Presentation given during the 2016 conference Analysis and Control on Networks: trends and perspectives in Padua, Italy. Presentation provides an engineerings perspective on the various issues with see with the modelling and management of crowds, and some of the new modelling approaches.

2. Crowd Dynamics
& Networks
Engineering perspective on Theory, Modelling and Applications
Prof. dr. Serge Hoogendoorn
2

3. 3
Engineering challenges
for events or regular
situations…
• Can we for a certain event / situation
predict if a safety or throughput
bottleneck occurs?
• Can we develop models & methods to
support organisation, planning and
design?
• Can we develop approaches to real-time
manage large pedestrian flows safely and
efficiently?
Deep knowledge network crowd
dynamics essential to answer these
questions!

4. Pedestrian flow operations…
Simple case example: how long does it take to
evacuate a room?
• Consider a room of N people
• Suppose that the (only) exit has capacity of C Peds/hour
• Use a simple queuing model to compute duration T
• How long does the evacuation take?
• Capacity of the door is very important
• Which factors determine capacity?
4
T =
N
C
N people in area
Door capacity: C
N
C

5. Pedestrian flow operations…
Simple case example: how long does it take to
evacuate a room?
• Wat determines capacity?
• Experimental research on behalf of Dutch Ministry of
Housing
• Experiments under different circumstances and
composition of flow
• Empirical basis to express the capacity of a door (per meter width, per second) as a
function of the considered factors:

6. 6
Increase in friction resulting in arc formation
by increasing pressure from behind (force-
Pedestrian capacity drop and
faster-is-slower effect
• Capacity drop also occurs in pedestrian flow
• Faster = slower effect
• Pedestrian experiments (TU Dresden, TU
Delft) have revealed that outflow reduces
substantially when evacuees try to exit room
as quickly as possible (rushing)
• Capacity reduction is caused by friction and
arc-formation in front of door due to
increased pressure
• Capacity reduction causes severe increases in
evacuation times

7. How old Dutch traditions may actually be of some use…

8. 8
• Real-life situations in (public)
spaces often more complex
• Limited empirical
knowledge on multi-
directional flows motivated
first walker experiments in
2002
• Worldpremiere, many have
followed!
• Resulted in a unique
microscopic dataset
First insights into importance
of self-organisation in
pedestrian flows

9. Fascinating self-organisation
• Example efficient self-organisation dynamic walking lanes in bi-directional flow
• High efficiency in terms of capacity and observed walking speeds
• Experiments by Hermes group show similar results as TU Delft experiments,
but at higher densities
9

10. Fascinating self-organisation
• Relatively small efficiency loss (around
7% capacity reduction), depending on
flow composition (direction split)
• Same applies to crossing flows: self-
organised diagonal patterns turn out to
be very efficient
• Other types of self-organised
phenomena occur as well (e.g. viscous
fingering)
• Phenomena also occur in the field…
10
Bi-directional experiment

11. Studying self-organisation during rock concert Lowlands…
Pedestrian flow operations…
So with this wonderful
self-organisation, why do
we need to worry about
crowds at all?

12. 12
Break-down of efficient self-
organisation
• When conditions become too crowded
(density larger than critical density), efficient
self-organisation ‘breaks down’ causing
• Flow performance (effective capacity)
decreases substantially, potentially causing
more problems as demand stays at same level
• Importance of ‘keeping things flowing’, i.e.
keeping density at subcritical level
maintaining efficient and smooth flow
operations
• Has severe implications on the network level

13. A New Phase in Pedestrian Flow Operations
• When densities become
very large (> 6 P/m2) new
phase emerges coined
turbulence
• Characterised by extreme
high densities and
pressure exerted by the
other pedestrians
• High probabilities of
asphyxiation

14. 14
Intermezzo: The SAIL
tallship event
• Biggest public event in the
Nederland, organised every 5
years since 1975
• Organised around the
IJhaven, Amsterdam
• This time around 600
tallships were sailing in
• Around 2,3 million national
and international visitors
• Modelling support of SAIL
project in planning and by
development of a crowd
management decision
support system

