from trafﬁc ﬂow modeling to demand modeling for large ... › physics_of_the_city › contributi...

From traffic flowmodeling to

demand modelingfor large scale

multi-agentsimulations ofurban systems

Kai Nagel, TUBerlin

Outline

Introduction

Conventionalmethod → MASim

The physical world(= mobilitysimulation)

The mental world(strategic level)

Learning

A real world casestudy

Towards the nextreal world casestudy

Overall summary

From traffic flow modeling todemand modeling for large scalemulti-agent simulations of urban

systems

Kai Nagel, TU Berlin

15. Dezember 2005

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Kai Nagel, TUBerlin

Outline

Introduction




Learning



Overall summary

Outline

Introduction

Conventional method → MASim

The physical world (= mobility simulation)

The mental world (strategic level)

Learning

A real world case study

Towards the next real world case study

Overall summary

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Kai Nagel, TUBerlin

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Learning



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Kai Nagel, TUBerlin

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Introduction




Learning



Overall summary

The questions

Assume a modification in the urban system, e.g.conversion of some car street into pedestrian mall.Consequences:

I Car traffic goes somewhere else (where?).I People switch from car to public transit.I People go somewhere else (e.g. avoid inner city).I People relocate (e.g. move to inner city).I Property prices change.I Emissions change.I Etc.

⇒ Useful: Tool that is able to approach thesequestions. (Cf. Bazzani presentation yesterday)

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Kai Nagel, TUBerlin

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Learning



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Kai Nagel, TUBerlin

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Introduction




Learning



Overall summary

Conventional method: 4-step process

1. Trip generation: Find sources and sinks for trips. ≈land use, makes sense.

2. Trip distribution: Connect sources and sinks ...pij ∝ 1/dij ...

3. Modal split: Determine fraction of trips that doesnot use cars ...

4. Route assignment: Find routes for car trips ...similar to current assignment in resistor networkexcept that particles have destination...

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Kai Nagel, TUBerlin

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Introduction




Learning



Overall summary

What’s good about 4-step process?

Solution has some uniqueness properties.

⇒ Any correct computation will yield same result.

Simplifies analysis enormously.

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Kai Nagel, TUBerlin

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Introduction




Learning



Overall summary

What’s bad about 4-step process?

Does not accomodate many modern questions: peakspreading, 2-destination plans, telematics, emissions,...

Incremental steps towards any of these (“physicalqueues”, spillback) destroy uniqueness property

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Kai Nagel, TUBerlin

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Introduction




Learning



Overall summary

Multi-agent simulation

Alternative to 4-step process: Multi-agent simulation

Everything (travelers, vehicles, traffic lights, etc.) isindividually resolved ...

... in principle. :–)In practice, limits of

I coding,I knowledge,I data needs.

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Kai Nagel, TUBerlin

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Introduction




Learning



Overall summary

Physical vs. strategical level in MASim

The mental world:

− limits on accel/brake− excluded volume− veh−veh interaction− veh−system interaction− ped−veh interaction− etc.

� ��

� ��

� � � �

� � � ��

� ��

Concepts which are insomeone’s head.

plans(acts,routes,...)

per−for−

manceinfo

The physical world:

(once more, cf. Bazzani yesterday)

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Kai Nagel, TUBerlin

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Introduction




Learning



Overall summary

Next three parts of talk

I Physical level: engineering, physics.

I Strategical level: psychology, sociology, AI

I Interaction between these two (learning,adaptation)

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Kai Nagel, TUBerlin

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Learning



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Kai Nagel, TUBerlin

Outline

Introduction




Learning



Overall summary

Techniques for the physical layer

I Cellular automata. On graphs/2d space.

I Molecular Dynamics / coupled maps. E.g. forpedestrians (Bazzani talk. Helbing talk?).

I Queue(ing) sim. “Hourglass:” Vehicles move onlink with free speed until they hit queue; queue isserved first come first serve according to capacity.

Essentially queueing theory, but link can be full(spillback). [[Vis big zrh]]

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Kai Nagel, TUBerlin

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Introduction




Learning



Overall summary

Summary of “physical world”

I There is technology to work with.

I Many of it comes from (computational) physics.

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Kai Nagel, TUBerlin

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Kai Nagel, TUBerlin

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From particles to agents

Make particles “intelligent” ⇒ agents.

E.g.: Destination, day-plan, weekly plan, socialstructure, beliefs/desires/commitments, etc.

