In this keynote, I discuss 25 years of active mode research performed at Transport & Planning. We discuss the role of data, and the use of game-theory to model active mode traffic. We also show how complex models can be simplified, looking at multi-scale approaches.

1. Prof. Dr. Ir. Serge Hoogendoorn, Delft University of Technology
Active mode Traffic
Science & Engineering
25 years of fascination for pedestrian and bicycle flows…

2. Four reasons to focus on
the active modes…

3. Active modes are wonderfully complex and showcase unexpected dynamics

4. Sustainable urban mobility is impossible without active modes

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

6. We can learn a lot from the active modes and the modelling
and control thereof…

7. Let us take a closer look at these
four themes…

8. Wonderfully complex phenomena
in active mode traffic & transport
Self-organisation, capacity drops, spontaneous break-downs

9. Known phenomena
In pedestrian dynamics
• Pedestrian flow is characterised
by fascinating self-organised
phenomena, including:
• Bi-directional lanes, diagonal stripes
in crossing flows
• Freezing by heating and flow
breakdowns
• Faster is slower effect
• Turbulence
• What about bicycle flows?

10. Controlled experiments
Most comprehensive cycling experiments performed so far
providing novel microscopic and macropscopic insights
Microscopic data (trajectories) for 25 different scenarios,
including bottlenecks, crossings, merges, etc.

11. Capacity of bottlenecks
Study reveals empirical relation between
width w of cycle path and capacity
Characteristics of self-organised staggered
patterns inside bottleneck determine capacity
No clear lane regime but complex interaction
of longitudinal ‘following’ and lateral
distance keeping
*) Fact: capacity bicycle flow is ~8 times higher than a car flow!
C = 1710 + 4248 ⋅ w

12. Bicycle capacity & drop
Via our experiments we established the
capacity drop for bicycle flows
Once queuing occurs (e.g. at intersection),
capacity reduces with 23%
Finding is extremely relevant for cycling
infrastructure and controller design

13. Relevantie onderzoek
lopen en fietsen
Relatie grote maatschappelijke vraagstukken
Societal relevance of
Active Modes
Sustainable modes are essential in achieving true sustainable
mobility in liveable cities

14. The grand societal challenges
Impact on climate change (~20%) Use of scarce resources
Liveability, health, safety
Impacts on equity and
inclusiveness Impacts on scarce space (~25%)
Negative impacts of
mobility are substantial

15. Active modes as a solution to societal issues
Towards mobility that is sustainable, efficient and fair
• Ecological impact of
different modes shows
limited impacts of
active modes
• This holds equally for
the spatial impact
• Taking a network
perspective, the
differences on spatial
impact are even larger!

16. Network size scaling for different modes
Linking city population to network sizes
• Sub-linear growth in infrastructures
size: big cities are more efficient
regarding infrastructure length:
networks become relatively shorter
(except for metros)
• Example: a city with twice as many
inhabitants has on average 89%
more car infrastructure and only
26% more bike paths!
• Relatively limited space taken by
active modes of transportation,
right?
Reggiani, G., et al (2022). A multi-city analysis of bicycle networks (under review)

17. The active modes play an
essential role in making mobility
more sustainable, healthier and
more inclusive…
As a individual mode As access or egress mode In case of transfers

18. Heath impacts? Back to
complexity
Bike ownership negatively correlated with BMI
What about the e-bike?
In collaboration with KIM,
Mathijs de Haas
Lower bicycle ownership
implies higher BMI
Higher e-bike ownership
means higher BMI

19. Proposition 1:
Cycling increases health
True (raise hand) or false (keep hand lowered)

20. Causality?
Using data from different MPN waves
(2013-2018) and advanced statistical
modelling*) reveals complexity of
relations…
• When someone’s BMI gets lower,
they cycle more
• But when people cycling more, this
does not (automatically) lead to a
lower BMI…
*) Random Intercept Crossed-Lagged Panel Model
In collaboration with KIM,
Mathijs de Haas

21. Proposition 2:
E-cycling reduces health
True (raise hand) or false (keep hand lowered)

22. Causality?
Using data from different MPN waves
(2013-2018) and advanced statistical modelling*)
reveals complexity of relations…
• No casual effect found between the use of the
e-bike and the BMI (either direction), but:
• Increase in e-bike use leads to decrease
bicycle use (all trip purposes)
• For work trips we see that increase in e-
bike use leads to decrease in car and
bicycle use
*) Random Intercept Crossed-Lagged Panel Model
In collaboration with KIM,
Mathijs de Haas

23. A bicycle is not a two-wheeled car…
And a pedestrian is not a cyclist who lost his bike…
Due to the urgency to make our societies less car-dependent and more
sustainable, we are in dire need of dedicated theory, models and tools to
support policy making, design, planning, and control to improve walkability
and cyclability
My proposition (2014): science has not yet delivered adequate tools
(empirical insights, theory, models, guidelines)

