The varying phenomena that characterize a pedestrian flow make it one of the most challenging traffic flow processes to manage and control. In the past three decades, we have started to unravel the science behind the crowd. This has led to some important insights that are not only needed to reproduce, predict, and manage pedestrian flow, but will also provide potential avenues to managing other phenomena. In this talk, we will provide a historic perspective on pedestrian flow theory and crowd management. We show some of the key phenomena that have been observed (in controlled experiments, in the field), and how these phenomena can be explained, used or prevented. We will also highlight some of the recent contributions in the field, including the role of AI, novel monitoring technology, and digital twins. We round up the talk showing how the finding can be generalized. We show how the game-theoretical modeling proposed for pedestrian flow models can form a basis for controlling connected autonomous vehicles. Using various examples, we show how self-organization, omnipresent in pedestrian flow, can inspire decentralized control approaches of other flow processes (e.g., autonomous vessels, drones). We show how approaches to reduce flow breakdown for pedestrian flows can be generalized for other flow processes.

1. Harnassing Crowd
Intelligence…
Prof. Dr. Serge Hoogendoorn
Transport & Planning Department
Transport & Mobility Institute
Delft University of Technology
What crowds
can teach us…

2. Stress testing crowds in CrowdLimits
In June 2018, we tried to establish the limits to self-organization in
pedestrian flows…

3. We did not succeed to
induce a breakdown…

4. Efficient self-organization is not
limited to bi-directional
pedestrian flows…

5. Examples of self-organisation
Formation of diagonal stripes in
crossing flows…
Viscous fingering when standing and
moving pedestrians interact
Efficient multi-direction flow
interactions

6. Massive pedestrian flows
during the Hajj remain efficient…

7. 25 years of fascination for pedestrian and bicycle flows:
Active modes are wonderfully complex and showcase unexpected dynamics

8. But there are other reasons to
focus on active modes…

9. Sustainable urban mobility is impossible without active modes
due to their limited spatial and ecological impact, health impact,
relevance as first / last mile / transfer mode

10. There are major scientific, technological and engineering
challenges to solve, including data collection

11. We can learn a lot from the active modes and the modeling
and control thereof…

12. Can we somehow harnass this
“Crowd Intelligence”?

13. Our first step?
Understand and mathematically
model these efficient
self-organized phenomena…

14. Continuum models
Cellular Automata models
(animation by Prof. Mahmassani)
Social Forces models (and variants)
by Prof. Helbing

15. Instead of borrowing from
traditonal traffic flow theory, we
looked for a model better rooted
in behavioral (game) theory…

16. Pedestrian
Games
Differential games as basis
for pedestrian modeling

17. Our take on pedestrian modeling…
Our behavioral model for pedestrian flow dynamics
• Main assumption “pedestrian economicus” based on
principle of least effort:
From all possible actions (accelerate, decelerate,
changing direction, do nothing) a pedestrian chooses
the action yielding smallest predicted effort (disutility)
• The predicted effort is the (weighed) sum of different
effort components (e.g., walking too close / colliding,
walking too slowly or too fast, straying from intended
path, etc.) - like attributes in utility models

18. How does the predicted effort work?
Path A
Path B
Path C
Destination
Shortest path
Effort component examples:
• Straying from shortest path
• Being too close to other pedestrians
• Accelerating / stopping
• Not adhering to traffic rules…
Possible paths result from candidate
control actions; note: there are an infinite
number of these paths possible

19. Anticipation strategies…
Furthering the behavioral foundation
• A key element in our modeling approach is that we assume that
the ego pedestrian anticipates on the behavior of other pedestrians…
• Research in the Seventies and Eighties have shown that:
• Pedestrians unconsciously communicate via very subtle movements
exchanging their intentions when interacting
• Communication sometimes fails, in particular when pedestrians from
different cultures interact (“reciprocal dance”)
• Our differential game model allows for three different strategies reflecting
different levels of (non-) cooperation

