This talk presents a novel microscopic modelling framework for bicycle flow operations. The model does justice to the kinematics of cyclists. Contrary to pedestrians, cyclist are more restricted in their movement. The model approximates these restrictions by considering speed and movement direction and changes therein. Secondly, the model includes different strategies (cooperative, zero-acceleration, demon opponent) in its underlying game-theoretical framework. This allows us to model different attitudes towards risk. The (qualitative) insights gained by application of the model pertain to one-on-one interactions between cyclists and the impact of the strategy assumptions and parameter choices on those interactions as well as on the collective phenomena that occur in the cyclist flow and their sensitivity to parameters (reflecting the extent of the prediction horizon, the level of anisotropy, and the relative importance of keeping the desired path). With respect to the collective phenomena, we look at efficiency and self-organised patterns. We conclude that the model acts in a plausible manner. While we do not aim to show absolute validity, we see that the qualitative behaviour of one-on-one interactions is plausible. We also observe plausible collective patterns, including self-organisation. The latter is not trivial given the fundamental differences in bicycle and pedestrian flow.

2. The “Patatzak”
Trapezium-shaped bicycle lane to provide
more queuing space for bicycles waiting for
traffic light
Why would this work? Do you expect any
issues?
Use the chat to type your answer…

3. The “Patatzak”
Trapezium-shaped bicycle lane to provide
more queuing space for bicycles waiting for
traffic light
From a traffic flow theory perspective, design
was “a stab in the dark”, since design seems
to reduce the capacity of the cycle path…

4. A bicycle is not a two-wheeled car…
And a pedestrian is not a cyclist who lost his bike…
Aiming to make our societies less car-dependent (and during the Covid-19
crisis, PT dependent?), we are in dire need of dedicated theory, models
and tools to support policy making, design, planning, and control to
improve walkability and bikeability of cities
My first proposition: science has not yet delivered the necessary insights
and tools (e.g. empirical insights, theory, models, guidelines)

5. ALLEGRO
ERC Advanced Grant (November 2015)
ALLEGRO provides new behavioural insights, novel theory,
and models for active modes at all behaviour levels
In doing so, we support control, planning and design
by providing these insights, methods and tools

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

7. ALLEGRO
With innOvative data to a new transportation and traffic
theory for pedestrians and bicycles
My second proposition: the science of active mode
mobility has been hampered by a serious lack of data
Innovative data collection is one of ALLEGRO’s
cornerstoner forming the basis of our theory, modeling, etc.

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

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

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

11. Some first results…
Study reveals empirical relation between
width w of cycle path and capacity
Characteristics of staggered patterns (zipper
effect) 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 and
provides explanation why patatzak works…
Why? Use the chat to share some arguments

13. Game-theoretical bicycle traffic model
An application of differential game theory
We see that macroscopic flow characteristics (e.g. capacity of bottleneck,
capacity of intersection) are directly related to the individual behaviour of
cyclists (following, lateral distance keeping, gap acceptance)
Validated models individual behaviour enables assessing different designs
(e.g. de Patatzak), control strategies, etc., before being implemented

14. Medium-Fidelity modelling challenge…
• To come up with a microscopic model (and underlying theory) that can predict
(macroscopic) observed relations (e.g. speed-density) and phenomena for
different situations (e.g. base cases considered in our experiments)
• For pedestrians*), we used differential game theory to model the behaviour
of pedestrians competing for the use of (scarce) space (similar to cyclists)
• Some motivation?
- Behavioural research on active modes from the late Seventies and Eighties
provides us with (a basis for) behavioural theory that could be used as a basis for a
game-theoretical model…
- We know that under specific conditions, differential game theory predicts
occurrence of (meta-) stable equilibrium state, which resemble our self-organised
patterns (staggered patterns in bottleneck, spontaneous group formation)…
14*) Hoogendoorn, S.P., Bovy, P.H.L. Simulation of pedestrian flows by optimal control and differential games (2003) Optimal Control Applications
and Methods, 24 (3), pp. 153-172. Cited 169 times.