15. Microscopic models for planning purposes
Application of differential game theory: the NOMAD model
• Pedestrians minimise predicted walking cost (effort), due
to straying from intended path, being too close to
others / obstacles and effort, yielding:
• This simplified model is similar to Social Forces model of Helbing
Face validity?
• Model results in reasonable macroscopic flow characteristics (capacity
values and fundamental diagram)
• What about self-organisation?
15
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.
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)
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
◆
Level of anisotropy
reflected by this
parameter
~vi
~v0
i
~ai
~nij
~xi
~xj

16. • Simple model shows
plausible self-
organised phenomena
• Model also shows flow
breakdown in case of
overloading
• Presented model is
however incomplete
as it requires
specification of a
(desired) route…
• General assumption of
cost minimisation
reasonable?
• What does data say?

17. Completing the model?
• The NOMAD / social-forces model requires information about the desired
walking direction
• General assumption is that pedestrians choose path / route that minimises
generalised cost (time or more generally effort or disutility)
• Different studies in pedestrian route choice show how cost definition depends
on walking purpose
• Example: pedestrian route choice during SAIL (can we find a cost definition?)
17
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.
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)
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
◆

18. 18
Route choice
behaviour at
events…
• Study into stated
and revealed
choice behaviour
shows which cost
components are
relevant
• Attributes include
attractions along
route, walking near
water, roadway
width, and
crowdedness
• Dependence on
context is huge!

19. Competing the model: route choice theory
Use of dynamic programming:
• Let W(t,x) denote the minimum cost of getting
from (t,x) to the destination area A
• We can then show that this value function W(t,x)
satisfies the HJB equation
• Optimal velocity follows steepest descent
towards destination A:
• Solution schemes (Fleming & Soner,1993) 0 20 40 60 80
x1-axis (m)
0
20
40
60
x2-axis(m)
16
20
24
28
28
28
28
32
32
32
36
40
40
44
4448
48
48
52
52
52
56
56
60
64
72
@W
@t
= L(t, ~x,~v⇤
) + ~v⇤
· rW +
2
2
W
~v⇤
= rW

20. Competing the model: route choice theory
Numerical approaches (which we will skip…) other than finite differences
• Discretise area using any type of meshing (e.g. triangular mesh, rectangles)
• Interpret mesh as network with nodes and links
• Probability of jumping from to is equal to
• Using these, we can compute the value function by solving the following
controlled stochastic Markovian jump process:
⌦
~x ~y p~v
(~x, ~y) =
t
||~y ~x||
✓
~v ·
~y ~x
||~y ~x||
◆+
W(t, ~x) = inf
~v2
2
4 tL(t,~v, ~x) +
X
~y2
p~v
W(t + t, ~y)
3
5

21. Competing the model: route choice theory
• Approach can be used to solve route
choice problem for generic cost
definitions without pre-specifying
network structure
• Generalisation to destination choice and
activity-scheduling is straightforward
(Hoogendoorn and Bovy, 2004)
• Drawbacks? Approach is
computationally demanding…
• Different heuristics to circumvent issues
proposed in literature…

22. • Application for
planning purposes
(e.g. SAIL)
• Questionable if for
real-time and
optimisation
purposes such a
model would be
useful, e.g. due to
complexity
• Coarser models
proposed so far turn
out to have limited
predictive validity,
and are unable to
reproduce self-
organised patterns

23. Macroscopic modelling
23
Multi-class macroscopic model of Hoogendoorn and Bovy (2004):
• Kinematic wave model for pedestrian flow for each destination d
• Here V is the (multi-class) equilibrium speed; the optimal direction:
• 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 route choice, the model will have unrealistic features
!
γd (t,
!
x) = −
∇Wd (t,
!
x)
|| ∇Wd (t,
!
x)||
∂ρd
∂t
+∇⋅
!
qd = r − s with
!
qd =
!
γd ⋅V(ρ1,...,ρD )
!
qd =
!
γd ⋅ ρd ⋅V(ρ1,...,ρD )

24. Macroscopic modelling
24
Solution? Include a term describing local route / direction choice
Ω
Fig. 1. Considered walking area ⌦
Fig. 2. Numerical experiment showing the impact of only considering global route choice on flow conditions.

