Morphology of urban conglomerations: experimental and theoretical modeling, and implications for everyday traffic Massimo Pica Ciamarra Dipartimento di.

Morphology of urban conglomerations:experimental and theoretical modeling,

and implications for everyday traffic

Massimo Pica Ciamarra

Dipartimento di Scienze FisicheUniversità di Napoli Federico IICrdc-AMRA

Antonio Coniglio

Physics and the city, Bologna, 15 Dic. 2005

Outline

Motivation

Urban morphology: empirical analysis

theoretical modeling

Evacuation

Conclusions

• Motivation • Urban morphology

• Evacuation • Conclusions

Mt. Vesuvius

• Motivation • Urban morphology

• Evacuation • Conclusions

People to be evacuated: 500.000

Eruption forecast

Mt. Vesuvius estimate: 14 days

-1980 Mt. St. Elena 24 h

- 1991 Mt. Pinatubo 48 h

- 1996 Mt. Ruapehu 6 days

- ??? Mt. Vesuvius 14 days

Population: 500.000

Mt. Vesuvius

Naples

Ercolano

Pompei

Evacuation time

Numbers

• People: 500.000• Safety distance: d = 50 Km

Evacuation time

v = 4 Km/h

T = 12h 30m

v = 20 Km/h

T = 2h 30m

v = 40 Km/h

T = 1h 15m

Congestion ?

no yes

?

• Motivation • Urban morphology

• Evacuation • Conclusions

The road network: Rome

20 Km

20 Km

1.5 Km

• Motivation • Urban morphology1. Empirical analysis2. Theoretical modeling• Evacuation • Conclusions

P.za Venezia

1.1 Km

A grid element

= # black pixels

# pixels

P.za N

avona

Via del C

orso

Via N

azio

nale

Campidoglio

1.5 Km

Maps: www.maporama.com

1px = 2 m2

• Motivation • Urban morphology1. Empirical analysis2. Theoretical modeling• Evacuation • Conclusions

0

Km7.8Nr

N

Nrrr

2Erfc

2)( 0max

0

0.3

0.2

0.1

10 20 30 400

)(r

(Km) r

Andamento di (r) per la città di Roma

Km7.1N

• Motivation • Urban morphology1. Empirical analysis2. Theoretical modeling• Evacuation • Conclusions

Cluster growth: background

• Motivation • Urban morphology 1. Empirical analysis

2. Theoretical modeling• Evacuation • Conclusions

DLA: T.A. Witten and L.M. Sander, Phys. Rev. Lett. 47, 1400 (1981).M. Batty and P. Longley, Area 19, 215 (1987); M. Batty and P. Longley, Env. and Planning B 14, 123 (1987).M. Batty et. al., Env. and Planning A 21, 1447 (1989).

Diffusion-Limited Aggregate Eden Model

M. Eden, Proc. 4° Berkeley Symp. On Mat. Stat. and Probability, Univ. California. Press, (1961).J.D. Weeks et. al., J. Chem. Phys. 65, 712 (1976).L. Benguigui, Physica A 219, 13 (1995).

2

2

2Exp

2

1),(

N

N

N

rrNrP

r

'

N

Nr

N

N

Random walk cluster growth model

• Motivation • Urban morphology 1. Empirical analysis

2. Theoretical modeling• Evacuation • Conclusions

2

2

2Exp

2

1),(),(

N

N

N

RWCG

rrrNrP

rNrP

2

0

r

rN N

Assumptions:

1: 2:

Nrrandom walk with a driftMean: St. Dev.:

0v

rrrP N )(3:

2

1;0 NrrN 4

1';'0 NN

Growth probability

• Motivation • Urban morphology 1. Empirical analysis

2. Theoretical modeling• Evacuation • Conclusions

Probability of building a city unit in a point at a distance r form the center

rNrP /),(

),( Nr

Radial density

• Motivation • Urban morphology 1. Empirical analysis

2. Theoretical modeling• Evacuation • Conclusions

N

NN

RWCG

rr(n,r)dnP

rNr

2Erfc

22

1),( 0max

0

0

Evacuation and bottlenecks: Rome

(Km) r10 20 30 40

0.3

0.1

0.2

0.25

0.15

0.050

10

20

)(Km

)(2

rS

)(r

expansion compression expansion

)(2)( rrrS

• Motivation • Urban morphology

• Evacuation • Conclusions

Optimization of the evacuation process

One entry ?Two entries ?

