation
Overloading causes phase transitions
Examples failing self-organisation
• When conditions become too crowded
efficient self-organisation ‘breaks
down’
• Flow performance (effective
capacity) decreases substantially,
causing cascade effect as demand
stays at same level
• New phases make occur: start-stop
waves, turbulence
Network level characteristics
• Generalised network fundamental
diagram can be sensibly defined for
pedestrian flows!

8. The Modelling Challenge
Reproducing key phenomena in pedestrian dynamics
Towards useful pedestrian flow models…
Challenge is to come up with a model that
can reproduce or predict pedestrian flow
dynamics under a variety of circumstances
and conditions
Inductive approach: when designing a model,
consider the following:
• Which are the key phenomena / characteristics
you need to represent?
• Which theories could be used to represent these
phenomena?
• Which mathematical constructs are applicable
and useful?
• Which representation levels are appropriate
• How to tackle calibration and validation?

9. Pedestrian modelling approaches
Representation and behaviour roles
Examples of micro, meso, and macroscopic pedestrian modelling approaches
Representation:
Behavioural rules:
Individual particles Continuum
Individual behaviour
(predictive)
Microscopic simulation
models (social forces,
CA, NOMAD, etc.)
Gas-kinetic models
(Hoogendoorn, Helbing)
Aggregate behaviour
(descriptive)
Particle discretisation
models (SimPed)
Macroscopic continuum
models (Hughes,
Columbo, Hoogendoorn)
Research emphasis on microscopic simulation models and on walking behaviour

10. 1. Introduction
Example: NOMAD Game Theoretical Model
Interaction modelling by using differential game theory
Or: Pedestrian Economicus as main theoretical assumption…
This memo aims at connecting the microscopic modelling principles underlying the
social-forces model to identify a macroscopic flow model capturing interactions amongst
pedestrians. To this end, we use the anisotropic version of the social-forces model pre-sented
by Helbing to derive equilibrium relations for the speed and the direction, given
the desired walking speed and direction, and the speed and direction changes due to
interactions.
Application of differential game theory:
• Pedestrians minimise predicted walking cost, due
to straying from intended path, being too close to
others / obstacles and effort, yielding ai(t):
Level of anisotropy
reflected by this
parameter
2. Microscopic foundations
We start with the anisotropic model of Helbing that describes the acceleration of
pedestrian i as influence by opponents j:
(1) ~ai =
~v0
i ~vi
⌧i Ai
X
j
exp

Rij
Bi
#
· ~nij ·
✓
#i + (1 #i)
• Simplified model is similar to Social Forces model of Helbing
Face validity?
• Model results in reasonable fundamental diagrams
• What about self-organisation?
1 + cos $ij
2
◆
where Rij denotes the distance between pedestrians i and j, ~nij the unit vector pointing
from pedestrian i to j; $ij denotes the angle between the direction of i and the postion
of j; ~vi denotes the velocity. The other terms are all parameters of the model, ~vi
that ~ai
will
be introduced later.
~xi
In assuming equilibrium conditions, we generally have ~ai = 0. The speed / direction
for which this occurs is given by:
(2) ~vi = ~v0
i ⌧iAi
X
j
exp

Rij
Bi
#
· ~nij ·
✓
#i + (1 #i)
~v0
i
1 + cos $ij
2
◆
~nij
~xj
Let us now make the transition to macroscopic interaction modelling. Let ⇢(t, ~x)

11. Example: NOMAD Game Theoretical Model
Interaction modelling by using differential game theory
Or: Pedestrian Economicus as main theoretical assumption…
Example shows lane formation process for
homogeneous groups...
NOMAD model (like social forces model) captures lane formation
•
Heterogeneity yields
less efficient lane formation (freezing by heating)

