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Unravelling	Urban	Traffic	
Flows
From new insights to advanced solutions… a work in progress

Prof. dr. Serge Hoogendoorn
1
AMSTERDAM INSTITUTE FOR
ADVANCED METROPOLITAN SOLUTIONS
TU DELFT, WAGENINGEN UR, MIT
ACCENTURE, ALLIANDER, AMSTERDAM
SMART CITY, CISCO, CITY OF BOSTON,
ESA, IBM, KPN, SHELL, TNO, WAAG SOCIETY,
WATERNET
CITY METABOLISM: URBAN FLOWS
WATER-ENERGY-WASTE-FOOD-DATA-PEOPLE
2
CIRCULAR
CITY
VITAL CITY
CONNECTED
CITY
Circular economy
Water, energy, food, waste
Smart infrastructures
Urban big data
Internet of Everything
Digital fabrication
Smart mobility
Resilient, clean and healthy
urban environment
Blue-green infrastructures
Social & responsible design
Proposition: using the cityas a living lab to exploreimpact and find possibilitiesof these (and other) trendson mobility and other
sectors…
3
AMSTERDAM INSTITUTE FOR
ADVANCED METROPOLITAN SOLUTIONS
TU DELFT, WAGENINGEN UR, MIT
ACCENTURE, ALLIANDER, AMSTERDAM
SMART CITY, CISCO, CITY OF BOSTON,
ESA, IBM, KPN, SHELL, TNO, WAAG SOCIETY,
WATERNET
AMBITIONS
An internationally renowned, public-private institution in the area
of metropolitan solutions that in 2022 has …
… 200-250 talented students participating in a new MSc …
… 100-150 researchers working on discovering, developing and implementing
metropolitan solutions …
… EUR 25-35 million annual budget for research and valorization …
… 30-50 public and private partners participating ...
… 500-1,000 publications, 10-15 spin-outs and 30-70 start-ups generated
between 2013 and 2022 …
… an excellent position for continued value creation in the next 20 years.
Entering	the	urban	age
• Urbanisation is a global trend: more
people live in cities than ever!

• City regions become focal points of the
world economy in terms of output,
productivity, decision making power,
innovation power

• Requirement for success: internal
connectivity (within city or city region)
and external connectivity (airport,
ports): importance of accessibility
4
Challenges…	
• Accessibility	is	a	major	issue	in	many	
cities	(Amsterdam,	Melbourne)	
• Most	delays	are	experienced	in	cities	
(not	on	freeways!),	yet	freeways	have	
received	much	attention	in	the	past…	
• At	the	same	time,	(re-)	urbanisation	
opens	up	many	new	alleyways	for	
sustainable	mobility	(active	modes,	
seamless	multi-modal	transport,	
shared	mobility,	autonomous	driving)		
• So	what	do	we	see	as	key	themes?
Challenges…	
• Accessibility	is	a	major	issue	in	many	
cities	(Amsterdam,	Melbourne)	
• Most	delays	are	experienced	in	cities	
(not	on	freeways!),	yet	freeways	have	
received	much	attention	in	the	past…	
• At	the	same	time,	(re-)	urbanisation	
opens	up	many	new	alleyways	for	
sustainable	mobility	(active	modes,	
seamless	multi-modal	transport,	
shared	mobility,	autonomous	driving)		
• So	what	do	we	see	as	key	themes?
Relevant	research	domains	for	mobility	theme
Research domains relevant to urban
transportation systems and mobility
involve (but not excluded to):
• Slow (or rather) active traffic modes
(pedestrians, crowds, bikes)

• Coordinated & cooperative traffic control,
management and information

• Automation & self-driving vehicles

• Resilient public transport systems and
sustainable multi-modal transport

• Urban distribution and city logistics
7
Trends	in	mode	share	in	Amsterdam	area
• Since 1990’s car use has been on
the decline in Amsterdam

• Cycling and walking are main
modes of transport in city

• Big impacts on emissions (4-12%
reduction), as well as accessibility
and health

• But these positive trends also has
some negative (but interesting)
impacts…
Side-effects	of	increasing	active	mode	shares…
Bike	congestion	causing	delays	
and	hindrance
Overcrowding	during	events	and	regular	
situations	also	due	to	tourists
Overcrowded	public	transport	hubs
Not-so-seamless	public	transport
Bike	parking	problems	&	orphan	bikes
Bike	congestion	causing	delays	and	
dangerous	behaviour	at	intersections
The	ALLEGRO	programme
unrAvelLing sLow modE travelinG and tRaffic: 

with innOvative data to a new transportation and traffic theory for
pedestrians and bicycles”

• 4.2 million AUD personal grant with a focus on developing theory (from an
application oriented perspective) sponsored by the ERC and AMS

• Relevant elements of the project: 

• Development of components for “living” data & simulation laboratory building on two decades of
experience in pedestrian monitoring, theory and simulation

• Outreach to cities by means of “solution-oriented” projects (“the AMS part”), e.g. event planning
framework, design and crowd management strategies, etc.

