Keynote provided during the Traffic Flow Theory summary meeting in Sydney, focussing on challenges in pedestrian and cycle traffic flow theory.

1. Unravelling Urban
Active Mode Traffic Flows
Challenges in Active Mode Traffic (and Transportation) Theory
Prof. dr. Serge Hoogendoorn
1

2. Important societal trends
• Urbanisation is a global trend: more people live in cities than ever
and the number is expected to grow further
• Keeping cities liveable requires an efficient and green
transportation system, which is less car-centric than many of
current cities
• Opportunities are there: the car is often not the most efficient mode
(in terms of operational speed) at all!
• e-Bikes extend average trip ranges (beyond average of 8 km)

3. Research motivation
• In many cities, mode shifts are very prominent!
• Example shows that walking and cycling as important urban
transport modes in Amsterdam
• Mode shifts go hand in hand with emission reduction (4-12%)!

4. Overcrowded PT hubs causing delays and unsafety
Any downsides?
Bike congestion causing delays and hindrance
Overcrowding during regular situations also due to tourists Overcrowding of streets during events
Theory and models for
pedestrian flow, bicycle
flow and mixed flow is still
immature!

5. Active Mode
UML
Engineering
Applications
Transportation and Traffic Theory
for Active Modes in an Urban Context
Data collection
and fusion toolbox
Social-media
data analytics
AM-UML app
Simulation
platform
Walking and
Cycling
Behaviour
Traffic Flow
Operations
Route Choice and
Activity
Scheduling Theory
Planning anddesign guidelines
Real-time
personalised
guidance
Data Insights
Tools
Models Impacts
Network Knowledge Acquisition (learning)
Factors
determining
route choice
ERC Advanced Grant ALLEGRO
Organisation of
large-scale
events

6. A taste of things to come…
• Large scale data collection
experiment (“fietstelweek”) with
more than 50.000 participants!
• GPS data allows analysing
revealed route choice
behaviour
• Route attributes derived from
GPS data and map-based
information
• First choice model estimates
show importance of build
environment factors next to
distance and delays

7. A taste of things to come…
• Data collection at events (i.c.: Mysteryland)
provides new insights into activity / route choices
• Example: relation route choice and music taste

8. A taste of things to come…
• Capacity estimation of bicycle lanes by
composite headway modelling
• Data collected at bicycle crossing
• Photo finish technique allows collection
of time headways on which composite
headway model can be estimated

9. Why is our knowledge limited?
• Traffic (and Transportation)
theory is an inductive
science
• Importance of data in
development of theory and
models (e.g. Greenshields)
• In particular theory for
active modes has suffered
from the lack of data
• Slowly, this situation is
changing and data is
becoming available…
Understanding transport
begins and ends with data

10. Let’s start with the pedestrians…Understanding Pedestrian Flows
Field observations, controlled experiments, virtual laboratories
Data collection remains a challenge, but many new opportunities arise!

11. Traffic flow characteristics for pedestrians…
Capacity, fundamental diagram, and influence of context
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

12. What happens if peds meet head-on?
• Experiment shows results if two groups of pedestrians in
opposite directions meet head-on
• Results from (at that time) unique controlled walking
experiments held at TU Delft in 2002

13. So, no chaos! Is this generic? Larger-scale experiments show similar results
for higher pedestrian demands…
Self-organisation yieldsvery efficient flowoperations in terms ofspeed and throughput

14. Also for crossing flows we see spontaneous self-
organisation (of diagonal lanes)…
So with this wonderful
self-organisation, why do
we need to worry about
crowds at all?