15. 15
Example self-organisation in pedestrian flow

16. 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?
16
Example self-organisation in simulation

17. Generalising the concept for cyclists…
Path A
Path B
Path C
• Rider has to choose a
path and speed along
path
• Each choice yields a
certain ‘effort’
• Effort is determined by:
a) moving away from the
desired path; b) driving
too close to other
pedestrians / bicycles
and c) required
acceleration and braking

18. 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)
• When predicting effort, she values and combines
predicted attributes characterising available
options (risk to collide, cycling too slow, straying
from intended path, etc.)
18

19. Six additional behavioural assumptions…
• Cyclist are feedback-oriented,
reconsidering their decisions
based on current situation
• They anticipate behaviour of others
by predicting their walking
behaviour according to non-co-
operative, co-operative strategies,
or ‘demon’ strategies
• Their predicting abilities are limited,
reflected by discounting effort over
time and space
• Cyclist are largely anisotropic in
that react mainly to stimuli in front
of them
• They minimise predicted discounted
effort resulting from: (a) straying
from planned path; (b) vicinity of
other cyclists (+ obstacles); (c)
applying control (= acceleration)
• Cyclists are more evasive
encountering a group than a single
pedestrian
Six behaviouralassumption formthe basis of ourmicroscopic model

20. Mathematical formalisation
• State equation describes ‘mental model’ rider to predict state
where the state describes the positions and velocities of rider p
and her opponents q (e.g. ), and were the control is the longitudinal
acceleration / braking and angular acceleration
• Prediction model describes kinematics of the cyclists, e.g.
• Rider p chooses control (accel.) minimising effort for
⃗u (t) = (a(t), ω(t))
˙x(t) = f(t, x, u) x(tk) = xksubject to
r(t) v(t)x(t)
rp(t) u(t)
˙r = v
[tk, tk + T)
Jp =
Z tk+T
tk
e ⌘s
Lp(s, x(s), u(s))ds + e ⌘(tk+T )
p(tk + T, x(tk + T))
u[tk,tk+T )

21. Using the assumptions to specify model
• Most behavioural assumptions are specified via running cost
where
• We use the following specifications for the running cost components:
Lp(t, ⃗x , ⃗u )
Lp = Lstray
p + Laccel
p + Lprox
p
onsider three different cost elements: cost of applying a certain control
, cost of straying from the desired speed v0 = v0(t,~x) and direction f0 =
nd the cost of being too close to other cyclists.
ntrol costs
e a simple specification of the cost or effort that is incurred by applying
ontrol. For the longitudinal acceleration we assume:
Laccel,v
p =
1
2ca
a2
p (5)
he angular acceleration we assume:
Laccel,f
p =
1
2cw
w2
p (6)
6
4.3.1 Control costs
We will use a simple specification of the cost or effort that is incurred by
a certain control. For the longitudinal acceleration we assume:
Laccel,v
p =
1
2ca
a2
p
while for the angular acceleration we assume:
Laccel,f
p =
1
2cw
w2
p
6
direction path f0(t,~x), which are both functions of time t and space~x.
mplies that the path changes in time and over space (in its most generic
).
p the model mathematically tractable, we again use simple quadratic
s. For the desired speed deviations, we propose the following cost spec-
Lstraying,v0
p =
cv
2
(v0
p v2
p)2
(7)
he angular acceleration we assume:
Lstraying,f0
p =
cf
2
(f0
p f2
p)2
(8)
oximity cost
ximity cost, we use the following basic specifications:
Lprox
p = Â e rrp/R0
p
✓
yp +(1 yp)
1+cosqqp
2
◆
(9)
To keep the model mathematically tractable, we again use simple
expressions. For the desired speed deviations, we propose the following
ification:
Lstraying,v0
p =
cv
2
(v0
p v2
p)2
while for the angular acceleration we assume:
Lstraying,f0
p =
cf
2
(f0
p f2
p)2
4.3.3 Proximity cost
For the proximity cost, we use the following basic specifications:
Lprox
p = Â
q2Q
e rrp/R0
p
✓
yp +(1 yp)
1+cosqqp
2
◆
with
cosq = cos(f b ) = cos(f )·cos(b )+sin(f )·sin(b
expressions. For the desired speed deviations, we propose the following cost spec-
ification:
Lstraying,v0
p =
cv
2
(v0
p v2
p)2
(7)
while for the angular acceleration we assume:
Lstraying,f0
p =
cf
2
(f0
p f2
p)2
(8)
4.3.3 Proximity cost
For the proximity cost, we use the following basic specifications:
Lprox
p = Â
q2Q
e rrp/R0
p
✓
yp +(1 yp)
1+cosqqp
2
◆
(9)
with
cosqqp = cos(fp bqp) = cos(fp)·cos(bpq)+sin(fp)·sin(bpq) (10)