• Looking for talented PhD students!
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 Choice and
Activity
Scheduling Theory
Planning anddesign guidelines
Organisation of
large-scale
events
Data Insights
Tools
Models Impacts
Network Knowledge Acquisition (learning)
Factors
determining
route choice
12
Engineering the future city.
Today’s	talk	
• Focus	on	active	modes	
in	particular	on	
pedestrian	and	crowds	
• Use	SAIL	event	as	the	
driving	example	to	
illustrate	various	
concepts	in	monitoring	
and	management	
• SAIL	project	entailed	
development	of	a	crowd	
management	decision	
support	system
13
SAIL?	
• Biggest	(and	free)	
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
14
Engineering	challenges

	for	events	or	regular	
situations…	
• Can	we	for	a	certain	event	predict	if	a	
safety	or	throughput	issue	will	occur?	
• Can	we	develop	methods	to	support	
organisation,	planning	and	design?		
• Can	we	develop	approaches	to	real-time	
manage	large	pedestrian	flows	safely	and	
efficiently?	
• Can	we	ensure	that	all	of	these	are	robust	
agains	unforeseen	circumstances?		
Deep	knowledge	of	crowd	dynamics	is	
essential	to	answer	these	questions!
Pedestrian	flow	operations…
Simple case example: how long does it take to
evacuatie a room?
• Consider a room of N people

• Suppose that the (only) exit has capacity of C Peds/hour

• Use a simple queuing model to compute duration T

• How long does the evacuation take? 

• Capacity of the door is very important

• Which factors determine capacity?
15
T =
N
C
N	people	in	area
Door	capacity:	C
N
C
Pedestrian	flow	operations…
Simple case example: how long does it take to
evacuatie a room?
• Wat determines capacity?

• Experimental research on behalf of Dutch Ministry of
Housing

• Experiments under different circumstances and
composition of flow
• Empirical basis to express the capacity of a door (per meter width, per second) as a
function of the considered factors:
Pedestrian	flow	operations…
Simple case example: how long does it take to
evacuatie a room?
• Wat determines capacity?

• Open door (90 degrees) yields a capacity reduction of 7%

• Detailed analysis of paths (by tracking of) pedestrian
reveals cause
0 1 2 3 4 5 6 7 8
1
2
3
4
5
6 Looprichting
X-positie (in m)
Y
-
p
o
s
i
t
i
e
(
i
n
m
) Walking direction
X-position (in m)
Y-position(inm)
• Pedestrians appear to walk very close together (short headways)
for a very short period of time (only at side where there is no door)

• Importance of detailed research in microscopic behaviour to
understand phenomena…
18
• Insight	in	more	complex	
situations	
• Real-life	situations	in	(public)	
spaces	often	more	complex	
• Limited	empirical	knowledge	
on	multi-directional	flows	
motivated	first	walker	
experiments	in	2002	
• Worldpremiere,	many	have	
followed!	
• Resulted	in	a	unique	
microscopic	dataset	
First	insights	into	importance	
of	self-organisation	in	
pedestrian	flows
Fascinating	self-organisation
• Example efficient self-organisation dynamic walking lanes in bi-directional flow

• High efficiency in terms of capacity and observed walking speeds

• Experiments by Hermes group show similar results as TU Delft experiments,
but at higher densities
19
Fascinating	self-organisation
• Relatively small efficiency loss (around
7% capacity reduction), depending on
flow composition (direction split)

• Same applies to crossing flows: self-
organised diagonal patterns turn out to
be very efficient 

• Other types of self-organised
phenomena occur as well (e.g. viscous
fingering)

• Phenomena also occur in the field…
20
Bi-directional	experiment
Studying	self-organisation	during	rock	concert	Lowlands…
Pedestrian	flow	operations…
So with this wonderful
self-organisation, why do
we need to worry about
crowds at all?
22
Increase	in	friction	resulting	in	arc	formation	
by	increasing	pressure	from	behind	(force-
Pedestrian	capacity	drop	and	
faster-is-slower	effect	
• Capacity	drop	also	occurs	in	pedestrian	flow	
• Faster	=	slower	effect	
• Pedestrian	experiments	(TU	Dresden,	TU	
Delft)	have	revealed	that	outflow	reduces	
substantially	when	evacuees	try	to	exit	room	
as	quickly	as	possible	(rushing)	
• Capacity	reduction	is	caused	by	friction	and	
arc-formation	in	front	of	door	due	to	
increased	pressure		
• Capacity	reduction	causes	severe	increases	in	
evacuation	times	
Intermezzo: given ourunderstanding of thecauses of the faster isslower effect, can youthink of a solution?
How	old	Dutch	traditions	may	actually	be	of	some	use…
24
Break-down	of	efficient	self-	
organisation	
• When	conditions	become	too	crowded	
(density	larger	than	critical	density),	efficient	
self-organisation	‘breaks	down’	causing		
• Flow	performance	(effective	capacity)	
decreases	substantially,	potentially	causing	
more	problems	as	demand	stays	at	same	level		
• Importance	of	‘keeping	things	flowing’,	i.e.	
keeping	density	at	subcritical	level	
maintaining	efficient	and	smooth	flow	
operations	
• Has	severe	implications	on	the	network	level
A	New	Phase	in	Pedestrian	Flow	Operations
• When densities become
very large (> 6 P/m2) new
phase emerges coined
turbulence