25. Modelling for planning and real-time predictions
• NOMAD / Social-forces model as starting point:
• Equilibrium relation stemming from model (ai = 0):
• Interpret density as the ‘probability’ of a pedestrian being present, which gives a macroscopic equilibrium
relation (expected velocity), which equals:
• Combine with conservation of pedestrian equation yields complete model, but numerical integration is
computationally very intensive
25
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.
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)
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 ✓
||~y ~x||
◆ ✓
1 + cos xy(~v)
◆
~y ~x
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)
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)
~v = ~v0
(~x) ⌧A
ZZ
~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:
pedestrian i as influence by opponents j:
(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)
~v = ~v0
(~x) ⌧A
ZZ
~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:
(4) cos xy(~v) =
~v
||~v||
·
~y ~x
||~y ~x||

26. Modelling for planning and real-time predictions
• First-order Taylor series approximation:
yields a closed-form expression for the equilibrium velocity , which is given by the equilibrium
speed and direction:
with:
• Check behaviour of model by looking at isotropic flow ( ) and homogeneous flow
conditions ( )
• Include conservation of pedestrian relation gives a complete model…
26
2 SERGE P. HOOGENDOORN
From this expression, we can find both the equilibrium speed and the equilibrium direc-
tion, which in turn can be used in the macroscopic model.
We can think of approximating this expression, by using the following linear approx-
imation of the density around ~x:
(5) ⇢(t, ~y) = ⇢(t, ~x) + (~y ~x) · r⇢(t, ~x) + O(||~y ~x||2
)
Using this expression into Eq. (3) yields:
(6) ~v = ~v0
(~x) ~↵(~v)⇢(t, ~x) (~v)r⇢(t, ~x)
with ↵(~v) and (~v) defined respectively by:
(7) ~↵(~v) = ⌧A
ZZ
~y2⌦(~x)
exp
✓
||~y ~x||
B
◆ ✓
+ (1 )
1 + cos xy(~v)
2
◆
~y ~x
||~y ~x||
d~y
and
(8) (~v) = ⌧A
ZZ
~y2⌦(~x)
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
them. To this end, we have chosen ~v( ) = V · (cos , sin ), for = 0...2⇡. Fig. 1 shows
FROM MICROSCOPIC TO MACROSCOPIC INTERACTION MODELING 3
Furthermore, we see that for ~↵, we find:
(10) ~↵(~v) = ↵0 ·
~v
||~v||
(Can we determine this directly from the integrals?)
From Eq. (6), with ~v = ~e · V we can derive:
(11) V = ||~v0
0 · r⇢|| ↵0⇢
and
(12) ~e =
~v0
0 · r⇢
V + ↵0⇢
=
~v0
0 · r⇢
||~v0
0 · r⇢||
Note that the direction does not depend on ↵0, which implies that the magnitude of
the density itself has no e↵ect on the direction, while the gradient of the density does
influence the direction.
2.1. Homogeneous flow conditions. Note that in case of homogeneous conditions,
FROM MICROSCOPIC TO MACROSCOPIC INTERACTION MODELING 3
Furthermore, we see that for ~↵, we find:
(10) ~↵(~v) = ↵0 ·
~v
||~v||
(Can we determine this directly from the integrals?)
From Eq. (6), with ~v = ~e · V we can derive:
(11) V = ||~v0
0 · r⇢|| ↵0⇢
and
(12) ~e =
~v0
0 · r⇢
V + ↵0⇢
=
~v0
0 · r⇢
||~v0
0 · r⇢||
Note that the direction does not depend on ↵0, which implies that the magnitude of
the density itself has no e↵ect on the direction, while the gradient of the density does
influence the direction.
2.1. Homogeneous flow conditions. Note that in case of homogeneous conditions,
i.e. r⇢ = ~0, Eq. (11) simplifies to
(13) V = ||~v0|| ↵0⇢ = V 0
↵0⇢
α0 = πτ AB2
(1− λ) and β0 = 2πτ AB3
(1+ λ)
4.1. Analysis of model properties
Let us first take a look at expressions (14) and (15) describing the equilibrium290
speed and direction. Notice first that the direction does not depend on ↵0, which
implies that the magnitude of the density itself has no e↵ect, and that only the
gradient of the density does influence the direction. We will now discuss some
other properties, first by considering a homogeneous flow (r⇢ = ~0), and then
by considering an isotropic flow ( = 1) and an anisotropic flow ( = 0).295
4.1.1. Homogeneous flow conditions
Note that in case of homogeneous conditions, i.e. r⇢ = ~0, Eq. (14) simplifies
sions (14) and (15) describing the equilibrium
at the direction does not depend on ↵0, which
density itself has no e↵ect, and that only the
nce the direction. We will now discuss some
ng a homogeneous flow (r⇢ = ~0), and then
= 1) and an anisotropic flow ( = 0).
ns
us conditions, i.e. r⇢ = ~0, Eq. (14) simplifies
| ↵0⇢ = V 0
↵0⇢ (16)
!
v =
!
e ⋅V