22. Using the assumptions to specify model
• Most behavioural assumptions are specified via running cost
where
• We use the following specifications for the running cost components:
Lp(t, ⃗x , ⃗u )
Lp = Lstray
p + Laccel
p + Lprox
p
4.3.1 Control costs
We will use a simple specification of the cost or effort that is incurred by
a certain control. For the longitudinal acceleration we assume:
Laccel,v
p =
1
2ca
a2
p
while for the angular acceleration we assume:
Laccel,f
p =
1
2cw
w2
p
6
To keep the model mathematically tractable, we again use simple
expressions. For the desired speed deviations, we propose the following
ification:
Lstraying,v0
p =
cv
2
(v0
p v2
p)2
while for the angular acceleration we assume:
Lstraying,f0
p =
cf
2
(f0
p f2
p)2
4.3.3 Proximity cost
For the proximity cost, we use the following basic specifications:
Lprox
p = Â
q2Q
e rrp/R0
p
✓
yp +(1 yp)
1+cosqqp
2
◆
with
cosq = cos(f b ) = cos(f )·cos(b )+sin(f )·sin(b
expressions. For the desired speed deviations, we propose the following cost spec-
ification:
Lstraying,v0
p =
cv
2
(v0
p v2
p)2
(7)
while for the angular acceleration we assume:
Lstraying,f0
p =
cf
2
(f0
p f2
p)2
(8)
4.3.3 Proximity cost
For the proximity cost, we use the following basic specifications:
Lprox
p = Â
q2Q
e rrp/R0
p
✓
yp +(1 yp)
1+cosqqp
2
◆
(9)
with
cosqqp = cos(fp bqp) = cos(fp)·cos(bpq)+sin(fp)·sin(bpq) (10)
Acceleration cost describe the cost of
applying the control acceleration in
movement direction
direction path f0(t,~x), which are both functions of time t and space~x.
mplies that the path changes in time and over space (in its most generic
).
p the model mathematically tractable, we again use simple quadratic
s. For the desired speed deviations, we propose the following cost spec-
Lstraying,v0
p =
cv
2
(v0
p v2
p)2
(7)
he angular acceleration we assume:
Lstraying,f0
p =
cf
2
(f0
p f2
p)2
(8)
oximity cost
ximity cost, we use the following basic specifications:
Lprox
p = Â e rrp/R0
p
✓
yp +(1 yp)
1+cosqqp
2
◆
(9)
Straying cost describe the impact of
not walking in the desired direction
and at the desired speed
onsider three different cost elements: cost of applying a certain control
, cost of straying from the desired speed v0 = v0(t,~x) and direction f0 =
nd the cost of being too close to other cyclists.
ntrol costs
e a simple specification of the cost or effort that is incurred by applying
ontrol. For the longitudinal acceleration we assume:
Laccel,v
p =
1
2ca
a2
p (5)
he angular acceleration we assume:
Laccel,f
p =
1
2cw
w2
p (6)
6

