Talk given at the kick-off of the ERC MAGnUM PhD week on the ALLEGRO program. The talk gives both an overview of ALLEGRO and then focusses more on active mode traffic operations.

1. unrAvelLing sLow modE
travelinG and tRaffic
With innOvative data to a new transportation and traffic
theory for pedestrians and bicycles
1

2. The battle for urban space
With increased densification of cities, where can we find the space for
performing those functions that the city was actually built for?
It is clear that active modes can play a major role in making cities liveable!
Car
50 km/h, driver only
Car
Parked
Tram
50 passangers
Cyclist
15 km/h
Bicycle
Parked
Pedestrian
Walking
Pedestrian
Standing140 m2
20 m2
7 m2
5 m2
2 m2
2 m2
0.5 m2

3. Towards greener, healthier, more liveable cities…
How active mode friendly is your city?
What makes people in
your city walk or cycle (or
not!) instead of using car
Can pedestrians and
cyclists find their way
easily through the city?
Can your city / transfer
hub deal with large
numbers of people?
Is your active mode
infrastructure (roads,
control) well designed?

4. Our central proposition…
Science has not yet delivered adequate tools (empirical insights, theory,
models, guidelines) to support planners, designers, and traffic managers…
The ‘science of active mode mobility’ has been hampered by lack of data!

5. Unique large-scale cycling experiments (pilot)
Large-scale experiment in May 2018 in AHOY
Revealed preference route choice data
Collaboration with MoBike, and The Student Hotel
Innovations in data collection for active modes
Active mode monitoring dashboard incl. Social Data
Short-run and long-run household travel dynamics
MPN longitudinal survey active mode “specials”

6. Active Mode
UML
Engineering
Applications
Transportation & Traffic Theory
for Active Modes in Cities
Data collection
and fusion toolbox
Social-media
data analytics
AM-UML app
Simulation
platform
Walking and
Cycling
Behaviour
Traffic Flow
Operations
Route and Mode
Choice and
Scheduling Theory
Planning anddesign guidelines
Organisation of
large-scale
events
Data Insights
Tools
Models Impacts
Network Knowledge Acquisition (learning)
Factors
determining
route choice
Real-timepersonalised
guidance

7. Active Mode
UML
Engineering
Applications
Transportation & Traffic Theory
for Active Modes in Cities
Data collection
and fusion toolbox
Social-media
data analytics
AM-UML app
Simulation
platform
Walking and
Cycling
Behaviour
Traffic Flow
Operations
Route and Mode
Choice and
Scheduling Theory
Planning anddesign guidelines
Organisation of
large-scale
events
Data Insights
Tools
Models Impacts
Network Knowledge Acquisition (learning)
Factors
determining
route choice
Real-timepersonalised
guidance

8. Active Mode Physics
Data, phenomena, modelling and solutions
Prof. dr. Serge Hoogendoorn
8

9. Complexity of pedestrian flow

10. An average cycling day in Amsterdam…
Understanding and
modelling require
access to data…
Which techniques
are available?

11. Advanced SP and Simulators
Field observations
Controlled experiments
Social Data Crawling

12. 0
2
4
6
8
10
Effort
ValidityControllability
Field observations Controlled Experiments
Advanced SP and Simulators Social Data Crawling
Trade-offs in data collection
• Selection of data collection
approach is trade-off between
different factors (e.g. effort,
controllability, data validity)
• In general strive for optimal mix
between different data collection
techniques
• Nevertheless, for young research
fields with limited prior knowledge,
advantage of controlled
conditions are compelling…
12
Ease data collection
Controllability Validity

13. Walker and cycling experiments
From experiments to theory and models

14. A bit of theory…
• Pedestrians moving with speed v (in m/s) need space A (in m2) to move
• The faster one walks, the more space one needs:
• Density = number of pedestrians / square meter:
• We can thus express the density as a function of speed:
• Equally, we can express speed as a function of density…
14
A(v) = A0 + γ ⋅ v
ρ = 1/A
ρ = ρ(v) =
1
A(v)
=
1
A0 + γ ⋅ v
ρ

15. • We have:
• Given that speed can
not be larger than
maximum speed,
we can rewrite:
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0.0 1.0 2.0 3.0 4.0 5.0 6.0
Speedv
Density k
A bit of theory…
15
ρ(v) =
1
A0 + γ ⋅ v
ρ(0) =
1
A0
= ρjam
v(ρ) =
{
v0
,
1
γ (
1
ρ
− A0)}
−
ρ