20. Solving the differential game…
Numerical solution scheme
• We determine the optimal acceleration
assuming predicted effort minimization:
⃗
𝑎[","$%)
∗
= arg min 𝐽(𝑢[","$%))
subject to pedestrians’ motion dynamics
• Minimum Principle of Pontryagin
results in necessary conditions, forms
basis for Iterative Real-time Trajectory
Optimization Algorithm (IRTA)
• IRTA computes equilibrium where ego-
pedestrian cannot improve her situation
given assumed reaction of others
4.2 Iterative numerical solution
In this section, we briefly discuss the iterative numerical solution approach.
The algorithm is shown for one prediction period only; the receding horizon
generalization is straightforward and left to the reader. Moreover, for the sake
of simplicity, we have omitted obstacles, and terminal costs.
1. Initialization of control variables (prediction horizon T, time step h);
2. Initialization of parameters (weights, desired speed; relaxation parameter
a, cut-o↵ error eps
3. For each pedestrian, initialization of initial position ~
r(0) and velocities
~
v(0) and target position ~
r1
4. Initialize co-states for the positions ~
⇤r(t) = ~
0 and velocities ~
⇤v(t) = ~
0 for
all t = 0 : t : T
5. While error > eps do
(a) Set ~r(t) = ~
⇤r(t) and ~v(t) = ~
⇤v(t)
(b) For t = 0 : t : T t
i. For i = 1 : n
A. ~
u(t|i) = ~v(t|i)
B. ~
v(t + t|i) = ~
v(t|i) + t · ~
u(t|i)
C. ~
x(t + t|i) = ~
x(t|i) + t · ~
v(t|i)
(c) For t = T : t : t
i. For i = 1 : n
A. Compute desired velocity ~
v0
i (t)
B. ~r(t t|i) = ~r(t|i) + t · d0
P
j6=i e dij /d0
~
nij
C. ~v(t t|i) = ~v(t|i) + t ·
⇣
↵(~
v0
i ~
v(t|i)) + ~r(t|i)
⌘
(d) Relaxation ~
⇤r(t) = (1 a) · ~
⇤r(t) + a · r(t) and ~
⇤v(t) = (1 a) ·
~
⇤v(t) + a · v(t)
(e) error = ||~
⇤ ~||
It is beyond the scope of the paper to analyze the performance of the numer-
ical solution in detail. For illustration purposes, Fig. 1 shows the convergence
properties of the scheme for a one-on-one drone interaction scenario, with a

21. Validation outcomes
• Calibration using ML approach + trajectory data
• Reproduces all coll. self-organized phenomena
• Model yields realistic flow – density relation for a
location (FD) and for an entire network (p-MFD)

22. Multi-scale
modelling
framework
Risk-
neutral
Nash game
Risk-prone
cooperativ
e game
‘Social-
forces’
model
Network-
wide
modelling
MFD
Simplification of
behavioural
assumptions
Assuming
equilibrium and
Taylor series
expansion
Spatial aggregation
under equilibrium
Risk-prone
pedestrian
game
Risk-
averse
demon
game
Continuum
modelling

23. Learning opportunities
Pedestrian flow theory as inspiration for other domains

24. Our proposition:
Game-theoretical approach
can be used as a basis for
decentralized control schemes
inheriting efficient self-organization
characteristics

25. ▪ Use of simple control strategy
Modelling cyclist & pedestrians
Control of connected & autonomous vessels
Lane-free control schemes for CAVs
Generic machinery:
Differential game theory
and dedicated numerical
solution algorithm IRTA
are broadly applicable
Cooperative decentralized schemes for drones

26. Decentralized multi-
drone conflict
resolution
• Prospect of drones in (urban) transport and logistics
depend on our ability to solve complex drone
interaction problems in high density airspace
• Multi-drone conflict resolution is a key challenge!
• Our proposition: use game-theoretical approach
used for pedestrian modeling to formulate and solve
multi-drone conflict resolution, assuming that many
of the self-organization properties carry over to 3D…

27. Game of
Drones*
Differential games as basis for
multi-drone conflict resolution

28. Multi-drone conflict resolution
Path A
Path B
Path C
Destination
Shortest path
Cost component examples:
• Straying from shortest path
• Being too close to the other drones
• Acceleration / braking
• Not adhering to airspace regulation…
Ego-drone can use different strategies that represent
different levels of risk taken by the drone given
sensor and communication accuracy and reliability
Adapted version of IRTA
used as solver

29. Learning from active modes?
Applications to decentralized control

30. Decentralized
multi-
drone
conflict
resolution
• As with
pedestrian
flows, we see
different forms
of self-
organization
• Example shows
formation of
diagonal
patterns in
case of two
crossing drone
flows
Top view Side view 1 Side view 2
y
y
y

31. Decentralized multi-drone conflict resolution
Self-organized drone roundabouts
• Scenario shows patterns drones generate at interaction (center-)point
N=10 N=20