• Characterised by extreme
high densities and
pressure exerted by the
other pedestrians

• High probabilities of
asphyxiation
Why	crowd	management	is	necessary!
Efficient	self-
organisation
Faster	=	slower	
effect
Blockades	and	
turbulence
“There	are	serious	limitations	to	the	self-organising	abilities

of	pedestrian	flow	operations”
Reduced	production	of	pedestrian	network
Why	crowd	management	is	necessary!
• Pedestrian Network Fundamental Diagram shows
relation between number of pedestrians in area

• P-NFD shows reduced performance of network
flow operations in case

of overloading causes by

various phenomena such

as faster-is-slower effect

and self-organisation

breaking down

• Current work focusses on

theory of P-NFD
27
28
Crowd	Management	for	Events	
• Unique	pilot	with	crowd	management	system	
for	large	scale,	outdoor	event	 	
• Functional	architecture	of	SAIL	2015	crowd	
management	systems	
• Phase	1	focussed	on	monitoring	and	
diagnostics	(data	collection,	number	of	
visitors,	densities,	walking	speeds,	
determining	levels	of	service	and	potentially	
dangerous	situations)		
• Phase	2	focusses	on	prediction	and	decision	
support	for	crowd	management	measure	
deployment	(model-based	prediction,	
intervention	decision	support)
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?
Tracking	SAIL	visitors	using	GPS	devices
Central	Station
Walking	and	choice	behaviour	of	SAIL	visitors

on	the	22nd	of	August
Veemkade
Sumatrakade
Example	dashboard	outcomes
• Newly developed algorithm to distinguish between
occupancy time and walking time

• Other examples show volumes and OD flows 

• Results used for real-time intervention, but also for
planning of SAIL 2020 (simulation studies)
0
5
10
15
20
25
30
11 12 13 14 15 16 17 18 19
verblijftijd looptijd
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
Example	dashboard	outcomes
• Social media analytics show potential of using information as an additional
source of information for real-time intervention and for planning purposes
32
Urban	Mobility	
Lab	Amsterdam	
• AMS	project	
• Multi-modal	data	
platform	to	unravel	
multi-model	traffic	
patterns	
• Example	application	
example	during	triple	
event	in	Arena	area	
• Shows	potential	for	
use	of	UML	in	crowd		
management	
(demand	prediction)	
and	in	more	
comprehensive	
multi-modal	
transportation	and	
traffic	management	
system
Freeway	and	urban	arterial	data Data	from	parking	garages	in	and	around	event	area
Chipcard	public	transport	data Pedestrian	counts	from	video
Loops FCD
GSM
Surveys Emissions
and energy Chip card
data
TwitterRoad works
maintenance
PT schedules
updates
Events,
incidents,
accidentsDemographic
data
REAL-TIME
INFORMATION
OFF-LINE MOBILITY INFORMATION
MOBILITY SERVICES
SHORT-CYCLIC
ASSESSMENT
LONG-TERM
PATTERNS
UML DATABASE
Status infrastructure weather News, information
Vecom data
Existing (open)
data platforms
DATA FUSION, PROCESSING & DIAGNOSTICS TOOLBOX
For SAIL, microscopicsimulation was used forplanning the event…How do these models
work?
Modelling	for	planning
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 (capacity

values and fundamental diagram)