27. Modelling for planning and real-time predictions
• 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
27
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 fa
the global route choice behaviour is determined pre-trip and does not include the impact of changing flow con
that may result in additional costs. To this end, we introduce a local route choice component that reflects add
local cost 'd (e.g. extra delays, discomfort) caused by the prevailing flow conditions. We assume that the
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
specific densities and density gradients. By di↵erentiating between the classes, we can distinguish between loca
costs incurred by interacting with pedestrians in the same class (walking into the same direction), and betwee
interactions. As a result, we have for the flow vector the following expression:
Our base model is defined by using a simple linear speed-density relation U(⇢) = v0·(1 ⇢/⇢jam) = 1.34·(1
We will use = ⌘ = 1 for = d and = ⌘ = 4 otherwise, meaning that the impact of the densities of th
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 th
2. Crossing flow scenario, where the first group of pedestrians is generated on the left, and walks to the righ
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 th
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-dire
pedestrian flow with fixed (global) route choice. The resulting flow operations showed no lateral dispersion of
trians, which appears not realistic since it caused big di↵erences in speeds and travel times for pedestrians t
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 r
that the situation that occurred in case the local route choice model was not included.

28. 28
Macroscopic model
yields plausible results…
• First macroscopic model able to
reproduce self-organised patterns
(lane formation, diagonal stripes)
• Self-organisation breaks downs in
case of overloading
• Continuum model seems to
inherit properties of the
microscopic model underlying it
• Forms solid basis for real-time
prediction module in dashboard
• First trials in model-based
optimisation and use of model for
state-estimation are promising

29. 29
Crowd Management for Events
• Unique pilot with crowd management system
for large scale, outdoor event
• Functional architecture of SAIL 2015 crowd
management systems
• Phase 1 focussed on monitoring and
diagnostics (data collection, number of
visitors, densities, walking speeds,
determining levels of service and potentially
dangerous situations)
• Phase 2 focusses on prediction and decision
support for crowd management measure
deployment (model-based prediction,
intervention decision support)
Data
fusion and
state estimation:
hoe many people
are there and how
fast do they
move?
Social-media
analyser: who are
the visitors and what
are they talking
about?
Bottleneck
inspector: wat
are potential
problem
locations?
State
predictor: what
will the situation
look like in 15
minutes?
Route
estimator:
which routes
are people
using?
Activity
estimator:
what are
people
doing?
Intervening:
do we need to
apply certain
measures and
how?

30. Example dashboard outcomes
• Density estimates based on data fusion by means of
data fusion and filtering (see figure)
• Other examples show volumes and OD flows
• Results used for real-time intervention, but also for
planning of SAIL 2020 (simulation studies)
1988
1881
4760
4958
2202
1435
6172
59994765
4761
4508
3806
3315
2509
1752
3774
4061
2629
1359
2654
2139
1211
1439
2209
1638
2581
31102465
3067
2760
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
11 12 13 14 15 16 17 18 19
dichtheid2(ped/m2)
Work in coming years will
be about use macroscopic
models for real-time
prediction

31. 31
Use of Social Media
data
• Next to traffic data collection,
social media data were
analysed to test its usability for
crowd monitoring
• Example shows Twitter activity
related to Sail and
“Crowdedness”
• In finding correlations between
these data and traffic data,
improvements in state
estimations are foreseen!
Foreign tourists
Residents of Amsterdam