• Motivation • Urban morphology

• Evacuation • Conclusions

Entry ramps

Qupstream Qexit

Qin

Qexit = Qupstream + Qin

Entry ramp model

p

If we can insert a car in the main flow without causing accidentsWe insert the car with probability p

p = 0: cars are never insertedp = 1: a car is inserted as soon as possible

M. Pica Ciamarra, Phys. Rev. E 72, 066102, (2005).

Simulation with the Extended Nagel - Schreckenberg modelKnospe et. al., Phys. Rev. E 70, 016115 (2004).

Qexit = Q(p1,…,pn)

• Motivation • Urban morphology

• Evacuation • Conclusions

p1

p2

0 10.50

1

0.5

Example: two entries – two lane road

1600

0

800

400

1200

Q (cars/h)

(p1, p2) (0.35,0.5)

Q1 900 cars/h

Q2 700 cars/h

Max:

• Motivation • Urban morphology

• Evacuation • Conclusions

Conclusions

1. Morphology of a city

Empirical study of digital maps (resolution: 2m2)

Simple model of cluster growth (anal. solvable)

Universality - Bottlenecks

2. Optimization of on-ramp entries

Simulation of the extended Nagel-Schreckenberg model

Control of the flux of entering cars

O posteri, o posteri si tratta di voiun giorno è lume all'altro

e il dì precedente è norma per il dì che segueudite

venti volte da che splende il solese non sbaglia la storia

arse il Vesuvio.Sempre con strage immane di chi a fuggir fu lento.

Affinché dopo l'ultimo lutto più non vi colpiscaio vi avviso.

Questo monte ha greve il seno di bitume,allume, zolfo, oro, argento, nitro, di fonte d'acque.

Presto o tardi si accende ma prima gemetrema, scuote il suolo mescola e fumo e fiamme e lampi

scuote l'aria, rimbomba, tuona, muggisce scaccia ai confini gli abitanti.Tu scappa finché lo puoi.

Ecco che scoppia e vomita di fuoco un fiumeche vien giù precipitando e sbarra la fuga a chi s'attarda

se ti coglie e' finita: sei mortodisprezzato apprese gli incauti e gli avidi

cui la casa e le suppellettili furono più care della vita.Ma tu, se hai senno, di un marmo che ti parla

di la voce non ti curar dei lari; senza indugi fuggi.

E. Fonseca y Zunica, Vicerè (1632)

Radial density (r)

Round cities

r

x

y

),( yx )(r• Motivation • Urban morphology

1. Empirical analysis2. Theoretical modeling• Evacuation • Conclusions

Deaths Volcano When Major Cause of Death (no starvation)

36,417 Krakatau, Indonesia 1883 Tsunami

29,025 Mt. Pelee, Martinique 1902 Ash town of Saint Pierre

25,000 Ruiz, Colombia 1985 Mudflows town of Armero

14,300 Unzen, Japan 1792 Volcano collapse, tsunami

5,110 Kelut, Indonesia 1919 Mudflows

4,011 Galunggung, Indonesia 1882 Mudflows

3,500 Vesuvius, Italy 1631 Mudflows, lava flows

3,360 Vesuvius, Italy 79 Ash flows and falls

2,957 Papandayan, Indonesia 1772 Ash flows

2,942 Lamington, Papua N.G. 1951 Ash flows

2,000 El Chichon, Mexico 1982 Ash flows

1,680 Soufriere, St Vincent 1902 Ash flows

1,475 Oshima, Japan 1741 Tsunami

1,377 Asama, Japan 1783 Ash flows, mudflows

1,335 Taal, Philippines 1911 Ash flows

1,200 Mayon, Philippines 1814 Mudflows

1,184 Agung, Indonesia 1963 Ash flows

1,000 Cotopaxi, Ecuador 1877 Mudflows

800 Pinatubo, Philippines 1991 Roof collapses and disease

Volcanic Hazards: A Sourcebook on the Effects of Eruptions, Russell J. Blong (Academic Press, 1984).