• What about self-organisation?
33
This memo aims at connecting the microscopic modelling principles underlying the
social-forces model to identify a macroscopic flow model capturing interactions amongst
pedestrians. To this end, we use the anisotropic version of the social-forces model pre-
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
◆
Level of anisotropy
reflected by this
parameter
~vi
~v0
i
~ai
~nij
~xi
~xj
• Simple	model	shows	plausible	self-
organised	phenomena	
• Model	also	shows	flow	breakdown	
in	case	of	overloading		
• Similar	model	has	been	successfully	
used	for	planning	of	SAIL,	but	it	is	
questionable	if	for	real-time	
purposes	such	a	model	would	be	
useful,	e.g.	due	to	complexity	
• Coarser	models	proposed	so	far	turn	
out	to	have	limited	predictive	
validity,	and	are	unable	to	
reproduce	self-organised	patterns	
• Develop	continuum	model	based	on	
game-theoretical	model	NOMAD…
Microscopic models aretoo computationallycomplex for real-timeapplication and lack niceanalytical properties…
Modelling	for	planning	and	real-time	predictions
• 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
35
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) 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||
Modelling	for	planning	and	real-time	predictions
• 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…
36
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
To investigate the behaviour of these integrals, we have numerically approximated
them. To this end, we have chosen ~v( ) = V · (cos , sin ), for = 0...2⇡. Fig. 1 shows
FROM MICROSCOPIC TO MACROSCOPIC INTERACTION MODELING 3
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 magnitude of
the density itself has no e↵ect on the direction, while the gradient of the density does
influence the direction.
2.1. Homogeneous flow conditions. Note that in case of homogeneous conditions,
FROM MICROSCOPIC TO MACROSCOPIC INTERACTION MODELING 3
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 magnitude of
the density itself has no e↵ect on the direction, while the gradient of the density does
influence the direction.
2.1. Homogeneous flow conditions. Note that in case of homogeneous conditions,
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) describing the equilibrium290
speed and direction. Notice first that the direction does not depend on ↵0, which
implies that the magnitude of the density itself has no e↵ect, and that only the
gradient of the density does influence the direction. We will now discuss some
other properties, first by considering a homogeneous flow (r⇢ = ~0), and then
by considering an isotropic flow ( = 1) and an anisotropic flow ( = 0).295
4.1.1. Homogeneous flow conditions
Note that in case of homogeneous conditions, i.e. r⇢ = ~0, Eq. (14) simplifies
sions (14) and (15) describing the equilibrium
at the direction does not depend on ↵0, which
density itself has no e↵ect, and that only the
nce the direction. We will now discuss some
ng a homogeneous flow (r⇢ = ~0), and then
= 1) and an anisotropic flow ( = 0).
ns
us conditions, i.e. r⇢ = ~0, Eq. (14) simplifies
| ↵0⇢ = V 0
↵0⇢ (16)
!
v =
!
e ⋅V
37
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	seems	to	
inherit	properties	of	the	
microscopic	model	underlying	it		
• Forms	solid	basis	for	real-time	
prediction	module	in	dashboard	
• First	trials	in	model-based	
optimisation	and	use	of	model	for	
state-estimation	are	promising
38
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!
Principles	of	crowd	
management	
• 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	
Application	example	during	
Al	Mataf	design
Using	insights	for	design	and	management
Separate	ingoing	
and	outgoing	flows Gates	limit	inflow	to	
mosque	and	Mutaaf
Pilgrims	are	guided	to	
first	and	second	flow
Pinch	points	in	current	
design	are	removed
Back	to	SAIL…	
…Integrated	Transport	Management	concepts	for	the	Amsterdam	Area
42
Practical	Pilot	Amsterdam	
• Unique	practical	pilot	INM	
• Fully	automated	coordinated	
deployment	of	traffic	management	
measures	to	improve	throughput	on	
A10	West	
• First	phase	successful,	second	phase	
currently	running	
• Towards	traffic	management	2.0:	
integrating	road-side	and	in-car	traffic	
measures	for	state	estimation	(data	
fusion)	and	actuation	(anticipatory	
traffic	management)	
• Working	on	Melbourne	pilot	(Hai	Le	
Vu,	Swinburne)
http://www.ipam.ucla.edu/programs/workshops/workshop-iv-decision-support-for-traffic/?tab=schedule
Future	of	Traffic	Management
• Transition from road-side based to in-car
based traffic management 

• Use of car as a sensor and as actuator

• Two examples: 

• Anticipatory Traffic Management
• Suppressing wide-moving jams using
individual speed control

• Bi-level game: users get information and
respond to ramp-metering and traffic control
• Example shows how by anticipated user-
response on changing conditions
Future	of	Traffic	Management
• Transition from road-side based to in-car
based traffic management 

• Use of car as a sensor and as actuator

• Two examples: 

• Anticipatory Traffic Management

• Suppressing wide-moving jams using
individual speed control
• SPECIALIST algorithm was designed to
remove wide-moving jams using VSL
• Successful tests (simulation) using vehicles
as actuators even at limited penetration levels
Practical	pilot	results	(VSL) In-car	Specialist	(5%	penetration)
Wide-moving	jam	reduces	road	capacity	with	30%!
Without	Specialist	wide	moving	jam	travels	with	a	fixed	speed	in	the	opposite	direction	of	traffic
Specialist	limits	the	inflow	into	the	jam	which	therefore	resolves
Closing	remarks
• Urbanisation yields both new challenges and new opportunities for sustainable
transport and accessibility (e.g. via seamless multi-modal transport) and motivates
focus on Intelligent Urban Mobility under umbrella of Smart City projects such as AMS 

• Increasing share of active modes can have major impacts on accessibility,
liveability and health! 

