GRIDLOCK IN CITIES

Nikolas Geroliminis Carlos Daganzo

Research Goal

• Model a city in macroscopic basis

AND

• Develop system-wide Control strategies

TO

IMPROVE MOBILITY

Why macroscopically?

• Prediction-based models require time dependent O-D tables

• Highly congested networks exhibit chaotic behavior1, 2

1, 2 Daganzo, 1998 and 2005

EXISTING MODELS ARE NOT REALISTIC AND APPROPRIATE TO DEAL WITH CROWDED CONDITIONS

URBAN GRIDLOCK: KEY ISSUES

• Move from PREDICTION to OBSERVATION

• ROBUST APPROACH

PROPOSE→ MONITOR→MODIFY

• Information Technology

Fundamental Diagram (FD) for a link i

• 3 Regimes I : UndersaturatedII : Efficient III : Oversaturated Growing queues from the downstream link block the arrivals

• Accumulation : ni (vehs)• Travel Production : Pi (veh-km/hr)• Output : ei (vh/hr)

Pi , ei

ni

Qi(ni)

αQi(ni)=Gi(ni)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

accumulation /( Length * Lanes)

Tra

vel

Pro

du

ctio

n /

( L

eng

th *

Lan

es *

Gre

en) (610, 139)

(154, 626)

(609, 610)

FD Generalization to networks

i i i i

i i i i

P P Q n Q n

e e G n G n

i i i

i i i

P P Q n

e e G n

AGGREGATE BEHAVIOR =

SCALED UP VERSION OF LINK BEHAVIOR

AGGREGATE DYNAMICS1

Given : inflow O

Exit function G(n)

dn tO t G n t

dt

e = G(n)

1 Daganzo (2005)

Theory Validation (I)

0.3 km1000ft

0

300000

600000

900000

1200000

1500000

0 2000 4000 6000 8000 10000

accumulation (vhs)

Tra

vel

Pro

du

ctio

n (

vh-m

eter

s p

er 2

cyc

les)

A

B

C

D

BIGGER IS BETTER!

Traffic Regimes

A B

C D

Theory Validation (II)

0

20000

40000

60000

0 20 40 60 80 100 120time

cum

ula

tive

(vh

s)

0

5000

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15000

20000

accu

mu

lati

on

(vh

s)

INPUT OUTPUT PREDICTION ACCUMULATION

Production OBSERVABLE - Output UNOBSERVABLE

0

20000

40000

60000

0 20 40 60 80 100 120time

cum

ula

tive

(vh

s)

0

5000

10000

15000

20000

accu

mu

lati

on

(vh

s)

Theory Validation (III)

R2 = 0.97

0

100

200

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400

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800

900

0.0E+00 2.0E+05 4.0E+05 6.0E+05 8.0E+05 1.0E+06 1.2E+06 1.4E+06 1.6E+06Travel Production (VMT)

OUTFLOW

1OUTFLOW

TRAVEL PRODUCTION AVERAGETRIP LENGTH

Theory Validation (Ongoing)

• Field ExperimentJapan – Yokohama

– 400 taxis (GPS data)

– Loop detector counts

Partner: Masao Kuwahara (University of Tokyo, Japan)

1 km0.62mil

11 2 2 2 12 1 1

1 1 1 21 2 2

11 1 1

min ,

min ,

dnq x C n f G n

dt

x C n f G n

f G n

R2

R1

R1

R2

inflow

ni

Ci(ni)outflow

ni

Gi(ni)

Dynamics of a 2-reservoir system

0

20000

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0 200 400 600 800 1000

time

vhs

cum trips endedR1cum trips endedR2cum trips endedR1,2

0

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100000

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0 200 400 600 800 1000

time

vhs

cum trips ended R1

cum trips ended R2

cum trips endedR1,2

0

20000

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0 200 400 600 800 1000

time

vhs

accumulation R1

accumulation R2

0

20000

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100000

120000

140000

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180000

0 200 400 600 800 1000

time

vhs

accumulation R1

accumulation R2

Gridlock Simulation

BE

FO

RE

CO

NT

RO

L

WIT

H C

ON

TR

OL

R2

R1

PARETO EFFICIENT

Applications (I)• Transport Modeling for Nairobi Metropolitan Area

– Improve the vehicle-carrying capacity

– Improve the passenger-carrying capacity

– Demand management

strategies

Joint project (Columbia University and UC Berkeley)

Applications (II)Xi’an (China)

Collaborator: Yuwei Li (University of California, Berkeley)

Ongoing Work (I) • Multi-reservoir systems

– more or less homogeneous in traffic loads

– reasonable static and dynamic system representation

• The effect of parking – Decrease in the outflow

– Dynamic Behavior

Ongoing Work (II) Optimum Control Strategies

• How and Where to control?– Efficient– Equitable

• Pricing – Parking– Tolls

• Multimodal Systems

R2

R1

QUESTIONS - SUGGESTIONS