15. Break-down of
self-organisation
• When conditions become
too crowded, efficient
self-organisation ‘breaks
down’
• Flow performance
decreases substantially,
potentially causing more
problems as demand
stays at same level
• Has severe implications
on the network level
• Importance of ‘keeping
things flowing’
Inflow (Ped/s)
Breakdown
prob.
0
1
1 2
Increasing
heterogeneity

16. A dangerous traffic state!
Failing self-organisation may lead to turbulent pedestrian flows…

17. 17
Prevent blockades by
separating flows in different
directions / use of reservoirs
Distribute traffic over available
infrastructure by means of
guidance or information provision
Increase throughput in
particular at pinch points in
the design…
Limit the inflow (gating) ensuring
that number of pedestrians stays
below critical value!
Using our empirical
knowledge:
Simple Principles
for design & crowd
management
• Use principles in design
and planning
• Developing crowd
management
interventions using
insights in pedestrian flow
characteristics
• Golden rules (solution
directions) provide
directions in which to
think when considering
crowd management
options

18. Engineering the future city.
Planning and
operations: 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

19. A bit of theory…
• We build a mathematical model on hypothesis of the “pedestrian
economicus” assuming that pedestrians aim to minimise predicted
effort (cost) of walking, defined by:
- Straying from desired direction and speed
- Walking close to other pedestrians (irrespective of direction!)
- Frequently slowing down and accelerating
• Pedestrians predict behaviour of others and may communicate
• Pedestrians choose acceleration to minimise predicted cost:
a⇤
p(t) = arg min J = arg min
Z 1
t
exp( ⌘s)Lds
L =
1
2
(~v0
p ~vp(t))2
+ 2
X
q
exp( ||~rq(t) ~rp(t)||/Bp) +
1
2
~a2
p(t)

20. A bit of theory…
• Framework generalises social-forces model under specific
assumptions of cooperation and cost specifications
• Assuming that other pedestrians will not change direction nor
speed yields the (anisotropic) social forces model:
• This model appears to be face valid…
- It gives a reasonable fundamental diagram
- It reproduces different forms of
self-organisations…
his memo aims at connecting the microscopic modelling principles underlyin
al-forces model to identify a macroscopic flow model capturing interactions am
strians. To this end, we use the anisotropic version of the social-forces mode
ed by Helbing to derive equilibrium relations for the speed and the direction,
desired walking speed and direction, and the speed and direction changes d
actions.
2. Microscopic foundations
We start with the anisotropic model of Helbing that describes the accelerati
strian 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
◆
re Rij denotes the distance between pedestrians i and j, ~nij the unit vector po
pedestrian i to j; ij denotes the angle between the direction of i and the po
~vi denotes the velocity. The other terms are all parameters of the model, tha
ntroduced later.
assuming equilibrium conditions, we generally have ~ai = 0. The speed / dire
which this occurs is given by:
~vi = ~v0
i ⌧iAi
X
exp

Rij
· ~nij ·
✓
i + (1 i)
1 + cos ij
◆
~vi
~v0
i
~ai
~nij
~xi
~xj

21. Fundamental diagram and anisotropy
• Consider situation where pedestrians walk in a straight line
behind each other
• Equilibrium: no acceleration, equal distances R between peds
• We can easily determine equilibrium speed for pedestrian i
(distinguishing between pedestrian in front i > j and back)
• Fundamental diagram looks reasonable for positive values of
anisotropy factor
• Example for specific values of A and B
V e
i = V 0
⌧ · A ·
0
@
X
j>i
exp [ (j i)R/B]
X
j<i
exp [ (i j)R/B]
1
A

22. Fundamental diagram and anisotropy
• Equilibrium relation for multiple values of
• Note impact of anisotropy factor on capacity and jam density
V e
i = V 0
⌧ · A ·
0
@
X
j>i
exp [ (j i)R/B]
X
j<i
exp [ (i j)R/B]
1
A
0 2 4 6
density (P/m)
0
0.5
1
1.5
speed(m/s)
0 2 4 6
flow (P/s)
0
2
4
6
8
10
speed(m/s)
= 0
= 1
= 1
= 0.6
= 0.8
= 0.6