• Focus on keeping urban pedestrian and bike safety and comfort at high levels by
means active mode traffic management (e.g. crowd management) offers
unprecedented scientific challenges in data collection, modelling and simulation,
and control and management!

• Co-existence with other future transport concepts such as self-driving vehicles will be
a challenge as will, in particular in dense cities such as Amsterdam
45
More	information?
• Hoogendoorn, S.P., van Wageningen-Kessels, F., Daamen, W., Duives, D.C., Sarvi, M. Continuum theory for pedestrian
traffic flow: Local route choice modelling and its implications (2015) Transportation Research Part C: Emerging
Technologies, 59, pp. 183-197. 

• Van Wageningen-Kessels, F., Leclercq, L., Daamen, W., Hoogendoorn, S.P. The Lagrangian coordinate system and what
it means for two-dimensional crowd flow models (2016) Physica A: Statistical Mechanics and its Applications, 443, pp.
272-285.

• Hoogendoorn, S.P., Van Wageningen-Kessels, F.L.M., Daamen, W., Duives, D.C. Continuum modelling of pedestrian
flows: From microscopic principles to self-organised macroscopic phenomena (2014) Physica A: Statistical Mechanics
and its Applications, 416, pp. 684-694.

• Taale, H., Hoogendoorn, S.P. A framework for real-time integrated and anticipatory traffic management (2013) IEEE
Conference on Intelligent Transportation Systems, Proceedings, ITSC, art. no. 6728272, pp. 449-454.

• Hoogendoorn, S.P., Landman, R., Van Kooten, J., Schreuder, M. Integrated Network Management Amsterdam: Control
approach and test results (2013) IEEE Conference on Intelligent Transportation Systems, Proceedings, ITSC, art. no.
6728276, pp. 474-479.

• Le, T., Vu, H.L., Nazarathy, Y., Vo, Q.B., Hoogendoorn, S. Linear-quadratic model predictive control for urban traffic
networks (2013) Transportation Research Part C: Emerging Technologies, 36, pp. 498-512. 46

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Unraveling urban traffic flows

