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Page 1: TFT 2016 summer meeting Sydney

UnravellingUrbanActiveModeTrafficFlows

Challenges in Active Mode Traffic (and Transportation) Theory Prof. dr. Serge Hoogendoorn

1

Page 2: TFT 2016 summer meeting Sydney

Importantsocietaltrends

• Urbanisation is a global trend: more people live in cities than ever and the number is expected to grow further

• Keeping cities liveable requires an efficient and green transportation system, which is less car-centric than many of current cities

• Opportunities are there: the car is often not the most efficient mode (in terms of operational speed) at all!

• e-Bikes extend average trip ranges (beyond average of 8 km)

Page 3: TFT 2016 summer meeting Sydney

Researchmotivation

• In many cities, mode shifts are very prominent! • Example shows that walking and cycling as important urban

transport modes in Amsterdam• Mode shifts go hand in hand with emission reduction (4-12%)!

Page 4: TFT 2016 summer meeting Sydney

OvercrowdedPThubscausingdelaysandunsafety

Anydownsides?

Bikecongestioncausingdelaysandhindrance

Overcrowdingduringregularsituationsalsoduetotourists Overcrowdingofstreetsduringevents

Theory and models for

pedestrian flow, bicycle

flow and mixed flow is still

immature!

Page 5: TFT 2016 summer meeting Sydney

Active Mode UML

Engineering Applications

Transportation and Traffic Theory for Active Modes in an Urban Context

Data collection and fusion toolbox

Social-media data analytics

AM-UML app

Simulation platform

Walking and Cycling BehaviourTraffic Flow Operations

Route Choice and Activity

Scheduling Theory

Planning and design guidelines

Real-time personalised

guidance

Data Insights

Tools

Models Impacts

Network Knowledge Acquisition (learning)

Factors determining route choice

ERC Advanced Grant ALLEGRO

Organisation of large-scale

events

Page 6: TFT 2016 summer meeting Sydney

Atasteofthingstocome…

• Large scale data collection experiment (“fietstelweek”) with more than 50.000 participants!

• GPS data allows analysing revealed route choice behaviour

• Route attributes derived from GPS data and map-based information

• First choice model estimates show importance of build environment factors next to distance and delays

Page 7: TFT 2016 summer meeting Sydney

Atasteofthingstocome…

• Data collection at events (i.c.: Mysteryland) provides new insights into activity / route choices

• Example: relation route choice and music taste

Page 8: TFT 2016 summer meeting Sydney

Atasteofthingstocome…

• Capacity estimation of bicycle lanes by composite headway modelling

• Data collected at bicycle crossing• Photo finish technique allows collection

of time headways on which composite headway model can be estimated

Page 9: TFT 2016 summer meeting Sydney

Whyisourknowledgelimited?

• Traffic (and Transportation) theory is an inductive science

• Importance of data in development of theory and models (e.g. Greenshields)

• In particular theory for active modes has suffered from the lack of data

• Slowly, this situation is changing and data is becoming available…

Understanding transport begins and ends with data

Page 10: TFT 2016 summer meeting Sydney

Let’sstartwiththepedestrians…UnderstandingPedestrianFlows

Fieldobservations,controlledexperiments,virtuallaboratoriesDatacollectionremainsachallenge,butmanynewopportunitiesarise!

Page 11: TFT 2016 summer meeting Sydney

Trafficflowcharacteristicsforpedestrians…Capacity,fundamentaldiagram,andinfluenceofcontext

Empirical characteristics and relations • Experimental research capacity values:

• Strong influence of composition of flow

• Importance of geometric factors

Fundamental diagram pedestrian flows • Relation between density and flow / speed

• Big influence of context!

• Example shows regular FD and FD determined from Jamarat Bridge

Page 12: TFT 2016 summer meeting Sydney

Whathappensifpedsmeethead-on?

• Experiment shows results if two groups of pedestrians in opposite directions meet head-on

• Results from (at that time) unique controlled walking experiments held at TU Delft in 2002

Page 13: TFT 2016 summer meeting Sydney

So,nochaos!Isthisgeneric?Larger-scaleexperimentsshowsimilarresultsforhigherpedestriandemands…

Self-organisation yields very efficient flow operations in terms of speed and throughput

Page 14: TFT 2016 summer meeting Sydney

Alsoforcrossingflowsweseespontaneousself-organisation(ofdiagonallanes)…

So with this wonderful

self-organisation, why do

we need to worry about

crowds at all?