24. ALLEGRO (2015-2020)
With innovative data to
a new traffic and transportation theory
for pedestrians and bicycles

25. Prof. Dr. Frank Koppelman, somewhere in Boston in 2000
“Transportation science is a research field
that is assumption rich and data poor”

26. Field data collection
Video, WiFi / Bluetooth, Social Data
Revealed preference route choice, wayfinding
Incl. collaboration with MoBike, and The Student H
VR and simulators
Pedestrian way finding through buildings
Short-run and long-run household travel dynamics
MPN longitudinal survey active mode “specials”

27. Data collected via controlled experiements Data collected with our Intelligent Bicycle Path
Stress data collected via FitBits Digitwin TU Campus

28. Traffic Operations
Route Choice
Mode and activity
choice
Wayfinding and
exploring
Control, Planning
and Design tools
and applications

29. Traffic Operations
Active mode traffic
operations theory and
modelling

30. Our aim is to model the behaviour
of an individual cyclist in
interaction with the other cyclists…

31. Game-theoretical micro modelling
Motivation for a game-theoretical approach
Inspired by previous work (pedestrian), we looked into differential game
theory (cooperative, non-cooperative) as a theoretical framework for active
mode operations modelling
The pedestrian model generalised established models (e.g., Social
Forces model) and reproduced most relevant dynamics
Framework is flexible (rules) and and has interpretable parameters

32. Microscopic rider modelling
• Main assumption “cyclist economicus” based on
principle of least effort:
For all available options (accel., changing direction,
do nothing) a cyclist chooses option yielding
smallest predicted effort (distulity)
• The predicted effort is the (weighed) sum of
different effort components (e.g., risk to collide,
cycling too slowly or too fast, straying from
intended path, etc.) - like attributes in utility models
• Rider predicts situation for various control actions

33. How does the ‘mental’ prediction work?
• A rider p predicts how applying control u
(steering , peddling / braking ) affects the
dynamics of her bicycle resulting in a predicted
path (location, speed, direction) for [t,t+T)
• Trivial model respecting basic dynamics:
ω a
Approach is generic: more advanced models can be used!

34. How does the ‘mental’ prediction work?
Path A
Path B
Path C
Destination
Shortest path
Effort component examples:
• Straying from shortest path
• Being too close to other cyclist*)
• Acceleration / braking
• Not adhering to traffic rules…
Possible paths result from candidate
control actions; there are an infinite
number of these paths possible

35. Next to own dynamics, the rider predicts the
behaviour of the other cyclists (the
‘opponents’ in game theoretical terms) - or
pedestrians, e-scooters, cars, etc.

36. 36
Non-cooperative
strategy
• Risk-neutral strategy
• Cyclist assumes that
other cyclists reacts
the same way as her-
of himself
• Nash game
Cooperative strategy
• Risk-prone strategy
• Cyclist assumes that
other cyclists
cooperate to reach a
common objective
• Cooperative game
Demon opponent
strategy
• Risk-averse strategy
• Cyclist assumes that
other cyclists aim to
minimise the distance
between him and the
cyclist
• Princes-demon game
Gavriilidou, A., Yuan, Y., Farah, H., Hoogendoorn, S.P.,
2017. Microscopic cycling behaviour model using
differential game theory. In: Proceedings of Traffic and
Granular Flow 2017.

37. Solving the problem…
• We determine the optimal path - via determining the optimal control trajectory -
by assuming the rider will minimise the predicted effort (or cost), i.e.:
where
• Running cost reflects the different components just discussed
• Computing the optimal control path?
• Minimum Principle of Pontryagin results in necessary conditions
• Basis for IRTA (Iterative Real-time Trajectory Optimization Algorithm)
which provides efficient numerical solutions
(a, ω)*
[t,t+T)
= argminJ(u[t,t+T)) J(u[t,t+T)) =
∫
t+T
t
e−ηs
Lds
L
37
Hoogendoorn, S., Hoogendoorn, R., Wang, M., Daamen, W., 2012. Modeling driver, driver support, and cooperative systems with dynamic optimal control.
Transp. Res. Rec. 2316, 20–30.

38. Overtaking example
• Figure shows results for overtaking
interaction for 5s prediction horizon
Faster cyclist
Current position
Predicted
path [20,25)
Direction

39. Crossing bicycle flow interactions
• Note that there are no traffic rules
implemented (no right of way for either
direction)
• Forms of self-organisations appear, and
flows are efficient (limited capacity loss)
• Self-organisation is affected by relative
cost of braking compared to steering
• Breakdown occurs for higher demand
levels, and is affected by heterogeneity
(freezing by heating)

40. Speed-density relation?
40
v0 ψ = 1
ψ = 0
• Assume cyclist riding in a single file
• Equilibrium: no acceleration, equal
distances d between cyclists
• We can easily determine equilibrium speed
for bicycle p (q > p means q is in front)
• Speed-density diagram looks reasonable for
positive values of anisotropy factor ψ
density (Cycle/m)
ρ = 1/d