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Kai Nagel, TUBerlin

Outline

Introduction




Learning



Overall summary

Physical level vs strategic level

The mental world:

− limits on accel/brake− excluded volume− veh−veh interaction− veh−system interaction− ped−veh interaction− etc.

� ��

� ��

� � � �

� � � ��

� ��

Concepts which are insomeone’s head.

plans(acts,routes,...)

per−for−

manceinfo

The physical world:

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Kai Nagel, TUBerlin

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Introduction




Learning



Overall summary

A census block (A):

Portland, Block Group 321012

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Kai Nagel, TUBerlin

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Introduction




Learning



Overall summary

Synthetic population (A)(from census data)

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193238126

165

2128 7

104 37

34

11 27

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321

19 26

239

33

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504

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307

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5437

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151

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1366

2131

3431

15

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98

16

30

HOUSEHOLDS BG 312002

•

see TRANSIMS www.Method by R.J. Beckman;

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Kai Nagel, TUBerlin

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Introduction




Learning



Overall summary

Individual plans (B), (C)

HOME

WORKLUNCH

WORK

DOCTOR

SHOP

HOME

HUSBAND’S ROUTES

Plans for routes ->

HOME

WORKLUNCH

WORK

DOCTOR

SHOP

HOME

HUSBAND’S ACTIVITIES <- Plans for activities

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Kai Nagel, TUBerlin

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Introduction




Learning



Overall summary

Plans in XML

<person id="241" income="50000"><plan score="123">

<act type="h" end_time="07:00" x100="7150"y100="2790" link="5834" />

<leg mode="car" dept_time="07:00" trav_time="00:25"><route>1932 1933 1934 1947</route>

</leg><act type="w" dur="09:00" x100="0650"

y100="3980" link="5844" /><leg mode="car" dept_time="16:25" trav_time="00:14">

<route>1934 1933</route></leg><act type="h" x100="7150" y100="2790" link="5834" />

</plan></person>

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Kai Nagel, TUBerlin

Outline

Introduction




Learning



Overall summary

Methods for plans

Try hierarchical model. For each agent:

1. Activity pattern (e.g.home-work-shop-leisure-home)

2. Approximate times (e.g. start in morning)

3. Locations for primary acts (work)

4. Mode choice

5. Locations for secondary acts

6. Precise times

7. Routes

Combinations possible (“simultaneous choice of ...”)

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Kai Nagel, TUBerlin

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Introduction




Learning



Overall summary

Methods for plans, ctd

The following techniques are useful on some levels ofdemand modelling (plans generation):

I Making draws from statistical distributionsI Discrete choice modelsI Rule-based systemsI OR-type optimization (e.g. shortest path)I Genetic algorithmI Q-learningI Mental map

These are not central to this talk; our preference wouldbe to receive them from outside as plug-in modules.

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Kai Nagel, TUBerlin

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Introduction




Learning



Overall summary

The mental world, summary

I Methods to construct complete daily plans ofagents (act patterns, act locations, act times,mode choice, routes).

I This is rather different from “mainstream” physics(computer science, combinatioral optimization,artificial intelligence, ...).

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Kai Nagel, TUBerlin

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Introduction




Learning



Overall summary

Outline

Introduction




Learning



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Kai Nagel, TUBerlin

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Introduction




Learning



Overall summary

Learning

Simultaneous execution of all plans causes emergenteffects (e.g. congestion) ...

... which means that “good” plans are no longer good.

⇒ agents revise plans

Co-evolution

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Kai Nagel, TUBerlin

Outline

Introduction




Learning



Overall summary

Learning, ctd

Standard method: Iterations:

1. All agents have an initial plan.

2. Plans are executed in the mob.sim.

3. Some or all agents revise their plans.

4. Goto 2.

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Kai Nagel, TUBerlin

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Introduction




Learning



Overall summary

Replanning example

TOP: initial plans BOTTOM: after 15 iterations

“Wider” spread of traffic.

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Kai Nagel, TUBerlin

Outline

Introduction




Learning



Overall summary

Strategy dimensions

home

route 1

route 2

workplace A

workplace B

route 3

Routes, modes, times, locactions, patterns,residences, life style, commercial location choice, ...

In words: Adaptation at all levels of the demandhierarchy.

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Kai Nagel, TUBerlin

Outline

Introduction




Learning



Overall summary

Traditional approach to learning (intraff sims)

Agents forget old plan when they get new one (noagent memory).

Disadvantages:I Conceptually problematic.I Not robust against small mis-specifications in

information exchange between modules.I External modules need to be “always” correct.