Page 15: TFT 2016 summer meeting Sydney

Break-downofself-organisation• Whenconditionsbecometoocrowded,efficientself-organisation‘breaksdown’

• Flowperformancedecreasessubstantially,potentiallycausingmoreproblemsasdemandstaysatsamelevel

• Hassevereimplicationsonthenetworklevel

• Importanceof‘keepingthingsflowing’

Inflow (Ped/s)

Bre

akdo

wn

prob

.

0

1

1 2

Increasing heterogeneity

Page 16: TFT 2016 summer meeting Sydney

Adangeroustrafficstate!

Failingself-organisationmayleadtoturbulentpedestrianflows…

Page 17: TFT 2016 summer meeting Sydney

17

Prevent blockades by separating flows in different directions / use of reservoirs

Distribute traffic over available infrastructure by means of guidance or information provision

Increase throughput in particular at pinch points in the design…

Limit the inflow (gating) ensuring that number of pedestrians stays below critical value!

Usingourempiricalknowledge:SimplePrinciplesfordesign&crowdmanagement• Useprinciplesindesignandplanning

• Developingcrowdmanagementinterventionsusinginsightsinpedestrianflowcharacteristics

• Goldenrules(solutiondirections)providedirectionsinwhichtothinkwhenconsideringcrowdmanagementoptions

Page 18: TFT 2016 summer meeting Sydney

Engineering the future city.

Planningandoperations:SAILtallshipevent• BiggestpubliceventintheNederland,organisedevery5yearssince1975

• OrganisedaroundtheIJhaven,Amsterdam

• Thistimearound600tallshipsweresailingin

• Around2,3millionnationalandinternationalvisitors

• ModellingsupportofSAILprojectinplanningandbydevelopmentofacrowdmanagementdecisionsupportsystem

Page 19: TFT 2016 summer meeting Sydney

Abitoftheory…

• We build a mathematical model on hypothesis of the “pedestrian economicus” assuming that pedestrians aim to minimise predicted effort (cost) of walking, defined by:- Straying from desired direction and speed- Walking close to other pedestrians (irrespective of direction!)- Frequently slowing down and accelerating

• Pedestrians predict behaviour of others and may communicate• Pedestrians choose acceleration to minimise predicted cost:

a⇤p(t) = argmin J = argmin

Z 1

texp(�⌘s)Lds

L =

�1

2

(~v0p � ~vp(t))2+ �2

X

q

exp(�||~rq(t)� ~rp(t)||/Bp) +1

2

~a2p(t)

Page 20: TFT 2016 summer meeting Sydney

Abitoftheory…

• Framework generalises social-forces model under specific assumptions of cooperation and cost specifications

• Assuming that other pedestrians will not change direction nor speed yields the (anisotropic) social forces model:

• This model appears to be face valid… - It gives a reasonable fundamental diagram- It reproduces different forms of

self-organisations…

FROM MICROSCOPIC TO MACROSCOPIC INTERACTIONMODELING

SERGE P. HOOGENDOORN

1. Introduction

This memo aims at connecting the microscopic modelling principles underlying thesocial-forces model to identify a macroscopic flow model capturing interactions amongstpedestrians. 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, giventhe desired walking speed and direction, and the speed and direction changes due tointeractions.

2. Microscopic foundations

We start with the anisotropic model of Helbing that describes the acceleration ofpedestrian i as influence by opponents j:

(1) ~ai

=~v0i

� ~vi

⌧i

�Ai

X

j

exp

�R

ij

Bi

�· ~n

ij

·✓�i

+ (1� �i

)1 + cos�

ij

2

where Rij

denotes the distance between pedestrians i and j, ~nij

the unit vector pointingfrom pedestrian i to j; �

ij

denotes the angle between the direction of i and the postionof j; ~v

i

denotes the velocity. The other terms are all parameters of the model, that willbe introduced later.

