The Urban Environment described by Models
The city is certainly a complex object evolving in a non linear way. The urban space-time topology is built up by the melting of aesthetics, biology, physics and sociology, planning and information theory. Moreover in metropolitan territories different citizen populations are mixing, sometime in an harmonic way, sometime conflicting each other.
Since the 60s some mathematical models have tried to describe and/or to explain the urban systems evolutions. In some cases they hoped to be able to predict the effects of planning and/or of the urban transformations, economic, social ones etc.
The first models were statics and/or stationary, with equilibrium or quasi-equilibrium solutions.
One of the most important application of mathematical modelling was on road traffic. Generally it was modelled like an hydrodynamics flux or by Origin-Destination (O-D) matrices, where the origin and the destination are well determined and precisely known in time and spatially.
Obviously when the situation is rapidly evolving and higly dynamical by these models we can't obtain solutions fitting with the observed phenomena. Further the asystematic (brownian) mobility in principle can not dealt with the O-D matrices.
The exponential growth of computing power, the developing of the information theory (automatons and artificial intelligences) and the complex system physics can set up a tools collection for microscopic and dynamic modelling.
The prevailing of asystematic over the origin-destination mobility concerned also the motion of private vehicles. The overall mobility, provided by several networks connected by interchange nodes, has an important chaotic component and often differs form equilibrium or quasi-equilibrium situations, which can be described by mean field theories, such as the origin destination models. The final goal is to reach a sustainable mobility where the different transportation means do not hinder (hamper) each other but cooperate in an intelligent way to a "fluid, comfortable, handsome mobility" (B. Giorgini), have a modest environmental impact and require require infrastructures economically affordable and socially acceptable. Private vehicles mobility is described by a dynamical model in which the vehicle and its driver are treated as an automaton, whose sensors make it aware of the environment (streets and traffic) and which moves according to the physical laws and obeying to the rules of the road. As for the pedestrians the private vehicles dynamics is microscopic and capable of describing fluid traffic conditions, the rise of queues or intermittent regimes. Introducing the private vehicles which occupy a finite physical space it is necessary to treat the parking areas and the transitions to other mobility networks (exit of the driver from the vehicle and transition to pedestrian or public transportation user).
The transformations of the society during the last decades have modified the relations between the citizens and the cities, previously based on house-work mobility. The increased flexibility of schedules allows a different organization of time during the day and a different fruition of the city. These considerations led some sociologists (G. Martinotti) to introduce the notion of "city-users", characterized by a mobility within the urban tissue, which is not amenable to an origin destination model (OD) and is therefore called "asystematic". Women had important role in this transformation process; being forced to accommodate the daily time schedule with the family needs and obligations they were forced to break the OD logic (S. Bonfiglioli). Urbanists have proposed a new paradigm for the interpretation of urban dynamics based on the role of the "urban time", or more precisely of the times appropriate to every social category. The time to which urbanists refer differs from the "physical time" scanned by a clock, but rather a "social time", emerging from the dynamics of urban mobility.