12. Example: NOMAD Game Theoretical Model
Interaction modelling by using differential game theory
Or: Pedestrian Economicus as main theoretical assumption…
Is NOMAD able to reproduce breakdown in case of oversaturation?
• Testing NOMAD / Social Forces model using different demand patterns to
investigate if and under which conditions breakdown occurs
• Large impact of population heterogeneity (‘freezing by heating’) + reaction time
Heterogeneity yields
less efficient lane formation (freezing by heating)
*) Work by Xiaoxia Yang, Winnie Daamen, Serge Paul Hoogendoorn, Yao Chen, Hairong Dong
•M ic ro s c o p ic m o de l s h ave b e e n
re l a t i v e l y s uc c e s s f u l , a l t h o u g h
s e ve r a l is s ue s a re s t i l l t o be
t ac k l e d
• Ca l i b ra t i o n a n d v a l i d a t i o n a re
c r i t ic a l i s s ue s t o t a c k le
• I n c l us io n o f c u l t u ra l
d i f fe re n c e s, i m p ac t s o f
wa l k i ng p u r p o s e
•R o u te c h o ic e i n ge ne r a l
re q u i re s m o re at te n t io n !

13. 60
40
20
48
28
44 48
0 20 40 60 80
x1-axis (m)
0
x2-axis (m)
16
20
24
28
28 28
32
32
32
36
40
40
44
48
52
52
52
56
56
60
64
72
Dynamic programming
• NOMAD route choice:
• Let W(t,x) denote minimum
expected cost (travel time)
from (t,x) to destination(s)
• W(t,x) satisfies HJB equation:
−
∂W
∂t
= L(t,
!
x,
!
v0 )+
!
vi
0 =
!γ
!
v0∇W +
0 ⋅V0
σ 2
2
ΔW
where
!γ
0 = −∇W/ ||∇W ||
!γ
0
• Optimal direction
perpendicular to iso-cost curves
• Efficient numerical solution
approaches available…
Completing the Model
Route choice modelling by Stochastic Optimal Control
Optimal routing in continuous time and space…

14. Continuum modelling
Dynamic assignment in continuous time and space
Macroscopic traffic flow modelling…
Multi-class macroscopic model of Hoogendoorn and Bovy (2004)
• Kinematic wave model for pedestrian flow for each destination d
∂ρd
∂t
+∇⋅
!
qd =
!
qd = r − s with
d !γ
!γ
d ⋅ρd ⋅V(ρ1,...,ρD )
d ⋅V(ρ1,...,ρD )
• Here V is the (multi-class) equilibrium speed; the optimal direction:
!γ
d (t,
!
x) = −
∇Wd (t,
!
x)
||∇Wd (t,
!
x) ||
• Stems from minimum cost Wd(t,x) for each (set of) destination(s) d
• Is this a reasonable model?
• No, since there is only pre-determined (global) route choice, the model will have
unrealistic features

15. Ω
Continuum modelling
Dynamic assignment in continuous time and space
Macroscopic traffic flow modelling…
Fig. 1. Considered walking area ⌦
Fig. 2. Numerical experiment showing the impact of only considering global route choice on flow conditions.
Solution? Include a term describing local route / direction choice…

16. social-forces model to identify a macroscopic flow model capturing interactions amongst
pedestrians. To this end, we 2. use Microscopic the anisotropic foundations
version of the social-forces model pre-sented
We start with the anisotropic model of Helbing that describes the acceleration of
Continuum modelling - part 2
Computationally efficient modelling
Connecting microscopic to macroscopic models…
by Helbing to derive equilibrium relations for the speed and the direction, given
pedestrian i as influence by opponents j:
We start with the anisotropic model of Helbing that describes the acceleration of
X