23. Self-organisation mathematically modelled…
Lane formation can be reproduced with simple mathematical models…
Model also predicts
breakdown of self-
organisation in case of
overloading the facility

24. • Application for planning purposes (e.g. SAIL)
• Questionable if for real-time and optimisation purposes such a model would be usefuly

25. 25
Towards dynamic
intervention…
• Unique pilot with crowd
management system for large
scale, outdoor event
• Functional architecture of SAIL
2015 crowd management
systems
• System deals with monitoring
and diagnostics (data
collection, number of visitors,
densities, walking speeds,
determining levels of service and
potentially dangerous
situations)
• Future work focusses on
prediction and decision
support for crowd management
measure deployment
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?

26. Example results dashboard
• Development of new measurement
techniques and methods for data
fusion (counting cameras, Wifi
sensors, GPS)
• New algorithms to estimate walking
and occupancy duration
• Many applications since SAIL
(Kingsday, FabCity, Europride)
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

27. Modelling for real-time applications
• 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
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)
0
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||

28. Modelling for real-time applications
• 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…
SERGE P. HOOGENDOORN
m this expression, we can find both the equilibrium speed and the equilibrium
n, which in turn can be used in the macroscopic model.
We can think of approximating this expression, by using the following linear ap
ation of the density around ~x:
⇢(t, ~y) = ⇢(t, ~x) + (~y ~x) · r⇢(t, ~x) + O(||~y ~x||2
)
Using this expression into Eq. (3) yields:
~v = ~v0
(~x) ~↵(~v)⇢(t, ~x) (~v)r⇢(t, ~x)
h ↵(~v) and (~v) defined respectively by:
~↵(~v) = ⌧A
ZZ
~y2⌦(~x)
exp
✓
||~y ~x||
B
◆ ✓
+ (1 )
1 + cos xy(~v)
2
◆
~y ~x
||~y ~x||
d~y
d
(~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 approxim
m. To this end, we have chosen ~v( ) = V ·(cos , sin ), for = 0...2⇡. Fig. 1 s
FROM MICROSCOPIC TO MACROSCOPIC INTERACTION MODELING
ermore, we see that for ~↵, we find:
~↵(~v) = ↵0 ·
~v
||~v||
we determine this directly from the integrals?)
m Eq. (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⇢||
that the direction does not depend on ↵0, which implies that the magnit
ensity itself has no e↵ect on the direction, while the gradient of the densit
nce the direction.
Homogeneous flow conditions. Note that in case of homogeneous cond
FROM MICROSCOPIC TO MACROSCOPIC INTERACTION MODELING
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 ma
the density itself has no e↵ect on the direction, while the gradient of the de
influence the direction.
2.1. Homogeneous flow conditions. Note that in case of homogeneous c
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) describ290
speed and direction. Notice first that the direction does not d
implies that the magnitude of the density itself has no e↵ect
gradient of the density does influence the direction. We wil
other properties, first by considering a homogeneous flow (
by considering an isotropic flow ( = 1) and an anisotropic295
4.1.1. Homogeneous flow conditions
Note that in case of homogeneous conditions, i.e. r⇢ = ~0,
ons (14) and (15) describing the equilibrium
the direction does not depend on ↵0, which
nsity itself has no e↵ect, and that only the
e the direction. We will now discuss some
g a homogeneous flow (r⇢ = ~0), and then
= 1) and an anisotropic flow ( = 0).
conditions, i.e. r⇢ = ~0, Eq. (14) simplifies
↵0⇢ = V 0
↵0⇢ (16)
!
v =
!
e ⋅V

29. 29
Macroscopic model
yields plausible
results…
• First macroscopic model able
to reproduce self-organised
patterns
• Self-organisation breaks
downs in case of overloading
• Continuum model seems to
inherit properties of
microscopic model
underlying it
• Forms basis for real-time
prediction
• First trials in model-based
optimisation and use of
model for state-estimation
are promising