16. F
0
5
10
15
20
25
30
0 200 400 600
Speedv(km/h)
Density k (bike/km)
• Do-It-Yourself bicycle
experiment revealing
fundamental diagram for
bicycle flows
• Single file assumption relaxed
with recently performed
experiments
• Fundamental diagram also
exist for bicycle flows

17. Bi-directional flows
Self-organisation of bi-directional lanes

18. Which fundamental diagram
is bi-directional flow (the
other is uni-directional)?
How many lanes are formed in a bi-directional flow (4 m wide)
3 4
s formed
25 Ped/m2
1 2 3 4
0
0.2
0.4
0.6
Number of lanes formed
Relativefrequency
Density = 0.25 to 0.5 Ped/m2
.75 Ped/m2
0.6
cy
Density = 0.75 to 1 Ped/m2
0 0.2 0.4 0.6 0.8
0.9
1
1.1
1.2
1.3
density (Ped/m2
)
speed(m/s)
1
2
3
4
1 2 3 4
0
0.2
0.4
0.6
Number of lanes formed
Relativefrequency
Density = 0 to 0.25 Ped/m2
1 2 3 4
0
0.2
0.4
0.6
Number of lanes formed
Relativefrequency
Density = 0.25 to 0.5 Ped/m2
1 2 3 4
0
0.2
0.4
0.6
Number of lanes formed
Relativefrequency
Density = 0.5 to 0.75 Ped/m2
1 2 3 4
0
0.2
0.4
0.6
Number of lanes formedRelativefrequency
Density = 0.75 to 1 Ped/m2
Figure (b) shows the data of the bi-
directional flow experiment
Clearly, bi-directional flows are very
efficient!
(a) (b)

19. !19
Example shared-space region
Amsterdam Central Station
Other forms of self-organisation?
Many other forms of self-organisation are found in pedestrian flow
Diagonal stripes in crossing flows, zipper effect in bottlenecks, viscous
fingering when group of pedestrians move through crowd, etc.

20. Self-organisation does not occur under all circumstances
Love Parade Duisburg

21. Understanding by game-theoretic modelling
• Main assumption “pedestrian economicus”
based on principle of least effort:
For all available options (accelerating, changing
direction, do nothing) she chooses option
yielding smallest predicted effort (i.e. predicting
behaviour of others)
• Under specific conditions, the game-theoretic
setting yields emergence of Nash equilibrium
situations in which no pedestrian can
unilaterally improve her situation
21

22. Game-theoretic pedestrian flow model
22
• Considering the following effort or cost components:
- Straying from desired direction and speed
- Walking close to or colliding with other pedestrians
- Frequently slowing down and accelerating
• Using a very simple prediction model for behaviour of others: i
j
Acceleration towards desired velocity Push away from ped j
+ …
1. Introduction
This memo aims at connecting the microscopic modelling principles underlying the
cial-forces model to identify a macroscopic flow model capturing interactions amongst
edestrians. To this end, we use the anisotropic version of the social-forces model pre-
nted by Helbing to derive equilibrium relations for the speed and the direction, given
e desired walking speed and direction, and the speed and direction changes due to
teractions.
2. Microscopic foundations
We start with the anisotropic model of Helbing that describes the acceleration of
edestrian i as influence by opponents j:
) ~ai =
~v0
i ~vi
⌧i
Ai
X
j
exp

Rij
Bi
· ~nij ·
✓
i + (1 i)
1 + cos ij
2
◆
here Rij denotes the distance between pedestrians i and j, ~nij the unit vector pointing
om pedestrian i to j; ij denotes the angle between the direction of i and the postion
j; ~vi denotes the velocity. The other terms are all parameters of the model, that will
⃗n ij
⃗v j
ϕij

23. Characteristics of the simplified model
• Simple model captures macroscopic characteristics of flows well
• Also self-organised phenomena are captured, including dynamic lane formation, formation of diagonal stripes, viscous fingering, etc.
• Does model capture ‘faster is slower effect’?
• If it does not, what would be needed to include it?
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:
• Simplified model is similar to Social Forces model of Helbing
Face validity?
• Model results in reasonable macroscopic flow characteristics
• What about self-organisation?
23
Characteristics of NOMAD
• Simple model captures some
key relations (e.g. speed-
density curve) reasonable well!
• All self-organised
phenomena are captured,
including dynamic lane
formation, formation of
diagonal stripes, viscous
fingering
• Playing around with model
input and parameters allows
us to understand conditions
for self-organisation better