32. Bi-level optimisation
• Find optimal routing / staging
• Formulate bi-level
optimisation problem
combining route choice and
assignment model
• Substantial improvements in
evacuation times!
Optimal routing
problem:
compute W(t,x)
First-order
pedestrian flow
model: compute
ρ(t,x)
ρ(t,x)
v*
(t,x)~v⇤
(t,~x)
⇢(t, ~x)
140
0
250
215
Remaining evacuees
Evacuation duration

33. Network Fundamental Diagram
• Much attention to network-scale models of vehicular
(urban) network traffic
• Proof of existence of Network Fundamental Diagram
• Yokohama example based on GPS data
• Recent work shows
importance of spatial
distribution of density
(g-NFD)
• What about
pedestrian networks?

34. Meta models and Macro Fundamental Diagrams
• NFD also exists for pedestrian networks!
• Example shows relation between accumulation and
production (exit-rates)
• Including spatial density
variation allows deriving
accurate relations
between average network
flow, density and density
variance:
34

35. Closing remarks
• Keeping pedestrian safety and comfort at high levels by means of crowd
management leads to many scientific challenges in data collection, modelling &
simulation, and control & management!
• Development of predictively valid models at microscopic and macroscopic scale,
involving both operations and route choice modelling
• Accurate models to predict phase transitions
• Efficient and accurate numerical solution approaches, in particular for macroscopic
models and for route choice modelling (e.g. via variational theory, Lagrangian
formulation)
• Methods for state estimation, data fusion and (real-time) crowd management
• Involving heterogeneity in behaviour and impacts thereof
35

36. More information?
• Hoogendoorn, S.P., van Wageningen-Kessels, F., Daamen, W., Duives, D.C., Sarvi, M. Continuum theory for pedestrian traffic flow: Local route choice
modelling and its implications (2015) Transportation Research Part C: Emerging Technologies, 59, pp. 183-197.
• Van Wageningen-Kessels, F., Leclercq, L., Daamen, W., Hoogendoorn, S.P. The Lagrangian coordinate system and what it means for two-dimensional
crowd flow models (2016) Physica A: Statistical Mechanics and its Applications, 443, pp. 272-285.
• Hoogendoorn, S.P., Van Wageningen-Kessels, F.L.M., Daamen, W., Duives, D.C. Continuum modelling of pedestrian flows: From microscopic principles to
self-organised macroscopic phenomena (2014) Physica A: Statistical Mechanics and its Applications, 416, pp. 684-694.
• Knoop, V.L., Van Lint, H., Hoogendoorn, S.P. Traffic dynamics: Its impact on the Macroscopic Fundamental Diagram (2015) Physica A: Statistical
Mechanics and its Applications, 438, art. no. 16247, pp. 236-250.
• Campanella, M., Halliday, R., Hoogendoorn, S., Daamen, W. Managing large flows in metro stations: The new year celebration in copacabana (2015) IEEE
Intelligent Transportation Systems Magazine, 7 (1), art. no. 7014395, pp. 103-113.
• Duives, D.C., Daamen, W., Hoogendoorn, S.P. State-of-the-art crowd motion simulation models (2014) Transportation Research Part C: Emerging
Technologies, 37, pp. 193-209.
• Huibregtse, O., Hegyi, A., Hoogendoorn, S. Robust optimization of evacuation instructions, applied to capacity, hazard pattern, demand, and compliance
uncertainty (2011) 2011 International Conference on Networking, Sensing and Control, ICNSC 2011, art. no. 5874936, pp. 335-340.
• Hoogendoorn, S.P., Daamen, W. Microscopic parameter identification of pedestrian models and implications for pedestrian flow modeling (2006)
Transportation Research Record, (1982), pp. 57-64.
• Daamen, W., Hoogendoorn, S.P., Bovy, P.H.L. First-order pedestrian traffic flow theory (2005) Transportation Research Record, (1934), pp. 43-52.
• Hoogendoorn, S.P., Bovy, P.H.L. Pedestrian travel behavior modeling (2005) Networks and Spatial Economics, 5 (2), pp. 193-216.
• Hoogendoorn, S.P., Bovy, P.H.L. Dynamic user-optimal assignment in continuous time and space (2004) Transportation Research Part B: Methodological,
38 (7), pp. 571-592.
36