The Dynamics of Complex Urban Systems

This chapter presents both a chronological and conceptual history of urban land use-transportation models movement in the context of current developments. Such models —‘urban models’ for short — first appeared in the 1950s in North America and were made possible by two interrelated forces: the development of digital computing from which large-scale simulation emanated, and policy imperatives for testing the effects of large-scale public investments on cities. Essentially, urban models are still pragmatically motivated tools for testing the impact of changes in the locations of land use and transportation on dense and usually large urban agglomerations. Planning and policy determine their rationale although their foundations are built on theoretical ideas which go back to the roots of modern social science and the influence of physics and mathematics from the time of the Enlightenment. During the brief but turbulent years since this field has developed, there have been substantial shifts in viewpoint. Indeed even the paradigms that condition what attributes of the city are to be modeled, and the way such modeling takes place, have changed. We will chart these changes, beginning with a set of intersecting time lines focusing on theoretical origins and practical applications. We will show how urban models were first conceived in aggregative, static terms when the concern was for simulating the way cities appeared at a cross-section in time. This aggregative, static conception of urban structure has slowly given way to one where much more detailed disaggregate activities appear more important and where dynamics rather than statics is the focus. This reflects as much our abilities to simulate more elaborate computational structures and collect better data as any grand theoretical revision of the way we look at the city, although such a revision is now under way As such, this chapter sets a context for many of the current advances in urban modeling reported elsewhere in this book.

Traditionally, science has attempted to understand urban systems using a reductionist approach in which the behaviour of a system (city or region) is represented as being an equilibrium, mechanical interaction of its components. These components are “representative agents” for the different categories of supply and demand that inhabit the system, and it is assumed that their spatial distribution reflects an optimised value of profit (supply) and utility (demand). Over recent decades many attempts have been made to introduce more dynamic approaches, in which equilibrium is not assumed, and there are many models and methods that attempt to do this. However, this still denies the essential complexity of the urban or regional system, in which activities, natural endowments, culture, skills, education, health, transport, house prices, the global economy, all combine to affect the evolution of the system. Just as in ecology, the key to the long-term structures that may emerge is the diversity, innovative and adaptive power of people and society to counter new difficulties and create new opportunities. This fluid, adaptive power is a product of the complex system, and can only be modelled and anticipated to a limited degree. However, cities and regions can limit the possibility of successful adaptation if they are too “wellorganized” or too unimaginative. New models of adaptive organisation allow us to understand better the need for integrated views linking land-use changes to environmental and socio-economic and cultural factors. These provide a new, more open way of considering the importance of adaptable, emergent networks, and the need for multiple and burgeoning accessibility to others.

In this paper the ontogeny of complex systems models is discussed: the historical aspect of model ontology. The theoretical framework that is applied is complex systems theory and more specifically evolution and dynamical hierarchies. Some issues relating to the role and applicability of complex systems models are also discussed.

We present an agent-based model to simulate the citizens mobility in a urban space. The request of mobility is determined by the “chronotopic areas”: i.e. urban areas where time-dependent activities are installed and attract the citizens according to their social categories. The core of the model is a decision mechanism for the agents based on a daily program, which chooses the transportation means and the roads to reach the scheduled chronotopic areas. The decision mechanism depends on some social characters of the agents, on the information at disposal, on the attraction force towards a chronotopos and on some random choices. The daily program can also be upgraded according to the information given to the agents. The finite volume congestion effects are present in the private transportation and in the finite capacity of the public means whereas the crowding in the chronotopic areas causes the extension of the elapsed time in the areas. We present a simulation on the campus of Milano Bicocca University where we take advantage of some experimental observations on the students mobility.

This paper provides an introduction to multi-agent traffic simulation. Metropolitan regions can consist of several million inhabitants, implying the simulation of several million travelers, which represents a considerable computational challenge. We reports on our recent case study of a real-world Berlin scenario. The paper explains computational techniques necessary to achieve results. It turns out that the difficulties there, because of data availability and because of the special situation of Berlin after the reunification, are considerably larger than in previous scenarios that we have treated.