In assuming equilibrium conditions, we generally have ~ai

= 0. The speed / directionfor which this occurs is given by:

(2) ~vi

= ~v0i

� ⌧i

Ai

X

j

exp

�R

ij

Bi

�· ~n

ij

·✓�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 onlocation ~x at time instant t. Let us assume that all parameters are the same for allpedestrian 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 theinteractions. Note that:

(4) cos�xy

(~v) =~v

||~v|| ·~y � ~x

||~y � ~x||1

~vi

~v0i

~ai

~nij

~xi

~xj

Page 21: TFT 2016 summer meeting Sydney

Fundamentaldiagramandanisotropy

• Consider situation where pedestrians walk in a straight line behind each other

• Equilibrium: no acceleration, equal distances R between peds• We can easily determine equilibrium speed for pedestrian i

(distinguishing between pedestrian in front i > j and back)

• Fundamental diagram looks reasonable for positive values of anisotropy factor

• Example for specific values of A and B

V ei = V 0 � ⌧ ·A ·

0

@X

j>i

exp [�(j � i)R/B]� �X

j<i

exp [�(i� j)R/B]

1

A

Page 22: TFT 2016 summer meeting Sydney

Fundamentaldiagramandanisotropy

• Equilibrium relation for multiple values of • Note impact of anisotropy factor on capacity and jam density

V ei = V 0 � ⌧ ·A ·

0

@X

j>i

exp [�(j � i)R/B]� �X

j<i

exp [�(i� j)R/B]

1

A

0 2 4 6density (P/m)

0

0.5

1

1.5

spee

d (m

/s)

0 2 4 6flow (P/s)

0

2

4

6

8

10

spee

d (m

/s)

� = 0

� = 1

� = 1

� = 0.6

� = 0.8

� = 0.6

Page 23: TFT 2016 summer meeting Sydney

Self-organisationmathematicallymodelled…Laneformationcanbereproducedwithsimplemathematicalmodels…

Model also predicts

breakdown of self-

organisation in case of

overloading the facility

Page 24: TFT 2016 summer meeting Sydney

• Applicationforplanningpurposes(e.g.SAIL)

• Questionableifforreal-timeandoptimisationpurposessuchamodelwouldbeusefuly

Page 25: TFT 2016 summer meeting Sydney

25

Towardsdynamicintervention…• Uniquepilotwithcrowdmanagementsystemforlargescale,outdoorevent

• FunctionalarchitectureofSAIL2015crowdmanagementsystems

• Systemdealswithmonitoringanddiagnostics(datacollection,numberofvisitors,densities,walkingspeeds,determininglevelsofserviceandpotentiallydangeroussituations)

• Futureworkfocussesonpredictionanddecisionsupportforcrowdmanagementmeasuredeployment

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?

Page 26: TFT 2016 summer meeting Sydney

Exampleresultsdashboard

• Development of new measurement techniques and methods for data fusion (counting cameras, Wifi sensors, GPS)

• New algorithms to estimate walking and occupancy duration

• Many applications since SAIL (Kingsday, FabCity, Europride)

1988

1881

4760

4958

2202

1435

6172

59994765 4761

4508

3806

3315

2509

17523774

4061

2629

13592654

21391211

1439

2209

1638

2581

311024653067

2760

Page 27: TFT 2016 summer meeting Sydney

Modellingforreal-timeapplications

• 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

FROM MICROSCOPIC TO MACROSCOPIC INTERACTIONMODELING

SERGE P. HOOGENDOORN

1. Introduction

This memo aims at connecting the microscopic modelling principles underlying thesocial-forces model to identify a macroscopic flow model capturing interactions amongstpedestrians. 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, giventhe desired walking speed and direction, and the speed and direction changes due tointeractions.

2. Microscopic foundations

We start with the anisotropic model of Helbing that describes the acceleration ofpedestrian i as influence by opponents j:

(1) ~ai

=~v0i

� ~vi

⌧i

�Ai

X

j

exp

�R

ij

Bi

�· ~n

ij

·✓�i

+ (1� �i

)1 + cos�

ij

2

where Rij

denotes the distance between pedestrians i and j, ~nij

the unit vector pointingfrom pedestrian i to j; �

ij

denotes the angle between the direction of i and the postionof j; ~v

i

denotes the velocity. The other terms are all parameters of the model, that willbe introduced later.

