Bursts and avalanches in the dynamics of polycentric cities

ENGINEERING LEADERSHIP BY SYSTEMS ENGINEERING18 January, 2012

Danny Czamanskihttp://complexcity.csregistry.org/

Technion - Israel Institute of Technology

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Activities in the labActivities in the lab

Analyses of the joint dynamics of cities and nature:

•ISF funded project – joint dynamics of cities and nature;

•Lower Saxony funded project – joint dynamics of cities, agriculture and biodiversity;

•Multi-year, on-going inter-university workshop of faculty members and grad students.

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Cities and Nature

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Series Editors: Daniel Czamanski, Israel Institute of

Technology (Coordinating Editor) Itzhak Benenson, Tel Aviv UniversityHenk Folmer, University of GroningenElena Irwin, The Ohio State University

Czamanski, D., Benenson, I., Malkinson, D., (eds.) Modeling of Land-Use and Ecological Dynamics, Berlin, Springer International Publishers, signed contract, forthcoming in 2013  Czamanski, D., Benenson, I., Malkinson, D., Cities and Nature, Berlin, Springer International Publishers, signed contract, forthcoming in 2012

Our goalOur goal

To depict and explain urban dynamics characterized by:

•Discontinuity in space;

•Non uniformity in time;

•Emergence of multiple sub-centers.

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MotivationMotivation

Dissatisfaction with classical urban models:

• Inability to generate polycentric spatial structures;

• Very limited dynamics;• Accord with reality at a crude spatial resolution

only.

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MotivationMotivation

Alonso type models:• Focus on the demand-side; • Depict spatial configuration once stable equilibrium has been achieved;• Results in mono-centric cities.

Real cities do not evolve as predicted by Alonso!

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MotivationMotivation

• Cities are discontinuous in space and time

Built area of Tel Aviv metropolis:1935, 1941, 1952, 1964,1974, 1985,1993, 2000

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MotivationMotivation

• Multiple high-rise buildings clusters

Building heights distribution in Tel Aviv: 1972, 1986, 2003 88

New agent-based CA modelNew agent-based CA model……

• Both demand and supply are taken into account

• Much of the urban space dynamics and configuration may be explained by out-of-equilibrium situations

• Out-of-equilibrium opportunities for developers lead to outcomes difficult to explain under strictly stable equilibrium frameworks.

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AssumptionsAssumptions

• Real-estate developers’ behavior is influenced by site specific parameters:

•Willingness to pay for real-estate products•Land purchase price•Characteristic time: Spans the time from

the purchase of property rights until realization of a return

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Previous WorkPrevious Work

• Developer’s behavior in a linear space between two cities

• Profits are influenced by time incidence of costs and revenues… there are local maxima…developers’ location decisions create edge cities.

Czamanski D., Broitman D. "Developers' choices under varying characteristic time and competition among municipalities". Annals of Regional Science

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• Two developers types:

• Impatient developers characterized by financial constraints and are therefore unable to wait long periods of time to realize a return of investment

• Patient developers have financial capabilities and can afford longer delay times risks in land purchase decisions.

AssumptionsAssumptions

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• The playground: A square grid of cells (parcels)• Cells attributes:

• Characteristic time• Status • Built height• WTP

• Land price

Dynamic model of sub-centersDynamic model of sub-centers

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Dynamic model of sub-centersDynamic model of sub-centers

• City’s population grows steadily

• City policy: • Characteristic time is a function of location and height

• Concentrated development around the CBD is preferred, but …

• Spatial policy adaptation

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Dynamic model of sub-centersDynamic model of sub-centers

City planners:

•Monitor the city evolution by means of:

•Excess of demand (ED)•Development pressure (P)

•Intervene if their combination is above a predefined “urbanization threshold”

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)max(PEDUTh

Dynamic model of sub-centersDynamic model of sub-centers

• City planners:

•Identify the cluster with maximal development pressure

•Change the local land use policy defining a low characteristic time circle around it

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Dynamic model of sub-centersDynamic model of sub-centers

• Each constructed building changes the WTP and the land price in its surroundings

• Developed high- building sites tend to attract more development in their surroundings

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• Impatient developers only

Dynamic model of sub-centersDynamic model of sub-centers

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• Mixed patient / impatient developers

Dynamic model of sub-centersDynamic model of sub-centers

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Dynamic model of sub-centersDynamic model of sub-centers

• A visual example of bursts creation and development pressure areas

Model results and Self Organizing Criticality (SOC)

• The SOC concept was coined in order to describe non-equilibrium systems which respond to an external perturbation with events of all sizes and no apparent characteristic scale.

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Model results and SOC

•Our model dynamics and results resemble the SOC metaphor;

•A stable system, driven out of equilibrium by endogenous agents, causing bursts of activity of several sizes at unexpected times.

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Model results and SOC

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Model results and SOC

The bursts distribution has two well-defined ranges:

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Patient developers only

Bursts created by mixed developers

Model results and SOC

The upper range represents the adversarial interaction between planning authorities and developers

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LN(Burst size)

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Model results and SOC

Interpreting “construction bursts” as “avalanches” leads to suggestive rank-size results:

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y = 11143x-0.6474

R2 = 0.9361

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ConclusionsConclusions

• Characteristic time is important determinant of profitability levels

• Developers’ time aversion influences site and intensity choices

• Urban spatial structure reflects different types of developers

• Polycentric structure emerges as a result of developers’ choices

• A self-organizing system approaching a critical state ?

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