24. Game-theoretic pedestrian flow model
• Breakdown probability demands on many
factors, including:
- Demand levels (see figure)
- Variability in desired walking speeds (see
figure: low (-), medium (-), high (-)
- Variability in physical size (limited)
- Level of anticipation / delayed response
• Calibration reveals substantial heterogeneity
in parameters (and correlation)
• No empirical basis for threshold values
formed motivation for CrowdLimits
experiment @TUDelft in May 2018
1.2 1.4 1.6 1.8 2.01.0
0
1
Demand (P/s)
Breakdownprob.
Parameter Mean CoV
Free speed (m/s) 1.34 0.23
Relaxation time (s) 0.74 0.23
Interaction strength (m/s2) 11.33 0.64
Interaction radius (m) 0.35 0.11
Reaction time (s) 0.28 0.07

25. CrowdLimits
Testing the limits of self-organisation

26. CrowdLimits
Testing the limits of self-organisation

27. Bicycle and mixed flows
Using game theory to model bicycle and mixed flows and
understanding conditions for self-organisation

28. Graphical explanation…
• Data collection for modelling
and capacity estimation
• 25 scenarios (overtaking,
merging, crossing, …)
• Structures in and upstream
b-n determine capacity
• Discovery of capacity drop
phenomenon for cycle flows
Bottleneck width (m)
Capacityflow(cyc/s)

29. Modelling waiting positions
• Capacity and flow operations is determined
by way queue is formed
• Discretisation of area using diamonds
(representing bicycle shape)
• Estimation of discrete choice model to
predict waiting location
• Waiting location choice determined by
various attributes (distance from stop line,
distance to others, distance curb)
• Use approach for other important
processes (waiting passengers on platform)
29

30. Active mode traffic management
Modelling for real-time prediction and control applications

31. Modelling for estimation and prediction
• 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:
31
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)
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
exp
✓
||~y ~x||
◆ ✓
+ (1 )
1 + cos xy(~v)
◆
~y ~x
⇢(t, ~y)d~y
(1) ~ai =
~vi ~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
Microscopic models
are great for off-line
assessment, but too
slow for real-time
applications….
Can we come up with a
macroscopic version?

32. Modelling for estimation and prediction
• Taylor series approximation:
yields a closed-form expression for the equilibrium velocity , which is given by the
equilibrium speed and direction:
• Equilibrium speed V shows that speed reduces with density / density gradient
• Equilibrium direction is function of desired walking direction and density gradient
(pedestrians move away from dense areas)
• Completing model by including ped. conservation:
32
!
v =
!
e ⋅V
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
FROM MICROSCOPIC TO MACROSCOPIC INTERACTION MODELING 3
, we see that for ~↵, we find:
~↵(~v) = ↵0 ·
~v
||~v||
ermine this directly from the integrals?)
(6), with ~v = ~e · V we can derive:
V = ||~v0
0 · r⇢|| ↵0⇢
~e =
~v0
0 · r⇢
V + ↵0⇢
=
~v0
0 · r⇢
||~v0
0 · r⇢||
he direction does not depend on ↵0, which implies that the magnitude of
tself has no e↵ect on the direction, while the gradient of the density does
direction.
FROM MICROSCOPIC TO MACROSCOPIC INTERACTION MODEL
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 t
the density itself has no e↵ect on the direction, while the gradient of
influence the direction.
2.1. Homogeneous flow conditions. Note that in case of homogen
i.e. r⇢ = ~0, Eq. (11) simplifies to
(13) V = ||~v0|| ↵0⇢ = V 0
↵0⇢
and
@⇢
@t
+ r · (⇢ · ~v) = r s
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⃗e

33. 33
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 inherits
properties of the microscopic
model underlying it
• Forms solid basis for real-time
prediction module
• First trials in model-based
optimisation and use of model for
state-estimation are promising

34. Centraal Metro Station
access to concourse gate line escalator
stairway railway line control area (PI)
0 20 40 60 80 100 m
Flurin H¨anseler (TU Delft) 20
Model Predictive Crowd Control (MPCC)
34
• Case: controlling turnstiles in
Amsterdam Central Station
• In the MPCC framework, the
macroscopic model is used
to compute predictions
given the current state and
the control signal
• The controller iteratively
determines the control
signal that optimised the
predicted objective function
Controller: Crowd dynamics
Crowd Dynamics Model
Optimizer
Objective
Function
Demand
Prediction Model
predicted
state
performance
control
signal
estimated
state
predicted
demand
historical
data
timetable,
schedule
optimal
control signal
Controller