In assuming equilibrium conditions, we generally have ~ai

= 0. The speed / directionfor which this occurs is given by:

(2) ~vi

= ~v0i

� ⌧i

Ai

X

j

exp

�R

ij

Bi

�· ~n

ij

·✓�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 onlocation ~x at time instant t. Let us assume that all parameters are the same for allpedestrian 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 theinteractions. Note that:

(4) cos�xy

(~v) =~v

||~v|| ·~y � ~x

||~y � ~x||1

FROM MICROSCOPIC TO MACROSCOPIC INTERACTIONMODELING

SERGE P. HOOGENDOORN

1. Introduction

This memo aims at connecting the microscopic modelling principles underlying thesocial-forces model to identify a macroscopic flow model capturing interactions amongstpedestrians. 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, giventhe desired walking speed and direction, and the speed and direction changes due tointeractions.

2. Microscopic foundations

We start with the anisotropic model of Helbing that describes the acceleration ofpedestrian i as influence by opponents j:

(1) ~ai

=~v0i

� ~vi

⌧i

�Ai

X

j

exp

�R

ij

Bi

�· ~n

ij

·✓�i

+ (1� �i

)1 + cos�

ij

2

where Rij

denotes the distance between pedestrians i and j, ~nij

the unit vector pointingfrom pedestrian i to j; �

ij

denotes the angle between the direction of i and the postionof j; ~v

i

denotes the velocity. The other terms are all parameters of the model, that willbe introduced later.

In assuming equilibrium conditions, we generally have ~ai

= 0. The speed / directionfor which this occurs is given by:

(2) ~vi

= ~v0i

� ⌧i

Ai

X

j

exp

�R

ij

Bi

�· ~n

ij

·✓�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 onlocation ~x at time instant t. Let us assume that all parameters are the same for allpedestrian 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 theinteractions. Note that:

(4) cos�xy

(~v) =~v

||~v|| ·~y � ~x

||~y � ~x||1

FROM MICROSCOPIC TO MACROSCOPIC INTERACTIONMODELING

SERGE P. HOOGENDOORN

1. Introduction

This memo aims at connecting the microscopic modelling principles underlying thesocial-forces model to identify a macroscopic flow model capturing interactions amongstpedestrians. 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, giventhe desired walking speed and direction, and the speed and direction changes due tointeractions.

2. Microscopic foundations

We start with the anisotropic model of Helbing that describes the acceleration ofpedestrian i as influence by opponents j:

(1) ~ai

=~v0i

� ~vi

⌧i

�Ai

X

j

exp

�R

ij

Bi

�· ~n

ij

·✓�i

+ (1� �i

)1 + cos�

ij

2

where Rij

denotes the distance between pedestrians i and j, ~nij

the unit vector pointingfrom pedestrian i to j; �

ij

denotes the angle between the direction of i and the postionof j; ~v

i

denotes the velocity. The other terms are all parameters of the model, that willbe introduced later.

In assuming equilibrium conditions, we generally have ~ai

= 0. The speed / directionfor which this occurs is given by:

(2) ~vi

= ~v0i

� ⌧i

Ai

X

j

exp

�R

ij

Bi

�· ~n

ij

·✓�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 onlocation ~x at time instant t. Let us assume that all parameters are the same for allpedestrian 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 theinteractions. Note that:

(4) cos�xy

(~v) =~v

||~v|| ·~y � ~x

||~y � ~x||1

Page 28: TFT 2016 summer meeting Sydney

Modellingforreal-timeapplications

• First-order Taylor series approximation: yields a closed-form expression for the equilibrium velocity , which is given by the equilibrium speed and direction:

with:

• Check behaviour of model by looking at isotropic flow ( ) and homogeneous flow conditions ( )

• Include conservation of pedestrian relation gives a complete model…

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 approximatedthem. To this end, we have chosen ~v( ) = V · (cos , sin ), for = 0...2⇡. Fig. 1 showsthe results from this approximation.

0 1 2 3 4 5 6 7−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25

angle

valu

e

α

1

α2

β

Figure 1. Numerical approximation of ~↵(~v) and �(~v).

For the figure, we can clearly see that � is independent on ~v, i.e.

(9) �(~v) = �0

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 ofthe 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⇢

i.e. we see a linear relation between speed and density. For the direction ~e, we then get:

(14) ~e =~v0

V + ↵0⇢= ~e0

In other words, in homogeneous density conditions the direction of the pedestrians isequal to the desired direction.