#
· ~nij ·
✓
#i + (1 #i)
◆
the desired walking ~v0
i ~speed vi
and direction, and the speed and direction changes due to
interactions.
Rij
Bi
pedestrian i as influence by opponents j:
⌧i Ai
j
exp
2. Microscopic foundations
(1) ~ai =
1 + cos $ij
2
where Rij denotes the distance between pedestrians i and j, ~nij the unit vector pointing
from pedestrian i to j; $ij denotes the angle between the direction of i and the postion
of j; ~vi denotes the velocity. The other terms are all parameters of the model, that will
be introduced later.
We start with the anisotropic model of Helbing that describes the acceleration of
• NOMAD / Social-forces model as starting point:
pedestrian i as influence by opponents j:
In assuming equilibrium conditions, we generally have ~ai = 0. The speed / direction
(1) ~ai =
~v0
i ~vi
⌧i Ai
X
for which this occurs is given by:
j
exp

Rij
Bi
#
· ~nij ·
✓
#i + (1 #i)
X

Rij
Bi
#
· ~nij ·
✓
#i + (1 #i)
• Equilibrium relation stemming from model (ai = 0):
1 + cos $ij
2
◆
1 + cos $ij
◆
where (2) Rij denotes ~vi = ~v0
the ⌧distance iAi
exp
between pedestrians i and j, ~nij the unit vector pointing
from pedestrian i to i j; $ij denotes the angle between the direction 2
of i and the postion
j
of j; ~vi denotes the velocity. The other terms are all parameters of the model, that will
be Let introduced us now later.
make the transition to macroscopic interaction modelling. Let ⇢(t, ~x)
denote the density, to be interpreted as the probability that a pedestrian is present on
location ~x at time instant t. Let us assume that all parameters are the same for all
pedestrian in the flow, e.g. ⌧i = ⌧ . We then get:
(3)
~v = ~v0(~x) ⌧A
In assuming equilibrium conditions, we generally have ~ai = 0. The speed / direction
• Interpret density as the ‘probability’ of a pedestrian being present, which gives a
for macroscopic which this occurs equilibrium is given relation by:
(expected velocity), which equals:
ZZ
(2) ~vi = ~v0
✓
||~y ~x||
i ⌧iAi
X
j
exp

Rij
Bi
#
· ~nij ·
✓
#i + (1 #i)
1 + cos $ij
◆
~y ~x
||~y ~x||
2
◆
exp
B
◆✓
# + (1 #)
1 + cos $xy(~v)
2
⇢(t, ~y)d~y
Let us now make the transition to macroscopic interaction modelling. Let ⇢(t, ~x)
~y2⌦(~x)
denote Here, ⌦(~the x) density, denotes to the be area interpreted around the as considered the probability point that ~x for a which pedestrian we determine is present the
on
location interactions. ~x at Note time that:
instant t. Let us assume that all parameters are the same for all
pedestrian in the flow, e.g. ⌧i = ⌧ . We then get:
((3)
4) cos $xy(~v) =
• Combine with conservation of pedestrian equation yields complete model, but
numerical integration is computationally very intensive
ZZ
~v
||~v|| ·
~y ~x
||~y ~x|| ✓
◆✓
◆
(1) ~ai =
~v0
i ~vi
⌧i Ai
X
j
exp

Rij
Bi
#
· ~nij ·
✓
#i + (1 #i)
1 + cos $ij
2
◆
where Rij denotes the distance between pedestrians i and j, ~nij the unit vector pointing
from pedestrian i to j; $ij denotes the angle between the direction of i and the postion
of j; ~vi denotes the velocity. The other terms are all parameters of the model, that will
be introduced later.
In assuming equilibrium conditions, we generally have ~ai = 0. The speed / direction
for which this occurs is given by:
(2) ~vi = ~v0
i ⌧iAi
X
j
exp

Rij
Bi
#
· ~nij ·
✓
#i + (1 #i)
1 + cos $ij
2
◆
Let us now make the transition to macroscopic interaction modelling. Let ⇢(t, ~x)
denote the density, to be interpreted as the probability that a pedestrian is present on
location ~x at time instant t. Let us assume that all parameters are the same for all
pedestrian in the flow, e.g. ⌧i = ⌧ . We then get:
(3)
ZZ
~v = ~v0(~x) ⌧A
~y2⌦(~x)
exp
✓
||~y ~x||
B
◆✓
# + (1 #)
1 + cos $xy(~v)
2
◆
~y ~x
||~y ~x||
⇢(t, ~y)d~y
Here, ⌦(~x) denotes the area around the considered point ~x for which we determine the
interactions. Note that:

17. Continuum modelling - part 2
Computationally efficient modelling
Connecting microscopic to macroscopic models…
SERGE P. HOOGENDOORN
FROM MICROSCOPIC TO MACROSCOPIC INTERACTION MODELING Furthermore, we see that for ~↵, we find:
From this expression, we can find both the equilibrium speed and the equilibrium direc-tion,
FROM MICROSCOPIC TO MACROSCOPIC INTERACTION MODELING Furthermore, we see that for ~↵, we find:
which in turn can be used in the macroscopic model.
We can think of approximating this expression, by using the following linear approx-imation
properties
• of Taylor the (10) series density approximation:
around ~x:
~v
~↵(~v) = ↵~↵(~·
v) ~v
= ↵0 0 ·
expressions (14) and ⇢((t, 15) ~y) describing = ⇢(t, ~x) + the (~y equilibrium
− ~x) · r⇢(||~t, v||
~x) + O(||~||~v||
y − ~x||2)
(Can we determine this directly from the integrals?)
Using that we determine yields the this direction expression a From closed-this Eq. does form directly into (not 6), 4.1. expression Eq. with depend Analysis from (~v 3) = yields:
for on ~e the of ↵the V 0, model integrals?)
we which
equilibrium can properties
derive:
velocity , which is
From Eq. given (6), by the with equilibrium ~v = ~e · V speed we can and · derive:
direction:
the density (itself 11) has no ~v e↵= ect, ~v0(~x) and − that ~↵(~v)⇢(only V t, = ~x) ||~the
v0 − − $(~#v)t, ~x)
0 · r⇢(r⇢|| − ↵0⇢
influence the and
direction. We will now discuss some
Note that in case of homogeneous conditions, i.e. r⇢ = ~0, Eq. 290 Let us first take a look at expressions (14) and (15) describing V = ||~v0 − #0 · r⇢|| − ↵0⇢
speed and direction. Notice first that the direction does not depend implies that the magnitude of the density itself has no e↵ect, gradient of the density does influence the direction. We will other properties, first by considering a homogeneous flow (r⇢ 295 ↵(~v) and $(~v) defined respectively by:
considering a homogeneous flow (r⇢ = ~0), and then
(12) ~e =
~↵(~v) = ⌧A
ZZ
($ = 1) and an anisotropic flow ($ = 0).
~y2⌦(~x)
exp
✓
−||~y − ~x||
~v0 − #0 · r⇢
V + ↵0⇢
~v0 B
− #0 · r⇢
V + ↵0⇢
◆✓
=
+ (1 − )
~v0 − #0 · r⇢
||~v0 − #0 · r⇢||
1 + cos 'xy(~v)
~v0 − #0 · r⇢
2
||~v0 − #0 · r⇢||
◆
~y − ~x
||~y − ~x||
d~y
~e =
=
Note that the direction does not depend on ↵0, which implies that the magnitude the density itself has no e↵ect on the direction, while the gradient of the density influence the direction.
α =πτ AB2 (1−λ ) and β= 2πτ AB3(1+λ )
0 0 ||~v0|| − 0 − • with:
• Check behaviour of model by looking at isotropic flow ( ) and homogeneous
flow conditions ( )
• Multi-class generalisation + Godunov scheme numerical approximation
conditions
that the direction does not depend on ↵0, which implies that the magnitude density $(~v) itself = ⌧A
has no e↵ect on the direction, while the gradient of the density influence the direction.
ZZ
by considering an isotropic flow ($ = 1) and an anisotropic flow 4.1.1. Homogeneous flow conditions
homogeneous conditions, i.e. r⇢ = ~0, Eq. (14) simplifies
2.1. Homogeneous flow conditions. Note that in case of homogeneous conditions,
~y2⌦(~x)
i.e. r⇢ = ~0, Eq. (11) simplifies to
exp
✓
−||~y − ~x||
B
◆✓
+ (1 − )
1 + cos 'xy(~v)
2
◆
||~y − ~x||d~y
To investigate the behaviour of these integrals, we have numerically approximated
Homogeneous flow conditions. Note that in case of homogeneous conditions,
v0|| − ↵0⇢ = V 0 − ↵0⇢ (16)
!
v = !
e ⋅V