35. 1. Monitoring
Microscopic data is collected
via video-based sensors, and
combined with smartcard data
Smart station and MPC
2. Estimation
Based on data, current state is
estimated and used as initial
state for prediction
3. Prediction & optimisation
Optimal control signal is
computed, yield a 10%
decrease in crowding cost

36. GPS tracks
Routes based on Instagram
Crowdedness
Social-media activiteit
Micro-posts related to ‘crowdedness’
From – To relations (WiFi + cam)Socio-demographics (Instagram / Twitter)
0
2000
4000
6000
8000
10000
12000
6 8 10 12 14 16 18
Ruijterkade
In Out Total
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
Dichtheden)Veemkade
dichtheid2(ped/m2)
Scaling up!
• Combination of mixed
datasources (counting
cameras, Wifi, social
data, GPS, apps, etc.)
• Reliable picture of
current situation in at
event site by fusion
of data sources
• Sentiment analysis
• Operational web-
based dashboard
• Development of
efficient models for
prediction

37. Cooperative
Bicycle Control
• Application of model-
based stochastic control
• Optimise trade-off between
missing green phase and
consuming energy for
traffic responsive control
• Inform rider using on-board
device (alt. road-side sign)
• Chance to catch green
phase +65%
• Energy consumption -30%

38. Large scale applications
Monitoring, estimation and prediction and MPC at the city scale
Possibilities of area-based models?

39. Recall: Fundamental Diagram for pedestrians
39
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0.0 1.0 2.0 3.0 4.0 5.0 6.0
Speedv
Density k
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0.0 1.0 2.0 3.0 4.0 5.0 6.0
Flowrateq
Density k
v(ρ) = v0
,
1
γ (
1
ρ
−
1
ρjam )
−
q(ρ) = ρ ⋅ v0
,
1
γ (
1 −
ρ
ρjam )
−
q = ρ ⋅ v
ρ ρ

40. Analytical derivation of P-MFD
• Suppose that we have an area that
we partition into subareas
• For each subarea, flow operations
are described by Greenshields FD:
• Then we can easily show that for the
entire area we have the P-MFD:
• where
denotes the spatial variation in density
Area U U
Ui
qi(t) = Q(⇢i) = v0
⇢i (1 ⇢i/⇢jam)
U
¯q(t) = Q(¯⇢(t)) (v0
/⇢jam) · 2
(t)
2
(t) = 1
m
P
m(⇢i ¯⇢)2
Ui
⇢i(t)
*) Illustration only: we consider walking pedestrians
Also for other FDs, we
can show that the P-
MFD exist! It is given
by the FD with a
correction due to
spatial variation!

41. Multi-scale modelling for large areas
• Coarse modelling of network flow operations, where dynamics
of (sub-)area are described via P-MFD:
where
• Requires specification of spatial variation; preliminary data
analysis points towards:
• Approach is equivalent to macroscopic model presented
before development of multi-scale simulation approach
dni
dt =
P
j fji(t) Fi(ni(t), i(t))
fji(t) = ji(t) · Fj(nj(t), j(t))
(¯⇢, ˙¯⇢) = 0.277 · ¯⇢ 0.039 · ˙¯⇢
n1(t)
n2(t) f21(t)
F1(t)

42. Closing
Relevance for Sustainable Urban Mobility
Need for investing in active mode mobility

43. Closing remarks
• Lecture provided insight into the
physics of active modes (empirics,
modelling, applications) allowing
efficient design and control active
mode infrastructure
• Only part of the puzzle!
• ALLEGRO also provides insight into
why people choice to walk or cycle
(top figure), or to understand which
are the determinants for route
choice (bottom table)
• Predict impact of policy interventions
Determinant Influence
Distance Negative
Distance in
morning peak hour
Negative
(stronger than other moments)
# Intersections / km Negative
% Separate cycle paths No / slightly positive
Overlap of routes Positive
Rain No
Daylight No

44. The battle for urban space
Should NOT a battle of the modes!
Rethinking the optimal mobility mix and the role of active modes
In the end, the key question is: what type of city do you want to live in
and which mobility mix best suits that desire!
Car
50 km/h, driver only
Car
Parked
Tram
50 passangers
Cyclist
15 km/h
Bicycle
Parked
Pedestrian
Walking
Pedestrian
Standing140 m2
20 m2
7 m2
5 m2
2 m2
2 m2
0.5 m2

45. Beyond the autonomous car…