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Kai Nagel, TUBerlin

Outline

Introduction




Learning



Overall summary

Better: multiple plans per agentI Each agent has several plans, with score:

Description of plan 1 Score of plan 1Description of plan 2 Score of plan 2

...

I “Period” (e.g. day, week) is run over and overagain; score is updated every time plan is used.

I Normally, agent selects a “good” plan.

I Sometimes, agent re-tries presumably bad plan.

I Sometimes, bad plans are replaced by new ones.

Essentially a classifier system/genetic algorithm onlevel of agent.

Much more robust ...32 / 55




Kai Nagel, TUBerlin

Outline

Introduction




Learning



Overall summary

Scoring function

Arbitrary scoring function can be used, e.g.:I Utility functionI Risk-averse averagingI Prospect theoryI ...

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Kai Nagel, TUBerlin

Outline

Introduction




Learning



Overall summary

Plans, ctd

I Plans are descriptions of intentions. They aresubmitted to the “physical world”, which executesthem, and returns performance information.

I They refer to a whole “period” (day, week, ...).

(This has something to do with game theory.)

I A plan can be conditional (“if jam then ..., else ...”).

I A plan can be revised during execution.

I A plan can be incomplete, filled during execution.

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Kai Nagel, TUBerlin

Outline

Introduction




Learning



Overall summary

Short excursion to game theory anddynamical systems

Our approach similar to evolutionary game theory:One “game” = one day (period); evol. dynamics fromone game to next.

Evolutionary games (with “best reply” or similar) canconverge to Nash Equilibrium (NE), but can also haveperiodic or chaotic attractors.

For our models, we do not know much about:I Type of attractor, basin of attractionI What happens when agents replan during the day.

(Subgame perfect equilibrium ... but how do youiterate (evolve) that??)

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Kai Nagel, TUBerlin

Outline

Introduction




Learning



Overall summary

Learning & Strategies, summary I

Plans

Module:RoutesActivities

Module:

Physical Simulation

(Interaction)

ag1 ag2 ag3 ...

Agent Database

mental level

physical level Eve

nts

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Kai Nagel, TUBerlin

Outline

Introduction




Learning



Overall summary

Learning & Strategies, summary II

I Co-evolutionary dynamical system.

I Has again a lot of physics (I think).

I Not enough explored (Cascetta; Watling)

I Enormous consequences of real-worldinterpretability of results.

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Kai Nagel, TUBerlin

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Introduction




Learning



Overall summary

Outline

Introduction




Learning



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Kai Nagel, TUBerlin

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Introduction




Learning



Overall summary

Scenario

I Network of CH with 20 000 links (major streetsonly).

I Demand: “Home-work-home” acts for all carcommuters in Zurich metro area (approx300 000 agents).

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Kai Nagel, TUBerlin

Outline

Introduction




Learning



Overall summary

Modules

timer

syn.pop

act.chains

prim.act.loc

mode choice

2nd.act.loc

timer

router

mob.sim

learning

learning depth

no memory

router

from census

from census

fixed fraction

fr. OD matrices

(GA−)optimizer

mental map

CA

gravity model

schedule based

mode

mental map

...

from time use survey

anchored (prim.act.loc)

from OD matrix

"fake"

OD matrices

car only

none

simple hill−climbing

best path (last it’n)

queue

agent memory

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Kai Nagel, TUBerlin

Outline

Introduction




Learning



Overall summary

Learning/feedback/agdb

I Scoring

Utotal =n∑

i=1

Uact,i +n∑

i=1

Ulate,i +n∑

i=1

Utrav ,i ,

Uact,i(tact,i) ∝ ln(tact,i) .

(Vickrey-type dp time choice ... but whole24h-days.)

I Choice between plans eβ Ui . IMPORTANT!!!!

I Sometimes new plans from time mutator, router.

I Many many iterations.