18. ~qd = ~#d(⇢1, ..., ⇢D, r⇢1, ..., r⇢D) · ⇢d · U(⇢1, ..., ⇢D) 5.1. Introducing the base model and the scenarios
Our base model is defined by using a simple linear speed-density relation U(⇢) = v0 ·(1⇢/⇢jam) = 1.34·(1We will use ! = ⌘ = 1 for = d and ! = ⌘ = 4 otherwise, meaning that the impact of the densities of groups are substantially higher. Finally, in the base model we will only consider the impact of the crowdedness i.e. ↵d = 0.
To test the base model, and the di↵erent variants on it, we will use three scenarios:
1. Unidirectional flow scenario, mostly used to show flow dispersion compared to the example presented in 3.2. In this scenario, pedestrians enter on the left side of the forty by forty meter area and walk towards 2. Continuum modelling - part 2
Computationally efficient modelling
Connecting microscopic to macroscopic models…
Crossing flow scenario, where the first group of pedestrians is generated on the left, and walks to the right, the second group is generated at the bottom of the area, and moves up.
3. Bi-directional flow scenario, where two groups of pedestrians are generated at respectively the left and side of the forty by forty meter area.
In all scenarios, pedestrians are generated on the edges of the area between -5 and 5.
5.2. Impact of local route choice of flow dispersion
Let us first revisit the example presented in section 3.2, shown in Fig. 1. The example considered a uni-directional
pedestrian flow with fixed (global) route choice. The resulting flow operations showed no lateral dispersion which appears not realistic since it caused big di↵erences in speeds and travel times for pedestrians spatially very close.
Including the local choice term 'd causes dispersion in a lateral sense: since pedestrians avoid high density densities will disperse and smooth over the area, see Fig. 3. The resulting flow conditions appear much more that the situation that occurred in case the local route choice model was not included.
• Uni-directional flow situation
• Picture shows differences
between situation without
and with local route choice
for two time instances
• Model introduces ‘lateral
diffusion’ since pedestrians
will look for lower density
areas actively
• Diffusion can be controlled by
choosing parameters
differently
• Model shows plausible
behaviour
Ω
y
y′
Fig. 1. Considered walking area ⌦
Fig. 2. Numerical experiment showing the impact of only considering global route choice on flow conditions.
To remedy these issues, in this paper we put forward a dynamic route choice model, that takes care of the the global route choice behaviour is determined pre-trip and does not include the impact of changing flow conditions
that may result in additional costs. To this end, we introduce a local route choice component that reflects additional
local cost 'd (e.g. extra delays, discomfort) caused by the prevailing flow conditions. We assume that these dependent on the (spatial changes in the) class-specific densities.
In the remainder, we will assume that the local route cost function 'd can be expressed as a function of the densities and density gradients. By di↵erentiating between the classes, we can distinguish between local costs incurred by interacting with pedestrians in the same class (walking into the same direction), and between interactions. As a result, we have for the flow vector the following expression:
Fig. 3. Numerical experiment showing the impact of only considering global route choice on flow conditions. For the simulations, we linear fundamental diagram U(⇢) = v0 ↵0⇢. The simulations where performed using a newly developed Godunov scheme for two dimensional