32. Decentralized multi-drone conflict resolution
Self-organized drone roundabouts
N=10 N=20

33. Decentralized multi-drone conflict resolution
Self-organized drone roundabouts
N=20
• Different factors influence self-
organized patterns, including
demand level
• Important factor: desired speed
variability
• Large variation breaks formation
of roundabouts
• Other self-organized patterns are
also influenced by heterogeneity

34. Limits to
self-organization
• Impact of heterogeneity well
known for pedestrian flows:
“freezing by heating” describes
the fact heterogeneity messes
up self organization
• As a result, heterogeneous flows
break down at a lower demand
than homogenous flows
• Shows possible impact of (local)
homogenization to increase
capacity of a bottleneck
1.2 1.4 1.6 1.8 2.0
1.0
0
1
Demand (P/s)
Breakdown
prob.
medium low
high

35. Limits to
self-organization
Higher pressure leads to reduced capacity and longer evacuation times
• Faster-is-slower effect
describes the reduction of
bottleneck capacity due to
increase haste due to arc
formation
• Insight leads to different types
of local interventions to improve
situation (e.g., placing obstacle
in front of door to reduce
pressure, or the ‘polonaise’)

36. Queues at local bottlenecks spill back, possibly causing grid-lock
effects, in turn leading to turbulence and asphyxiation…
When self-organization fails:
Local problems may eventually lead
to deterioration at network level

37. Using insights for design and management
Improved design to
limit crossing flows
prev. spill-back
Inflow reduction by using
gating
Spreading of Pilgrims
using different flows
Remove bottlenecks
in design Testing interventions by simulation
Using our understanding for Management &
Design: Example Grand Mosque

38. Towards effective crowd management
Classify intervention strategies at 3 levels…
INDIVIDUAL
Efficient decentralised strategies
Influencing individual behaviour
BOTTLENECK
Increase bottleneck capacity
Reduce break-down probability
by homogenisation
NETWORK
Reduce inflow into network
Increase network outflow
Spread traffic over network and
separate flows
Increasing traffic demand

39. Similar approach could work for drones!
Three level approach to managing drone traffic operations
INDIVIDUAL
Efficient decentralised strategies
LOCAL
Priority regulations
Speed homogenisation
Control of interacting flows
NETWORK
Schedule inflow into network
Reroute drone flows
Increasing traffic demand

40. But if we understand the
processes so well…
Why does it still go wrong?

41. Lack of accurate
and reliable real-
time datasources
Lack of effective
decision support
tools for real-time
decision making
and planning

42. Data collection
Sensing technology
• Adequate data collection
technologies have become
available only recently
• Still, single datasources
seldom provide complete
picture (spatial coverage,
granularity, bias)
• Acurate / complete
information requires
methods to process, fuse,
and enrich multi-source data
3D camera, BT scanner, and
climate sensor
Mood & stress detection (DCM,
GreshamSmith)
Use of
location-based
services
(Resono)
Social-data
crawler

43. Use of AI for prediction and risk assessment
Digital Twin for Real-Time Decision Support and event planning
• Advanced multi-source
data collection and
effective decision
support come together
in CSM
• XAI technology for data
fusion, short-term and
long-term prediction of
crowdedness
• Future work focusses
on risk assessment
(EMERALDS)

44. Risk assessment is about much
more than crowding…

45. Asphyxiation due to overcrowding Riots during the pandemic
Stabbing incidents after a hot and
crowded day at the beach
Risk of being pushed of platform
(courtesy of J van den Heuvel, NS Stations)

46. Our current work focuses on using
advanced monitoring, data fusion,
XAI, and decision support tools for
advanced predictive risk
assessment

48. Making impact!
Keeping education open
during the pandemic…
• Sensing locations and distances with
wearables and beacons
• Dashboard shows areas of concern:
where do the critical interactions occur?
• Design interventions (floorplans,
circulation strategies, occupancy limits)
• Establish critical interactions between
“bubbles” (groups/classes), so that only
students at risk had to be isolated in
case of infection

49. Main take aways
From Crowd Intelligence to Artifical Crowd Intelligence
• Show how efficient self-organized phenomena in active mode traffic can be
modeled using decentralized schemes, generalizing well-known models
• Show how approaches can be generalized to other problems, including multi-
drone conflict resolution
• Show (limits to) self-organization and how interventions can help improve
• Discuss future steps in decision support using Artificial Crowd Intelligence
Overall, I aimed to show you the importance of sharing knowledge across
domains and not reinventing the wheel!