  • 1. Unravelling Urban Traffic Flows From new insights to advanced solutions… a work in progress
 Prof. dr. Serge Hoogendoorn 1
  • 2. AMSTERDAM INSTITUTE FOR ADVANCED METROPOLITAN SOLUTIONS TU DELFT, WAGENINGEN UR, MIT ACCENTURE, ALLIANDER, AMSTERDAM SMART CITY, CISCO, CITY OF BOSTON, ESA, IBM, KPN, SHELL, TNO, WAAG SOCIETY, WATERNET CITY METABOLISM: URBAN FLOWS WATER-ENERGY-WASTE-FOOD-DATA-PEOPLE 2 CIRCULAR CITY VITAL CITY CONNECTED CITY Circular economy Water, energy, food, waste Smart infrastructures Urban big data Internet of Everything Digital fabrication Smart mobility Resilient, clean and healthy urban environment Blue-green infrastructures Social & responsible design Proposition: using the cityas a living lab to exploreimpact and find possibilitiesof these (and other) trendson mobility and other sectors…
  • 3. 3 AMSTERDAM INSTITUTE FOR ADVANCED METROPOLITAN SOLUTIONS TU DELFT, WAGENINGEN UR, MIT ACCENTURE, ALLIANDER, AMSTERDAM SMART CITY, CISCO, CITY OF BOSTON, ESA, IBM, KPN, SHELL, TNO, WAAG SOCIETY, WATERNET AMBITIONS An internationally renowned, public-private institution in the area of metropolitan solutions that in 2022 has … … 200-250 talented students participating in a new MSc … … 100-150 researchers working on discovering, developing and implementing metropolitan solutions … … EUR 25-35 million annual budget for research and valorization … … 30-50 public and private partners participating ... … 500-1,000 publications, 10-15 spin-outs and 30-70 start-ups generated between 2013 and 2022 … … an excellent position for continued value creation in the next 20 years.
  • 4. Entering the urban age • Urbanisation is a global trend: more people live in cities than ever! • City regions become focal points of the world economy in terms of output, productivity, decision making power, innovation power • Requirement for success: internal connectivity (within city or city region) and external connectivity (airport, ports): importance of accessibility 4
  • 5. Challenges… • Accessibility is a major issue in many cities (Amsterdam, Melbourne) • Most delays are experienced in cities (not on freeways!), yet freeways have received much attention in the past… • At the same time, (re-) urbanisation opens up many new alleyways for sustainable mobility (active modes, seamless multi-modal transport, shared mobility, autonomous driving) • So what do we see as key themes?
  • 6. Challenges… • Accessibility is a major issue in many cities (Amsterdam, Melbourne) • Most delays are experienced in cities (not on freeways!), yet freeways have received much attention in the past… • At the same time, (re-) urbanisation opens up many new alleyways for sustainable mobility (active modes, seamless multi-modal transport, shared mobility, autonomous driving) • So what do we see as key themes?
  • 7. Relevant research domains for mobility theme Research domains relevant to urban transportation systems and mobility involve (but not excluded to): • Slow (or rather) active traffic modes (pedestrians, crowds, bikes) • Coordinated & cooperative traffic control, management and information • Automation & self-driving vehicles • Resilient public transport systems and sustainable multi-modal transport • Urban distribution and city logistics 7
  • 8. Trends in mode share in Amsterdam area • Since 1990’s car use has been on the decline in Amsterdam • Cycling and walking are main modes of transport in city • Big impacts on emissions (4-12% reduction), as well as accessibility and health • But these positive trends also has some negative (but interesting) impacts…
  • 10. The ALLEGRO programme unrAvelLing sLow modE travelinG and tRaffic: 
 with innOvative data to a new transportation and traffic theory for pedestrians and bicycles”
 • 4.2 million AUD personal grant with a focus on developing theory (from an application oriented perspective) sponsored by the ERC and AMS • Relevant elements of the project: • Development of components for “living” data & simulation laboratory building on two decades of experience in pedestrian monitoring, theory and simulation • Outreach to cities by means of “solution-oriented” projects (“the AMS part”), e.g. event planning framework, design and crowd management strategies, etc. • Looking for talented PhD students!
  • 11. 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 Choice and Activity Scheduling Theory Planning anddesign guidelines Organisation of large-scale events Data Insights Tools Models Impacts Network Knowledge Acquisition (learning) Factors determining route choice
  • 12. 12 Engineering the future city. Today’s talk • Focus on active modes in particular on pedestrian and crowds • Use SAIL event as the driving example to illustrate various concepts in monitoring and management • SAIL project entailed development of a crowd management decision support system
  • 13. 13 SAIL? • Biggest (and free) 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
  • 14. 14 Engineering challenges
 for events or regular situations… • Can we for a certain event predict if a safety or throughput issue will occur? • Can we develop methods to support organisation, planning and design? • Can we develop approaches to real-time manage large pedestrian flows safely and efficiently? • Can we ensure that all of these are robust agains unforeseen circumstances? Deep knowledge of crowd dynamics is essential to answer these questions!
  • 15. Pedestrian flow operations… Simple case example: how long does it take to evacuatie a room? • Consider a room of N people • Suppose that the (only) exit has capacity of C Peds/hour • Use a simple queuing model to compute duration T • How long does the evacuation take? • Capacity of the door is very important • Which factors determine capacity? 15 T = N C N people in area Door capacity: C N C
  • 16. Pedestrian flow operations… Simple case example: how long does it take to evacuatie a room? • Wat determines capacity? • Experimental research on behalf of Dutch Ministry of Housing • Experiments under different circumstances and composition of flow • Empirical basis to express the capacity of a door (per meter width, per second) as a function of the considered factors:
  • 17. Pedestrian flow operations… Simple case example: how long does it take to evacuatie a room? • Wat determines capacity? • Open door (90 degrees) yields a capacity reduction of 7% • Detailed analysis of paths (by tracking of) pedestrian reveals cause 0 1 2 3 4 5 6 7 8 1 2 3 4 5 6 Looprichting X-positie (in m) Y - p o s i t i e ( i n m ) Walking direction X-position (in m) Y-position(inm) • Pedestrians appear to walk very close together (short headways) for a very short period of time (only at side where there is no door) • Importance of detailed research in microscopic behaviour to understand phenomena…
  • 18. 18 • Insight in more complex situations • Real-life situations in (public) spaces often more complex • Limited empirical knowledge on multi-directional flows motivated first walker experiments in 2002 • Worldpremiere, many have followed! • Resulted in a unique microscopic dataset First insights into importance of self-organisation in pedestrian flows
  • 19. Fascinating self-organisation • Example efficient self-organisation dynamic walking lanes in bi-directional flow • High efficiency in terms of capacity and observed walking speeds • Experiments by Hermes group show similar results as TU Delft experiments, but at higher densities 19
  • 20. Fascinating self-organisation • Relatively small efficiency loss (around 7% capacity reduction), depending on flow composition (direction split) • Same applies to crossing flows: self- organised diagonal patterns turn out to be very efficient • Other types of self-organised phenomena occur as well (e.g. viscous fingering) • Phenomena also occur in the field… 20 Bi-directional experiment
  • 21. Studying self-organisation during rock concert Lowlands… Pedestrian flow operations… So with this wonderful self-organisation, why do we need to worry about crowds at all?
  • 22. 22 Increase in friction resulting in arc formation by increasing pressure from behind (force- Pedestrian capacity drop and faster-is-slower effect • Capacity drop also occurs in pedestrian flow • Faster = slower effect • Pedestrian experiments (TU Dresden, TU Delft) have revealed that outflow reduces substantially when evacuees try to exit room as quickly as possible (rushing) • Capacity reduction is caused by friction and arc-formation in front of door due to increased pressure • Capacity reduction causes severe increases in evacuation times Intermezzo: given ourunderstanding of thecauses of the faster isslower effect, can youthink of a solution?
  • 25. A New Phase in Pedestrian Flow Operations • When densities become very large (> 6 P/m2) new phase emerges coined turbulence • Characterised by extreme high densities and pressure exerted by the other pedestrians • High probabilities of asphyxiation
  • 27. Why crowd management is necessary! • Pedestrian Network Fundamental Diagram shows relation between number of pedestrians in area • P-NFD shows reduced performance of network flow operations in case
 of overloading causes by
 various phenomena such
 as faster-is-slower effect
 and self-organisation
 breaking down • Current work focusses on
 theory of P-NFD 27
  • 28. 28 Crowd Management for Events • Unique pilot with crowd management system for large scale, outdoor event • Functional architecture of SAIL 2015 crowd management systems • Phase 1 focussed on monitoring and diagnostics (data collection, number of visitors, densities, walking speeds, determining levels of service and potentially dangerous situations) • Phase 2 focusses on prediction and decision support for crowd management measure deployment (model-based prediction, intervention decision support) 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?
  • 30. Example dashboard outcomes • Newly developed algorithm to distinguish between occupancy time and walking time • Other examples show volumes and OD flows • Results used for real-time intervention, but also for planning of SAIL 2020 (simulation studies) 0 5 10 15 20 25 30 11 12 13 14 15 16 17 18 19 verblijftijd looptijd 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
  • 31. Example dashboard outcomes • Social media analytics show potential of using information as an additional source of information for real-time intervention and for planning purposes
  • 32. 32 Urban Mobility Lab Amsterdam • AMS project • Multi-modal data platform to unravel multi-model traffic patterns • Example application example during triple event in Arena area • Shows potential for use of UML in crowd management (demand prediction) and in more comprehensive multi-modal transportation and traffic management system Freeway and urban arterial data Data from parking garages in and around event area Chipcard public transport data Pedestrian counts from video Loops FCD GSM Surveys Emissions and energy Chip card data TwitterRoad works maintenance PT schedules updates Events, incidents, accidentsDemographic data REAL-TIME INFORMATION OFF-LINE MOBILITY INFORMATION MOBILITY SERVICES SHORT-CYCLIC ASSESSMENT LONG-TERM PATTERNS UML DATABASE Status infrastructure weather News, information Vecom data Existing (open) data platforms DATA FUSION, PROCESSING & DIAGNOSTICS TOOLBOX For SAIL, microscopicsimulation was used forplanning the event…How do these models work?
  • 33. Modelling for planning 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 (capacity
 values and fundamental diagram) • What about self-organisation? 33 This memo aims at connecting the microscopic modelling principles underlying the social-forces model to identify a macroscopic flow model capturing interactions amongst pedestrians. To this end, we use the anisotropic version of the social-forces model pre- 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 ◆ Level of anisotropy reflected by this parameter ~vi ~v0 i ~ai ~nij ~xi ~xj
  • 34. • Simple model shows plausible self- organised phenomena • Model also shows flow breakdown in case of overloading • Similar model has been successfully used for planning of SAIL, but it is questionable if for real-time purposes such a model would be useful, e.g. due to complexity • Coarser models proposed so far turn out to have limited predictive validity, and are unable to reproduce self-organised patterns • Develop continuum model based on game-theoretical model NOMAD… Microscopic models aretoo computationallycomplex for real-timeapplication and lack niceanalytical properties…
  • 35. Modelling for planning and real-time predictions • 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 35 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) 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||