41. Outcomes
Does the model provide reasonable results?
• Model behaviour is plausible, yet needs to be further validated using real
data (e.g., for our controlled experiments)
• Impact of behavioural strategies is plausible, data needs to reveal which
strategy best represents cycling behaviour
• Intuitive impact of behavioural parameters
• Easy integration of traffic rules

42. But is this model not too complex
for large scale applications?

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

44. Model simplifications
From micro to macroscopic modelling
• Straightforward derivation of social-forces Helbing (pedestrians) / Gavriilidou
(bicycles) model from Nash-game theoretical model
• Subsequently, social-forces model forms the bases of continuum model,
consisting of:
- Conservation of pedestrian equation (trivial)
- Equation for velocity (speed AND direction) can be derived from SF by careful
interpretation of the density and Taylor series expansion…
⃗
v

45. Derivation of macroscopic model
Because you are always dissappointed when there is not math…
• Social-forces model as starting point:
• Equilibrium relation stemming from model ( ):
• Interpret density as the ‘probability’ of a pedestrian being present, which gives a
macroscopic equilibrium relation (expected velocity), which equals:
ai = 0

46. Derivation of macroscopic model
Because you are always dissappointed when there is not math…
• Taylor series approximation:
yields a closed-form expression for equilibrium velocity , which is given by
the equilibrium speed and direction:
• Speed has two components: density (the denser, the lower the speed) and the
density gradient (when density increases, speed is also lower)
• Direction is trade-off desired dir. and dir. in which density reduces quickest
⃗
v =
⃗
e ⋅ V
V
⃗
e

47. Macroscopic modelling results
Plausible outcomes, difficult numerics
• Model inherits properties from SF model (e.g., lane formation,
diagonal stripes, breakdown at high demands)
Bottleneck experiment SPH model Bi-direction flow experiment

48. 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

49. Active Mode traffic dynamics of networks
Towards the pedestrian MFD
• We can then derive the average flow-
rate for the entire area:
• Here, denotes the spatial variation
of the density:
• Equation shows how the MFD is a
function of the spatial averaged
density and the spatial variation
q
σ2
Area
*) Illustration only: we consider walking pedestrians
Ω
Ωi
ρi

50. Active Mode traffic dynamics of networks
Towards the pedestrian MFD
• Let us simplify our model even further by assuming no influence of the density
gradient on the speed (i.e., ):
• Note: this is exactly the Greenshields FD with
• Let us now consider an area that is made up from small areas
• We assume that for all small areas, the Greenshields FD applies (i.e., flow is a
function of the density in the area )
β0 = 0
α0 = v0
/ρjam
Ω Ωi
ρi Ωi
V = v0
− α0ρ Q = ρ ⋅ V = ρ(v0
− α0ρ)

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

52. Some notes on the MFD…
Uses and misuses…
• MFD (pedestrians / cyclists) relates average flow-rate in (large)
area to space-averaged density and spatial density variation :
• Great tool to describe flow conditions and causes for flow degradation on a network level
• The (factors that determine) the shape helps in determining management schemes (e.g.,
perimeter control, density balancing)
• Not so useful for prediction purposes, unless can be predicted as well which is often
not the case (e.g., depends on applied control) - this also limits control applications
• Other approaches for coarse applications may be more appropriate…
q
ρ σ2
q = Q(ρ) − γ ⋅ σ2
σ2
σ2

53. Use of AI for prediction and risk assessment
Digital Twin for Risk Decision Support
• Using ‘basic’ AI
technology for short-
term prediction (for
operational support)
and 6 day ahead (for
planning) forecasting
• Infusing our domain
knowledge yields
approaches that
better generalise
(Graph-based Neural
Networks)

54. Learning opportunities
Active mode theory as inspiration for other domains

55. Active modes show efficient
interactions and self-organisation + we
have advanced modelling schemes =
applications to other domains?

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

57. Learning from active modes?
Applications to distributed cooperative control
• Capitalise on efficient self-
organisation properties of
pedestrians for distributed control
of autonomous (flying) vehicles
• Example shows distributed control
of drones, revealing self-
organisation in 3D using IRTA
• Provides efficient solution to hard
problem (multi-drone conflict
resolution) for different risk-attitude
strategies

58. • Note 1: Multi-scale approach for pedestrians / bikes
will also carry over to drones / 3D, with similar benefits
and downsides
Learning from active modes?
Applications to distributed cooperative control
• Note 2: failing self-organisation
for high demands will eventually
result in need to intervene
• We are currently developing a
hierarchal control approach to
tackle impact of failing self-
organisation

59. Summary of talk
• Discuss the importance of the active mode via four themes:
- Fascinating complexity
- Societal relevance
- Scientific challenges
- As an inspiration for other applications
• Generic game theory framework
• Multi-scale framework
• Distributed cooperative control schemes for multi-drone conflict resolution