30. What about cyclists and mixed flows?
Is self-organisation also present there?
Cycle behaviour (interaction) experiements…

31. A closer look at self-organisation
• The game-theoretic model allows
studying which factors and
processes affect self-organisation:
- Breakdown probability is directly
related to demand (or density)
- Heterogeneity negatively affects self-
organisation (“freezing by heating”)
- Anisotropy affects self-organisation
negatively
- Cooperation and anticipation improve
self-organisation (see example)
• Let us pick out some examples…

32. Modelling bicycles flows
• Game-theoretical framework can be “relatively easily” generalised
to model behaviour of cyclists
• Main differences entail “physical differences” between pedestrians
and cyclists, implying that we describe cycle acceleration in terms
of longitudinal and angular acceleration:
• Note that we left out the anisotropy terms to keep equation
relatively simple
ap(t) =
v0
v
⌧
Ap
X
q
exp

||~rq(t) ~rp(t)||
Rp
· ~npq(t) · ~ep(t)
!p(t) =
0
(t)
⌧!
+ Cp
X
q
exp

||~rq(t) ~rp(t)||
Rp
· ~npq(t) ⇥ ~ep(t)

33. Next step: calibration and validation
• Model calibration and validation based
on experimental data and data
collected in the field…
• Advanced video analyses software to
get microscopic trajectory data
• First datasets are becoming available…

34. Mixing pedestrian and cycle flows…
• Does self-organisation occur in shared-space contexts? Yes!
• There are some requirements that need to be met!
- Load on facility should not be too high
- Heterogeneity limits self-organisation efficiency
- Works better if there is communication (subconscious?) and
cooperation between traffic participants (pedestrians,
cyclists)
• Real-life example shows that under specific circumstances
shared-space can function efficiently….
• First modelling results show which factors influence self-
organisation (e.g. in case of crossing pedestrian and cycle flows)

35. Successful shared-space implementation
Example shared-space region Amsterdam Central Station

36. Mixing pedestrian and cycle flows…
• Preliminary simulation results
are plausible and self-
organisation occurs under
reasonable conditions
• Assumption: bikes are less
prone to divert from path than
pedestrian
• Interesting outcome:
pedestrian’s anisotropy
improves ‘neatness’ of self-
organised patterns
• Further work focusses on getting a validated bicycle model and see
characteristics of self-organisation (and the limits therein)
• Outcomes will prove essential for sensible design decisions!
-60 -40 -20 0 20 40 60
x (m)
-30
-20
-10
0
10
20
30
y(m)
25 30 35 40 45 50 55 60 65 70 75
time (s)
0
0.5
1efficiency(-)

37. Mixing pedestrian and cycle flows…
• Preliminary simulation results
are plausible and self-
organisation occurs under
reasonable conditions
• Assumption: bikes are less
prone to divert from path than
pedestrian
• Interesting outcome:
pedestrian’s anisotropy
improves ‘neatness’ of self-
organised patterns
-60 -40 -20 0 20 40 60
x (m)
-30
-20
-10
0
10
20
30
y(m)
25 30 35 40 45 50 55 60 65 70 75
time (s)
0
0.5
1efficiency(-)
• Further work focusses on getting a validated bicycle model and see
characteristics of self-organisation (and the limits therein)
• Outcomes will prove essential for sensible design decisions!

38. Closing remarks…
• Presentation provides overview of past and current activities
• Focus on monitoring, modelling (macro and micro), prediction
and intervention and design
• Amongst challenges is understanding interaction between
different modes (pedestrians, cyclists) and understanding level
and need of cooperation / communication
• What about interactions between cars and vulnerable modes?
• What about interactions between automated cars and
vulnerable modes? What are the impacts to design of streets,
crossings, and networks?
• Topic requires more attention!

39. Flow operations for automated bicycles?
The Google bike…
Cycle behaviour (interaction) experiements…