Morphology of urban conglomerations:
experimental and theoretical modeling,
and implications for everyday traffic
Massimo Pica Ciamarra
Antonio Coniglio
Dipartimento di Scienze Fisiche
Università di Napoli Federico II
Crdc-AMRA
Physics and the city, Bologna, 15 Dic. 2005
Outline
Motivation
Urban morphology: empirical analysis
theoretical modeling
Evacuation
Conclusions
• Motivation
• Evacuation
• Urban morphology
• Conclusions
Mt. Vesuvius
Eruption
forecast
-1980
Mt. St. Elena
24 h
Mt. Vesuvius
- 1991
Mt. Pinatubo
48 h
Population: 500.000
- 1996
Mt. Ruapehu
6 days
Ercolano
Mt. Vesuvius
Pompei
estimate: 14 days
People to be evacuated: 500.000
Naples
- ???
Mt. Vesuvius
14 days
• Motivation
• Evacuation
• Urban morphology
• Conclusions
Evacuation time
Numbers
• People: 500.000
• Safety distance: d = 50 Km
Evacuation time
no
?
v = 4 Km/h
T = 12h 30m
v = 20 Km/h
T = 2h 30m
yes
v = 40 Km/h
T = 1h 15m
Congestion ?
• Motivation
• Evacuation
• Urban morphology
• Conclusions
The road network: Rome
20
Km
1.5 Km
20 Km
• Motivation
• Evacuation
• Urban morphology 1. Empirical analysis
• Conclusions
2. Theoretical modeling
A grid element
Maps: www.maporama.com
=
# black pixels
# pixels
1px = 2 m2
1.1 Km
P.za Venezia
Campidoglio
1.5 Km
• Motivation
• Evacuation
• Urban morphology 1. Empirical analysis
• Conclusions
2. Theoretical modeling
Andamento di (r) per la città di Roma
0.3
 (r )   0 
 (r )
 max   0
2
 r  rN
Erfc 
 2 N




rN  8.7 Km
 N  1.7 Km
0.2
0
0.1
0
10
20
• Motivation
• Evacuation
30
40
r (Km)
• Urban morphology 1. Empirical analysis
• Conclusions
2. Theoretical modeling
Cluster growth: background
Diffusion-Limited Aggregate
r
P(r , N ) 
1
2  N
Eden Model
 r  rN 2 

Exp  
2

2

N


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).
rN  N 
 N  N '
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).
• Motivation
• Evacuation
• Urban morphology 1. Empirical analysis
• Conclusions
2. Theoretical modeling
Random walk cluster growth model
Assumptions:
 rN
1: N  
 r0



2
PRW CG (r , N ) 

2: rN 

r

1
rN  r0 N ;  
2

random walk with a drift
Mean: v  0
St. Dev.: 
P(r , N ) 
r
1

2  N
3: P(r  rN )  r
 r  rN 2 

Exp  
2

2

N


1
 N   0 N ; ' 
4
'
• Motivation
• Evacuation
• Urban morphology 1. Empirical analysis
• Conclusions
2. Theoretical modeling
Growth probability
Probability of building a city unit in a point
at a distance r form the center
 (r , N )
P(r , N ) / r
• Motivation
• Evacuation
• Urban morphology 1. Empirical analysis
• Conclusions
2. Theoretical modeling
Radial density
 (r , N ) 
1
N
P

2 r
(n,r)dn   0 
RW CG
0
• Motivation
• Evacuation
 max   0
2
 r  rN
Erfc 
 2 N




• Urban morphology 1. Empirical analysis
• Conclusions
2. Theoretical modeling
Evacuation and bottlenecks: Rome
expansion compression
expansion
S (r )  2 r  (r )
20
0.3
 (r )
0.25
S (r )
(Km 2 )
0.2
10
0.15
0.1
0
10
20
30
r (Km)
0.05
40
• Motivation
• Urban morphology
• Evacuation • Conclusions
Optimization of the evacuation process
One entries
entry ? ?
Two
• Motivation
• Urban morphology
• Evacuation • Conclusions
Entry ramps
Simulation with the Extended Nagel - Schreckenberg model
Knospe et. al., Phys. Rev. E 70, 016115 (2004).
Qexit = Qupstream + Qin
Qupstream
Qexit
Qin
p
Entry ramp model
If we can insert a car in the main flow without causing accidents
We insert the car with probability p
p = 0: cars are never inserted
p = 1: a car is inserted as soon as possible
Qexit = Q(p1,…,pn)
M. Pica Ciamarra, Phys. Rev. E 72, 066102, (2005).
• Motivation
• Urban morphology
• Evacuation • Conclusions
Example: two entries – two lane road
1
Q (cars/h)
1600
p2
1200
800
400
0.5
0
Max:
(p1, p2)  (0.35,0.5)
0
0
0.5
p1
1
Q1  900 cars/h
Q2  700 cars/h
• 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 voi
un giorno è lume all'altro
e il dì precedente è norma per il dì che segue
udite
E. Fonseca y Zunica,
venti volte da che splende il sole
Vicerè (1632)
se 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 colpisca
io 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 geme
trema, 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 fiume
che vien giù precipitando e sbarra la fuga a chi s'attarda
se ti coglie e' finita: sei morto
disprezzato 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.
Radial density (r)
Round cities

y
r
 ( x, y )
 (r )
• Motivation
• Evacuation
x
• Urban morphology 1. Empirical analysis
• Conclusions
2. Theoretical modeling
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).