23. Using the assumptions to specify model
• Most behavioural assumptions are specified via running cost
where
• We use the following specifications for the running cost components:
Lp(t, ⃗x , ⃗u )
Lp = Lstray
p + Laccel
p + Lprox
p
onsider three different cost elements: cost of applying a certain control
, cost of straying from the desired speed v0 = v0(t,~x) and direction f0 =
nd the cost of being too close to other cyclists.
ntrol costs
e a simple specification of the cost or effort that is incurred by applying
ontrol. For the longitudinal acceleration we assume:
Laccel,v
p =
1
2ca
a2
p (5)
he angular acceleration we assume:
Laccel,f
p =
1
2cw
w2
p (6)
6
4.3.1 Control costs
We will use a simple specification of the cost or effort that is incurred by
a certain control. For the longitudinal acceleration we assume:
Laccel,v
p =
1
2ca
a2
p
while for the angular acceleration we assume:
Laccel,f
p =
1
2cw
w2
p
6
direction path f0(t,~x), which are both functions of time t and space~x.
mplies that the path changes in time and over space (in its most generic
).
p the model mathematically tractable, we again use simple quadratic
s. For the desired speed deviations, we propose the following cost spec-
Lstraying,v0
p =
cv
2
(v0
p v2
p)2
(7)
he angular acceleration we assume:
Lstraying,f0
p =
cf
2
(f0
p f2
p)2
(8)
oximity cost
ximity cost, we use the following basic specifications:
Lprox
p = Â e rrp/R0
p
✓
yp +(1 yp)
1+cosqqp
2
◆
(9)
To keep the model mathematically tractable, we again use simple
expressions. For the desired speed deviations, we propose the following
ification:
Lstraying,v0
p =
cv
2
(v0
p v2
p)2
while for the angular acceleration we assume:
Lstraying,f0
p =
cf
2
(f0
p f2
p)2
4.3.3 Proximity cost
For the proximity cost, we use the following basic specifications:
Lprox
p = Â
q2Q
e rrp/R0
p
✓
yp +(1 yp)
1+cosqqp
2
◆
with
cosq = cos(f b ) = cos(f )·cos(b )+sin(f )·sin(b
Proximity cost shows spatial discounting of
cost impact using distance
Impact of ‘groups’ by
adding proximity
costs over opponents
Anisotropy is reflected
by making cost
dependent on angle ✓pq
p
q
✓pq
rq rp
vp
dpq = ||rq rp||
expressions. For the desired speed deviations, we propose the following cost spec-
ification:
Lstraying,v0
p =
cv
2
(v0
p v2
p)2
(7)
while for the angular acceleration we assume:
Lstraying,f0
p =
cf
2
(f0
p f2
p)2
(8)
4.3.3 Proximity cost
For the proximity cost, we use the following basic specifications:
Lprox
p = Â
q2Q
e rrp/R0
p
✓
yp +(1 yp)
1+cosqqp
2
◆
(9)
with
cosqqp = cos(fp bqp) = cos(fp)·cos(bpq)+sin(fp)·sin(bpq) (10)

24. Solving the problem?
• Problem can be solved using the Minimum Principle of Pontryagin
• Without going into details…
• Define Hamiltonian function:
and use it for necessary conditions for optimality of control signal
• Next to the state equation + initial conditions, we can derive an equation for
the co-states (a.k.a. marginal costs) + terminal condition
and optimality conditions to determine optimal acceleration
24
Hp = e ⌘t
Lp + 0
p · f
u⇤
[tk,tk+T )
˙ p = @Hp/@xp p(tk + T) = @ p/@xand
u⇤
p = arg min H(t, x, u, p)
Standard
application oftextbook optimalcontrol theory

25. Solving the problem…
• Optimality conditions yield:
and
• This shows that:
- The acceleration increases in the marginal cost of the speed is negative
- The angular acceleration increases in the marginal cost of the angular
speed is negative
• Mixed initial / terminal state problem is solved via a newly developed iterative
scheme, which provides solution sufficiently quick from medium-scale
simulations
a*p (t) = − caλv ω*p = − cωλϕ
25
Standard
application oftextbook optimalcontrol theory

26. The strategies…
26
Non-cooperative
strategy
• Risk-neutral strategy
• Cyclist assume that
other cyclists do not
react on expected
proximity of p
• Each cyclist minimise
own effort, conditional
on expected behaviour
of opponents
Cooperative strategy
• Risk-prone strategy
• Cyclist assume that
other cyclists behave
in the same way as
they do
• Each cyclist minimises
own effort, conditional
on expected
behaviour of
opponents
Demon opponent
strategy
• Risk-averse strategy
• Cyclist assume that
other cyclists aim to
minimise the distance
between her and the
cyclist
• Each cyclist minimises
own effort, conditional
on expected behaviour
of opponents

27. Speed-density relation?
27
0 2 4 6
density (P/m)
0
0.5
1
1.5
speed(m/s)
1
speed(m/s)
ve
p = v0
p ⌧pAp
X
q>p
e (q p)d/Rp
X
q<p
e (p q)d/R
!
1
ψ
ψ = 1
ψ = 0
• Assume cyclist riding in a single file
• Equilibrium: no acceleration, equal
distances R between cyclists
• We can easily determine equilibrium speed
for bicycle q (q > p means q is in front)
• Speed-density diagram looks reasonable
for positive values of anisotropy factor
density (Cycle/m)ρ = 1/d

