The mathematical model of urban dynamics introduced in an earlier paper is applied to a case study in a small region in the southern part of Switzerland. The model mixes the point of view of cellular automata (cellular decomposition of the space, neighbourhood relations among cells, dynamics based on local evolution rules) with the approach to multiagent systems: the dynamics of the urban system are described in terms of decision processes of agents formalized using fuzzy-decision-theory methods. The region chosen for the case study evolves under the pressure of the nearby city of Lugano, owing to several factors: the accessibility of the area from Lugano, the availability of spatial resources for new development, the high level of quality of space, and the high level of congestion of Lugano. Local changes in the master plan from agricultural to residential use are taken into account, by introducing suitable memory variables that keep track of the demand of spatial resources for building in the recent past. Computer simulations showing the time evolution of the spatial distribution of the population and the real estate value are presented. The use of measures of attractiveness based on a fuzzy logic approach, and of Poisson-distributed events, enables us to introduce new effective approaches to parameter calibration and model validation.
A new kind of cellular automaton (CA) for the study of the dynamics of urban systems is proposed. The state of a cell is not described using a finite set, but by means of continuum variables. A population sector is included, taking into account migration processes from and towards the external world. The transport network is considered through an integration index describing the capability of the network to interconnect the different parts of the city. The time evolution is given by Poisson distributed stochastic jumps affecting the dynamical variables, with intensities depending on the configuration of the system in a suitable set of neighbourhoods. The intensities of the Poisson processes are given in term of a set of potentials evaluated applying fuzzy logic to a practical method frequently used in Switzerland to evaluate the attractiveness of a terrain for different land uses and the related rents. The use of a continuum state space enables one to write a system of differential equations for the time evolution of the CA and thus to study the system from a dynamical systems theory perspective. This makes it possible, in particular, to look systematically for bifurcations and phase transitions in CA based models of urban systems.
A new modelling framework for the study of the dynamics of urban systems is proposed. We generalize the notion of cellular automaton, using continuous variables to describe the state of a cell. The time evolution is given by Poisson-distributed stochastic jumps corresponding to urban interactions, with intensities depending on the configuration of the system in a suitable set of neighbourhoods. These interactions result from decision processes of populations of cognitive agents modelled in the framework of fuzzy decision theory. The behaviour of agents is driven by goals and constraints, partially defined using a fuzzy logic formalization of a real estate appraisal method based on the evaluation of the attractiveness of a terrain for different land uses. Randomness of the dynamics is a consequence of the fuzziness of these decisions. Hence the model can be seen as a multiagent system with sound mathematical foundation. For example, the use of a continuum-valued state space enables us to prove that the expectation of state variables verify a system of differential equations, and thus to study the system from a dynamical systems theory perspective. In this paper we present the theoretical setting, leaving the applications to a second paper.
In this paper, we present an agent-based model aiming at supporting decisions about the planning of shopping malls (SM), with a main focus about their environmental impact. The model forecasts the traffic flows induced by SM at the regional level on the whole road network of Canton Ticino (Switzerland), and has been used by the public administration as a support to decide master plan rules. The system has been modeled as an interaction space, a new type of modeling framework that includes both multi-agent systems and cellular automata as a particular case. We define a grammar to specify different agents' trips, and we associate a fuzzy logic based indicator to each one of these specifications. Similarly, we define attractiveness indicators for zones containing economical activities related to agents' trips. The use of these indicators permits to obtain agents' location choices of secondary activities with a great computational efficiency. Simulations include several environmental indicators, like concentrations of nitrogen dioxide, counting changes in a given small part of a road or an estimation of roads' level of service.
The purpose of the paper is to discuss some potential applications of random media theory to urban modelling, with the emphasis on the intermittency phenomenon. The moment test of intermittency is explained using the model of continuous-time branching random walk on the integer lattice Z d with random branching rates. Statistical moments of the population density are studied using a Cauchy problem for the Anderson operator with random potential. The Feynman-Kac representation of the solution is discussed, and Lyapunov exponents responsible for the super-exponential growth of the moments are evaluated. The higher-order Lyapunov exponents are also obtained. The results suggest that the higher-order intermittency is reduced, in a sense, to that of the mean population density.
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