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Kai Nagel, TUBerlin

Outline

Introduction




Learning



Overall summary

Scoring, exampletime

@home @workplace @lunchtravel

workplace opening time

Notes:I Blue dots = values that are added up.I Marginal utls (red) need to be same at optimal

solution.42 / 55




Kai Nagel, TUBerlin

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Introduction




Learning



Overall summary

Application

[[Vis: ch w times-rt]]

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Kai Nagel, TUBerlin

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Introduction




Learning



Overall summary

Departure time distribution

[[bigfiles/movies/dp-time-histos.eps]]

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Kai Nagel, TUBerlin

Outline

Introduction




Learning



Overall summary

Validation (7am to 8am, volumes)

This study:

1000

1000

Eve

nts-

base

d T

hrou

ghpu

t

Count Data

counts_vs_350.acts-routes_all6am_hrs7-8.out

datay=x

y=2xy=x/2

VISUM (“best effort”):

1000

1000

Vis

um A

ssig

nem

ent

Count Data

count_vs_visum_hrs7-8.out

datay=x

y=2xy=x/2

This study:. VISUM:.Mean Rel. Bias: +9.4% +42.4%Mean Rel. Error: 30.4% 42.1%

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Kai Nagel, TUBerlin

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Introduction




Learning



Overall summary

A real world case, summary

I About as good as traditional method

I Other results (not shown) similar

I Internalized time choice and resulting microscopictemporal structure goes beyond traditionalmethods

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Kai Nagel, TUBerlin

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Introduction




Learning



Overall summary

Outline

Introduction




Learning



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Kai Nagel, TUBerlin

Outline

Introduction




Learning



Overall summary

Modules, in study just shown

timer

syn.pop

act.chains

prim.act.loc

mode choice

2nd.act.loc

timer

router

mob.sim

learning

learning depth

no memory

router

from census

from census

fixed fraction

fr. OD matrices

(GA−)optimizer

mental map

CA

gravity model

schedule based

mode

mental map

...



from OD matrix

"fake"

OD matrices

car only

none



queue

agent memory

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Kai Nagel, TUBerlin

Outline

Introduction




Learning



Overall summary

Modules, next study

timer ...

...

syn.pop

act.chains

prim.act.loc

mode choice

2nd.act.loc

timer

router

mob.sim

learning

learning depth

no memory

router

fixed fraction

fr. OD matrices

mental map

CA

gravity model

schedule based

mode

mental map

car only


queue

agent memory

from OD matrix

"fake"

OD matrices

none


from census


from census


(GA−)optimizer

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Kai Nagel, TUBerlin

Outline

Introduction




Learning



Overall summary

Departure time distributions, initially

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Kai Nagel, TUBerlin

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Introduction




Learning



Overall summary

Departure time distributions, after 400iterations

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Kai Nagel, TUBerlin

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Overall summary

Outline

Introduction




Learning



Overall summary

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Kai Nagel, TUBerlin

Outline

Introduction




Learning



Overall summary

Summary

I Individual agents.

I Separation into “physical world” (CA et al) and“mental world”.

I We are slowly approaching a fully resolvedsimulation laboratory of human spatio-temporalbehavior in real-world urban systems.

I Theoretial issues coming up, some of them ratherclose to interdisciplinary physics.

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Kai Nagel, TUBerlin

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Introduction




Learning



Overall summary

Space-time plot, principle

..5.......2..1...2......1..2.....4............4..........

.......3....1.2....2.....1...2.......4............4......

..........1..1..3....2....1....2.........5............4..

.4.........1..2....2...3...2.....3............4..........

.....5......2...2....3....1..3......4.............5......

..........3...3...3.....1..1....4.......4..............5.4............3...2...3...2..1.......5.......4................4...........2..2....1..1.1...........4......5................4.........1..2...2..1.2..............5.......4.....4.........4......2...3...1.1..2.................4............5.........4....2....1.0.2...2...................4.............5........2..3...01...2...2....................5...............4.....2...00.1....3...3.......................4..............2...0.01..2......3...3................5.......4............1.0.0.1...3.......3...3..................5......5.........00.1..2.....3.......3...4....................5......3....00..1...3......3.......4....4.....................4....0.01...1.....4......4........4....5.....................01.0.1...2........4......5........4......................1.00..1....3..........4.......4...........................000...2......3...........5.......4......5................000.....3.......3.............5.......4......5...........001........3.......4...............5......5.......4......00.1..........3........5............5..........5......1..01..2............3..........5............5..........2..1.0.2...3.............3............5.....4......4.......1.00...2....3.............3...................4......3....001.....2.....3.............3....................5.....1.00.1......3......4.............4........4.............1.000..1........3.......5.............5..

......4.....1..2.....3...2....3..........5..........5....

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Kai Nagel, TUBerlin

Outline

Introduction




Learning



Overall summary

For experts: Phase trans’n(space-time plots)

↑ weak slow-to-start property

↓ strong slow-to-start property

low density high density

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Kai Nagel, TUBerlin

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Introduction




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Overall summary

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from trafﬁc ﬂow modeling to demand modeling for large ... › physics_of_the_city › contributi...

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