28. Overtaking example
-4-2 0 2 4
x-position (m)
-5
0
5
10
15
20
y-postion(m)
tk
= 8
-4-2 0 2 4
x-position (m)
-5
0
5
10
15
20
y-postion(m)
tk
= 10
-4-2 0 2 4
x-position (m)
-5
0
5
10
15
20
y-postion(m)
tk
= 12
-4-2 0 2 4
x-position (m)
-5
0
5
10
15
20
y-postion(m)
tk
= 14
-4-2 0 2 4
x-position (m)
-5
0
5
10
15
20
y-postion(m)
tk
= 16
-4-2 0 2 4
x-position (m)
-5
0
5
10
15
20
y-postion(m)
tk
= 18
-4-2 0 2 4
x-position (m)
-5
0
5
10
15
20
y-postion(m)
tk
= 20
-4-2 0 2 4
x-position (m)
-5
0
5
10
15
20
y-postion(m)
tk
= 22
-4-2 0 2 4
x-position (m)
-5
0
5
10
15
20
y-postion(m)
tk
= 24
-4-2 0 2 4
x-position (m)
-5
0
5
10
15
20
y-postion(m)
tk
= 26
-4-2 0 2 4
x-position (m)
-5
0
5
10
15
20
y-postion(m)
tk
= 28
-4-2 0 2 4
x-position (m)
-5
0
5
10
15
20
y-postion(m)
tk
= 30
Figure 3: Example of model behavior for overtaking for T = 5s.
this scenario assumes full anisotropy, the overtaken cyclist does not respond while
being overtaken.
• Figure shows results for overtaking
interaction for 5 s prediction horizon
-4-2 0 2 4
x-position (m)
-5
0
-4-2 0 2 4
x-position (m)
-5
0
-4-2 0 2 4
x-position (m)
-5
0
-4-2 0 2 4
x-position (m)
-5
0
-4-2 0 2 4
x-position (m)
-5
0
-4-2 0 2 4
x-position (m)
-5
0
-4-2 0 2 4
x-position (m)
-5
0
5
10
15
20
y-postion(m)
tk
= 20
-4-2 0 2 4
x-position (m)
-5
0
5
10
15
20
y-postion(m)
tk
= 22
-4-2 0 2 4
x-position (m)
-5
0
5
10
15
20
y-postion(m)
tk
= 24
-4-2 0 2 4
x-position (m)
-5
0
5
10
15
20
y-postion(m)
tk
= 26
-4-2 0 2 4
x-position (m)
-5
0
5
10
15
20
y-postion(m)
tk
= 28
-4-2 0 2 4
x-position (m)
-5
0
5
10
15
20
y-postion(m)
tk
= 30
Figure 3: Example of model behavior for overtaking for T = 5s.
Faster cyclist
Current position
Predicted
path [20,25)
Direction

29. Overtaking example
• Tabels shows impacts of different
choices on model behaviour, were is
the prediction horizon, and are
weights of straying from the desired
speed and direction respectively,
describes preference for overtaking on
left, etc.
• Parameter sensitive is as expected (also
from studying the animations)
• Increased prediction horizon yields
improved individual performance
T
cϕ cv
dθ0
the slow cyclist in front.
Table 2: Impact of prediction horizon on speed and distance
Scenario E(v1) E(v2) min(d) (in m)
Base case 1.1210 0.9647 1.4255
T = 1.0 1.0911 0.9529 0.7982
T = 2.5 1.0962 0.9646 1.1780
T = 10.0 1.1759 0.9630 1.540
c0
f = 0.1 1.1653 0.9357 1.7036
c0
f = 5 0.9977 0.9353 1.4093
c0
v = 0.1 0.9367 0.8915 1.7360
y = 1 1.1029 1.0560 1.5942
dq0 = 0 1.0117 0.9606 1.4556
5.2.2 Impact of strategy
The previous experiments consider the situation where the considere
Average speed overtaker Average speed overtakee
Min. distance