  • 36. Modelling for planning and real-time predictions • 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… 36 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 To investigate the behaviour of these integrals, we have numerically approximated them. To this end, we have chosen ~v( ) = V · (cos , sin ), for = 0...2⇡. Fig. 1 shows FROM MICROSCOPIC TO MACROSCOPIC INTERACTION MODELING 3 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 magnitude of the density itself has no e↵ect on the direction, while the gradient of the density does influence the direction. 2.1. Homogeneous flow conditions. Note that in case of homogeneous conditions, FROM MICROSCOPIC TO MACROSCOPIC INTERACTION MODELING 3 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 magnitude of the density itself has no e↵ect on the direction, while the gradient of the density does influence the direction. 2.1. Homogeneous flow conditions. Note that in case of homogeneous conditions, 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) describing the equilibrium290 speed and direction. Notice first that the direction does not depend on ↵0, which implies that the magnitude of the density itself has no e↵ect, and that only the gradient of the density does influence the direction. We will now discuss some other properties, first by considering a homogeneous flow (r⇢ = ~0), and then by considering an isotropic flow ( = 1) and an anisotropic flow ( = 0).295 4.1.1. Homogeneous flow conditions Note that in case of homogeneous conditions, i.e. r⇢ = ~0, Eq. (14) simplifies sions (14) and (15) describing the equilibrium at the direction does not depend on ↵0, which density itself has no e↵ect, and that only the nce the direction. We will now discuss some ng a homogeneous flow (r⇢ = ~0), and then = 1) and an anisotropic flow ( = 0). ns us conditions, i.e. r⇢ = ~0, Eq. (14) simplifies | ↵0⇢ = V 0 ↵0⇢ (16) ! v = ! e ⋅V
  • 37. 37 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 seems to inherit properties of the microscopic model underlying it • Forms solid basis for real-time prediction module in dashboard • First trials in model-based optimisation and use of model for state-estimation are promising
  • 38. 38 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! Principles of crowd management • 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 Application example during Al Mataf design
  • 39.
  • 42. 42 Practical Pilot Amsterdam • Unique practical pilot INM • Fully automated coordinated deployment of traffic management measures to improve throughput on A10 West • First phase successful, second phase currently running • Towards traffic management 2.0: integrating road-side and in-car traffic measures for state estimation (data fusion) and actuation (anticipatory traffic management) • Working on Melbourne pilot (Hai Le Vu, Swinburne) http://www.ipam.ucla.edu/programs/workshops/workshop-iv-decision-support-for-traffic/?tab=schedule
  • 43. Future of Traffic Management • Transition from road-side based to in-car based traffic management • Use of car as a sensor and as actuator • Two examples: • Anticipatory Traffic Management • Suppressing wide-moving jams using individual speed control • Bi-level game: users get information and respond to ramp-metering and traffic control • Example shows how by anticipated user- response on changing conditions
  • 44. Future of Traffic Management • Transition from road-side based to in-car based traffic management • Use of car as a sensor and as actuator • Two examples: • Anticipatory Traffic Management • Suppressing wide-moving jams using individual speed control • SPECIALIST algorithm was designed to remove wide-moving jams using VSL • Successful tests (simulation) using vehicles as actuators even at limited penetration levels Practical pilot results (VSL) In-car Specialist (5% penetration) Wide-moving jam reduces road capacity with 30%! Without Specialist wide moving jam travels with a fixed speed in the opposite direction of traffic Specialist limits the inflow into the jam which therefore resolves
  • 45. Closing remarks • Urbanisation yields both new challenges and new opportunities for sustainable transport and accessibility (e.g. via seamless multi-modal transport) and motivates focus on Intelligent Urban Mobility under umbrella of Smart City projects such as AMS • Increasing share of active modes can have major impacts on accessibility, liveability and health! • Focus on keeping urban pedestrian and bike safety and comfort at high levels by means active mode traffic management (e.g. crowd management) offers unprecedented scientific challenges in data collection, modelling and simulation, and control and management! • Co-existence with other future transport concepts such as self-driving vehicles will be a challenge as will, in particular in dense cities such as Amsterdam 45
  • 46. More information? • Hoogendoorn, S.P., van Wageningen-Kessels, F., Daamen, W., Duives, D.C., Sarvi, M. Continuum theory for pedestrian traffic flow: Local route choice modelling and its implications (2015) Transportation Research Part C: Emerging Technologies, 59, pp. 183-197. • Van Wageningen-Kessels, F., Leclercq, L., Daamen, W., Hoogendoorn, S.P. The Lagrangian coordinate system and what it means for two-dimensional crowd flow models (2016) Physica A: Statistical Mechanics and its Applications, 443, pp. 272-285. • Hoogendoorn, S.P., Van Wageningen-Kessels, F.L.M., Daamen, W., Duives, D.C. Continuum modelling of pedestrian flows: From microscopic principles to self-organised macroscopic phenomena (2014) Physica A: Statistical Mechanics and its Applications, 416, pp. 684-694. • Taale, H., Hoogendoorn, S.P. A framework for real-time integrated and anticipatory traffic management (2013) IEEE Conference on Intelligent Transportation Systems, Proceedings, ITSC, art. no. 6728272, pp. 449-454. • Hoogendoorn, S.P., Landman, R., Van Kooten, J., Schreuder, M. Integrated Network Management Amsterdam: Control approach and test results (2013) IEEE Conference on Intelligent Transportation Systems, Proceedings, ITSC, art. no. 6728276, pp. 474-479. • Le, T., Vu, H.L., Nazarathy, Y., Vo, Q.B., Hoogendoorn, S. Linear-quadratic model predictive control for urban traffic networks (2013) Transportation Research Part C: Emerging Technologies, 36, pp. 498-512. 46