2.2. Isotropic walking behaviour. Let us also note that in case � = 1 (isotropicflow), and assuming that ⌦ is symmetric around ~x, we get:

(15) ~↵(~v) = ⌧A

ZZ

~y2⌦(~x)

exp

✓� ||~y � ~x||

B

◆~y � ~x

||~y � ~x||d~y = ~0

which means ↵0 = 0. In this case, we have:

(16) V = ||~v0 � �0 ·r⇢||

This expression shows that in this case, the speed is only dependent on the densitygradient. If a pedestrian walks into a region in which the density is increasing, the speedwill be less than the desired speed; and vice versa. Also note that in case of homogenousconditions, the speed will be constant and equal to the free speed. Note that this isconsistent with the results from Hoogendoorn, ISTTT-2003.

For the direction, we find:

(17) ~e =~v0 � �0 ·r⇢

||~v0 � �0 ·r⇢||

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 ofthe 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⇢

i.e. we see a linear relation between speed and density. For the direction ~e, we then get:

(14) ~e =~v0

V + ↵0⇢= ~e0

In other words, in homogeneous density conditions the direction of the pedestrians isequal to the desired direction.

2.2. Isotropic walking behaviour. Let us also note that in case � = 1 (isotropicflow), and assuming that ⌦ is symmetric around ~x, we get:

(15) ~↵(~v) = ⌧A

ZZ

~y2⌦(~x)

exp

✓� ||~y � ~x||

B

◆~y � ~x

||~y � ~x||d~y = ~0

which means ↵0 = 0. In this case, we have:

(16) V = ||~v0 � �0 ·r⇢||

This expression shows that in this case, the speed is only dependent on the densitygradient. If a pedestrian walks into a region in which the density is increasing, the speedwill be less than the desired speed; and vice versa. Also note that in case of homogenousconditions, the speed will be constant and equal to the free speed. Note that this isconsistent with the results from Hoogendoorn, ISTTT-2003.

For the direction, we find:

(17) ~e =~v0 � �0 ·r⇢

||~v0 � �0 ·r⇢||

α 0 = πτAB2 (1− λ) and β0 = 2πτAB3(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

to

V = ||~v0||� ↵0⇢ = V 0 � ↵0⇢ (16)

i.e. we see a linear relation between speed and density. The term ↵0 � 0

describes the reduction of the speed with increasing density.300

For the direction ~e, we then get:

~e =~v0

||~v0|| = ~e0 (17)

In other words, in homogeneous density conditions the direction of the pedestri-

ans is equal to the desired direction. Clearly, the gradient of the density yields

pedestrians to divert from their desired direction.

Looking further at the expressions for ↵0 and �0, we can see the influence of305

the various parameters on their size; ↵0 scales linearly with A and ⌧ , meaning

that the influence of the density on the speed increases with increasing values

of A and ⌧ . At the same time, larger values for B imply a reduction of the

influence of the density. Needs to be revised!

The same can be concluded for the influence of the gradient: we see linear310

scaling for A and ⌧ , and reducing influence with larger values of B. This holds

for the equilibrium speed and direction. Needs to be revised!

13

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

to

V = ||~v0||� ↵0⇢ = V 0 � ↵0⇢ (16)

i.e. we see a linear relation between speed and density. The term ↵0 � 0

describes the reduction of the speed with increasing density.300

For the direction ~e, we then get:

~e =~v0

||~v0|| = ~e0 (17)

In other words, in homogeneous density conditions the direction of the pedestri-

ans is equal to the desired direction. Clearly, the gradient of the density yields

pedestrians to divert from their desired direction.

Looking further at the expressions for ↵0 and �0, we can see the influence of305

the various parameters on their size; ↵0 scales linearly with A and ⌧ , meaning

that the influence of the density on the speed increases with increasing values

of A and ⌧ . At the same time, larger values for B imply a reduction of the

influence of the density. Needs to be revised!

The same can be concluded for the influence of the gradient: we see linear310

scaling for A and ⌧ , and reducing influence with larger values of B. This holds

for the equilibrium speed and direction. Needs to be revised!

13

!v = !e ⋅V

Page 29: TFT 2016 summer meeting Sydney

29

Macroscopicmodelyieldsplausibleresults…• Firstmacroscopicmodelabletoreproduceself-organisedpatterns

• Self-organisationbreaksdownsincaseofoverloading

• Continuummodelseemstoinheritpropertiesofmicroscopicmodelunderlyingit

• Formsbasisforreal-timeprediction

• Firsttrialsinmodel-basedoptimisationanduseofmodelforstate-estimationarepromising

Page 30: TFT 2016 summer meeting Sydney

Whataboutcyclistsandmixedflows?Isself-organisationalsopresentthere?