19. Continuum modelling - part 2
Computationally efficient modelling
Connecting microscopic to macroscopic models…
• Simulation results
also show formation
of diagonal stripes…
• Patterns which are
formed depend on
parameters of models
• In particular, non-equal
impact of own
class and other
classes on diversion
behaviour appears
important

20. demand is very small. The reason is that we considered the average outflow for the entire the start-up period where (0.1 P/m/the s), no outflow self-organised is patterns still zero.
occur: the resulting densities are suciently low implying that there Continuum modelling room to simply pass trough the other flow without the need to form structures to increase ecient interaction.
The figure shows clearly For higher how demands, self-- we organisation part see self-organised 2
and patterns. the failing thereof impacts Until a demand of say 0.18 P/m/the s, we efficiency see diagonal moment Computationally that the demand formation. efficient exceeds However, modelling
0.18 if the P/demand m/s, becomes the outflow too large, / the demand neat self-organisation ratio decreases seen at lower strongly demand seems to fail. We still see forms of self-organisation, where pedestrians walking into a certain direction Also note that between in homogeneous 0.22 P/m/groups s ad that 0.38 move as P/a m/block s, though the demand the other classes. - outflow If the demand relation increases appears further, Connecting microscopic stagnates to macroscopic completely and a full models…
still some self-organised patterns occur that gridlock sometimes results.
leads to (temporary) reasonable 0.38 P/m/s onward, the outflow completely stagnates and a grid-lock situation occurs.
• Whether self-organisation
occurs depends on
demand level
• Low demand levels, no
self-organisation
• Self-organisation fails for
high demands and results
in complete grid-lock (no
outflow)
• Macroscopic model
appears able to
qualitatively reproduce
crowd characteristics!
Demand = 0.15 P/m/s
Demand = 0.10 P/m/s
1
0.8
0.6
0.4
Demand = 0.18 P/m/s Demand = 0.25 P/m/s
0.2
0 0.1 0.2 0.3 0.4 0.5
Fig. 6. Density contour plot (left) and scaled outflow rate (right).
0
demand
outflow / demand
left to right
down to up
Failing self-organisation
Grid-lock
Fig. 7. Density contour plot (left) and scaled outflow rate (right).

21. Continuum modelling - part 2
Computationally efficient modelling
Connecting microscopic to macroscopic models…
• Model seems to reproduce self-organised patterns (e.g. example below shows
lane formation for bi-directional flows)

22. Applications?
Use of macroscopic flow model in optimisation
• Work presented at TRB 2013 proposes optimisation technique to minimise
evacuation times
• Bi-level approach combining optimal routing (HJB equation) and continuum flow
model (presented here)
• Preliminary results are very promising
No redistribution of 5
queues (initial iteration)
x−axis (m)
50
45
40
35
30
y−axis (m)
Densities at t = 25.1 s
5 10 15 20 25 30 35 40 45 50
50
45
40
35
30
25
25
20
20
15
15
10
10
5
5
4.5
4.5
4
3.5
4
3.5
3
3
2.5
2.5
2
2
1.5
1.5
1
1
0.5
0.5
0
x−axis (m)
y−axis (m)
Densities at t = 125.1 s
5 10 15 20 25 30 35 40 45 50
50
45
40
35
30
25
20
15
10
5
5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
45 50
5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
x−axis (m)
y−axis (m)
Densities at t = 125.1 s
5 10 15 20 25 30 35 40 45 50
5
0
Distribution of queues
considering reduced speeds

23. Want to know more? Stay in touch!
• Validation and calibration is a major challenge: need
methodologies, data and information extraction methods
• Specialised models may be needed e.g. for train stations, for
evacuations and for areas where pedestrians interact with vehicles
• Differences between cultures, genders, ages, climates should be
considered
• Route choice models are even less developed than flow models
and therefore also need more attention
• Operations are strongly context dependent as so should the
models! No ‘one size fits all’!
• Professionals should also be considered in our efforts and be
educated n how to use our tools and models and what they can
expect from them and what not