30. Crossing example
• Also here, table shows that longer
prediction horizon also has a positive
impact on efficiency, while risk
(expressed in minimum distance)
decreases
• Impact of strategy shows impact of
non-cooperation:
• = 0 implies belief that opponent will not
react to actions p
• > 0 implies belief that opponent will try
to get close to p
ζ
ζ
Table 3: Impact of prediction horizon on speed and distance
T (in s) E(v1) E(v2) min(d) (in m)
1.0 0.8961 0.9099 0.7821
2.5 0.8957 0.9330 0.9500
5.0 0.8946 0.9323 1.0492
10.0 0.8881 0.9337 1.1971
c0
f = 0.1 0.9284 0.9190 1.3136
c0
f = 5 0.8719 0.9358 1.0780
c0
v = 0.1 0.8619 0.7471 1.2544
z = 0.8 0.9407 0.9121 1.4392
z = 0 0.8967 0.9412 1.2169
5.3.2 Impact of strategy
The previous experiments consider the situation where the considered cyc
sumes that the opponent follows the same strategy as she does. That me
the opponent effectively cooperates. Fig. 7 shows the results for the hea
teraction case if we consider the demon opponent strategy with z = 0.8, a
that both cyclists use this strategy. From the figure, we see that both cycli
a larger circumventing movement to ensure that the opponent will not b
cause a crash. In the end, the minimum distance is much larger than in
-5 0 5
x-position (m)
-5
0
5
y-postion(m)
tk
= 6
-5 0 5
x-position (m)
-5
0
5
y-postion(m)
tk
= 7
-5 0 5
x-position (m)
-5
0
5
y-postion(m)
tk
= 8
-5 0 5
x-position (m)
-5
0
5
y-postion(m)
tk
= 9
-5 0 5
x-position (m)
-5
0
5
y-postion(m)
tk
= 10
-5 0 5
x-position (m)
-5
0
5
y-postion(m)
tk
= 11
-5 0 5
x-position (m)
-5
0
5
y-postion(m)
tk
= 12
-5 0 5
x-position (m)
-5
0
5
y-postion(m)
tk
= 13
-5 0 5
x-position (m)
-5
0
5
y-postion(m)
tk
= 14
-5 0 5
x-position (m)
-5
0
5
y-postion(m)
tk
= 15
-5 0 5
x-position (m)
-5
0
5
y-postion(m)
tk
= 16
-5 0 5
x-position (m)
-5
0
5
y-postion(m)
tk
= 17

31. Crossing flow example
• Figure shows crossing bicycle flow
interactions
• Note that there are no traffic rules
implemented (no right of way for
either direction)
• Forms of self-organisations appear,
flows are relatively efficient
• Counter-intuitive impact prediction
horizon (larger prediction horizon
yields reduced efficiency)
Figure 10: Example of model behaviour for crossing flow for multiple cyclists for
T = 2.5s.
Fig. 10 shows the behaviour in case of a crossing flow for a number of one-
second consecutive time steps. The figure shows a form of self-organisation. Look-

32. Crossing flow example
• Counter-intuitive impact prediction
horizon (larger prediction horizon
yields reduced efficiency)
• More research is needed to see why
efficiency reduces:
- Large distances between all cyclists
- Grouping still occurs, by it appears
harder to cross the other flow
- Flow becomes less efficient
• What else is next?
Figure 12: Example of model behavior for crossing flow for multiple cyclists for
T = 2.5s and c0
f = 0.1.
can be clearly observed from the figure. The overall efficiency is slightly increased,

33. Next steps
• Model calibration using microscopic data for
experiments and from the field using 3D camera’s using
experience with model identification proces from our
vehicular traffic*) and pedestrian research
• Interpret parameters and parameter variation, validation
• Study cycling behaviour for different contexts, including
Covid-19 (e.g. for ped behaviour inside Utrecht station)
• Use identified parameter values
• Look which strategy best represents behaviour
(demon interaction, cooperative interaction, non-
cooperative interactions)
0 1 2 3 4 5
Afstand d tussen voetgangers (m)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Kansafstand<d
= 0.25
= 0.5
= 0.75
= 1
= 1.5
= 0.44
*) Hoogendoorn, S.P., Hoogendoorn, R.G. Calibration of microscopic traffic-flow models using multiple data sources
(2010) Philosophical Transactions of the Royal Society A, 368 (1928), pp. 4497-4517. Cited 41 times.

34. Example 3D camera footage
3D camera provides depth information making it easier to track objects

35. Q&A
Science has not yet delivered the necessary insights and tools (e.g. empirical insights,
theory, models, guidelines)
The science of active mode mobility has been hampered by a serious lack of data
The ALLEGRO team has been successfully working on solving both gaps