Cyclebehaviour(interaction)experiements…

Page 31: TFT 2016 summer meeting Sydney

Acloserlookatself-organisation

• The game-theoretic model allows studying which factors and processes affect self-organisation:- Breakdown probability is directly

related to demand (or density)

- Heterogeneity negatively affects self-organisation (“freezing by heating”)

- Anisotropy affects self-organisation negatively

- Cooperation and anticipation improve self-organisation (see example)

• Let us pick out some examples…

Page 32: TFT 2016 summer meeting Sydney

Modellingbicyclesflows

• Game-theoretical framework can be “relatively easily” generalised to model behaviour of cyclists

• Main differences entail “physical differences” between pedestrians and cyclists, implying that we describe cycle acceleration in terms of longitudinal and angular acceleration:

• Note that we left out the anisotropy terms to keep equation relatively simple

ap(t) =v0 � v

⌧�Ap

X

q

exp

� ||~rq(t)� ~rp(t)||

Rp

�· ~npq(t) · ~ep(t)

!p(t) =�0 � �(t)

⌧!+ Cp

X

q

exp

� ||~rq(t)� ~rp(t)||

Rp

�· ~npq(t)⇥ ~ep(t)

Page 33: TFT 2016 summer meeting Sydney

Nextstep:calibrationandvalidation

• Model calibration and validation based on experimental data and data collected in the field…

• Advanced video analyses software to get microscopic trajectory data

• First datasets are becoming available…

Page 34: TFT 2016 summer meeting Sydney

Mixingpedestrianandcycleflows…

• Does self-organisation occur in shared-space contexts? Yes!• There are some requirements that need to be met!

- Load on facility should not be too high- Heterogeneity limits self-organisation efficiency- Works better if there is communication (subconscious?) and

cooperation between traffic participants (pedestrians, cyclists)

• Real-life example shows that under specific circumstances shared-space can function efficiently….

• First modelling results show which factors influence self-organisation (e.g. in case of crossing pedestrian and cycle flows)

Page 35: TFT 2016 summer meeting Sydney

Successfulshared-spaceimplementation

Exampleshared-spaceregionAmsterdamCentralStation

Page 36: TFT 2016 summer meeting Sydney

Mixingpedestrianandcycleflows…

• Preliminary simulation results are plausible and self-organisation occurs under reasonable conditions

• Assumption: bikes are less prone to divert from path than pedestrian

• Interesting outcome: pedestrian’s anisotropy improves ‘neatness’ of self-organised patterns

• Further work focusses on getting a validated bicycle model and see characteristics of self-organisation (and the limits therein)

• Outcomes will prove essential for sensible design decisions!

-60 -40 -20 0 20 40 60x (m)

-30

-20

-10

0

10

20

30

y (m

)

25 30 35 40 45 50 55 60 65 70 75time (s)

0

0.5

1ef

ficie

ncy

(-)

Page 37: TFT 2016 summer meeting Sydney

Mixingpedestrianandcycleflows…

• Preliminary simulation results are plausible and self-organisation occurs under reasonable conditions

• Assumption: bikes are less prone to divert from path than pedestrian

• Interesting outcome: pedestrian’s anisotropy improves ‘neatness’ of self-organised patterns

-60 -40 -20 0 20 40 60x (m)

-30

-20

-10

0

10

20

30

y (m

)

25 30 35 40 45 50 55 60 65 70 75time (s)

0

0.5

1ef

ficie

ncy

(-)

• Further work focusses on getting a validated bicycle model and see characteristics of self-organisation (and the limits therein)

• Outcomes will prove essential for sensible design decisions!

Page 38: TFT 2016 summer meeting Sydney

Closingremarks…

• Presentation provides overview of past and current activities• Focus on monitoring, modelling (macro and micro), prediction

and intervention and design• Amongst challenges is understanding interaction between

different modes (pedestrians, cyclists) and understanding level and need of cooperation / communication

• What about interactions between cars and vulnerable modes? • What about interactions between automated cars and

vulnerable modes? What are the impacts to design of streets, crossings, and networks?

• Topic requires more attention!

Page 39: TFT 2016 summer meeting Sydney

Flowoperationsforautomatedbicycles?TheGooglebike…

Cyclebehaviour(interaction)experiements…