The chapter explores the introduction of simple behavioural mechanisms into a spatial microsimulation model. It is hypothesised that the representation of individual behaviour using appropriate rules can allow the outcome from meso-level models, such as spatial interaction models, to be reproduced. The dynamic properties of these models are also explored. Therefore the research seeks to establish links between microsimulation, agent-based approaches and spatial interaction models, at a variety of scales. The simulations are operationalised in the context of a British city.

The difficulty in dealing with urban systems’ complexity and the related difficulty to analyse and forecast is twofold: one kind of difficulty lies in the complexity of the system itself, and the other is due to the actions of actors, which are “acts of freedom”. In our contribution we would like to present a set of techniques and models, with respective software packages (MaGIA, The Time Machine, CAGE and GioCoMo), that have proven to be of great potential for enactment and management of communication, participatory, consensus-building and simulation processes. As such, our approach tries to cope with both aspects of complexity mentioned above.

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.

This paper is a report on the configurational theory, the unconventional approach to urban phenomena that was introduced by Bill Hillier in the mid ’80s and still attracts and stimulates researchers all over the world. It won’t be exhaustive, since it can’t but neglect most of the several techniques that, on the common configurational basis, have been worked out so far. It won’t be ultimate, since at present researchers are still working hard and carrying on developments on the matter. It won’t be objective either, since the stated purpose of the paper is the introduction and the discussion of a new, original method, the MaPPA, and its placement as the logical terminus of decades of studies and experimentations.

But, all in all, the underlying purpose of the paper is to outline the usefulness and the reliability of such approach, to highlight benefits and limits of the several techniques, as well as to figure possible lines of improvement and development of the presented methods.

Realistic high-resolution cellular automata based models of urban and regional systems raise significant problems of calibration and validation. In this chapter we examine first the major philosophical and methodological issues involved in the validation of models that produce as output patterns that are complex but non-deterministic due to stochasticity and bifurcations. Some related problems of map comparison that are significant for both validation and calibration are also examined. Calibration problems are then treated in more detail by means of a case study involving an application of the Environment Explorer model of The Netherlands as well as two semiautomatic calibration techniques that were developed in this context. The calibration tools are shown to be useful if imperfect, and even in some cases to outperform manual calibration.

Urban growth generates nowadays patterns, which look rather irregular. Planning policy regrets the lack of compactness and density of these agglomerations, but controlling urban sprawl turns out to be difficult. Obviously a new type of spatial organisation emerges, which is rather the result of a self-organisation process to which a high number of social agents contribute. In the present contribution we focus on the use of fractal geometry which turned out to be a powerful instrument for describing the morphology of these patterns.

After an introduction about the context of research, fractal models are presented, which serve as reference models for better understanding the spatial organisation of settlement patterns. Then the methodology for measuring their morphology by means of fractal parameters is explained. Moreover different peculiar topics are considered like a specific approach of urban boundaries. Then an overview is given over results obtained for a couple of agglomerations in different European countries. The interpretation of these results allows establishing links between urban planning policy and pattern morphology. Applying the idea of self-organisation leads to introducing a fractal order parameter for studying the emergent fractal order in urban patterns. The presentation of these quantitative results will be completed by some reflections about how planning concepts based on fractal geometry may help to manage more efficiently urban sprawl.

In order to understand current settlement pattern and its future development the essential characteristics of the interrelated dynamics of the transport system, the urban/regional settlement pattern, demographic effects and the impacts of different policy measures and external effects have to be considered in an interdisciplinary approach. The modelling of the spatio-temporal patterns of a system consisting of different sub-models (population, transport, production, etc.) is used to demonstrate the necessity to link different theoretical frameworks. External shocks may sometimes require a modification of the system under consideration in the sense that new dynamic variables appear or previously useful variables disappear.

Policy advises on the base of different scenarios are useful in a planning context in the attempt to shape the future taking into account different scenario results, instead of just adapting to what may emerge. This procedure is especially important when essential parts of the system cannot be controlled by policy measures and depend on exogenous factors.

For the region of Stuttgart, the model framework was used within the SCATTER project. Four different policy scenarios: reference scenario (no additional policy measure applied); fiscal measures; regulatory measures applied to companies and increase of car use costs will be simulated in an recursive procedure. The results of the different policy measures will be discussed and critically evaluated with respect to urban sprawl and sustainable development aspects. The developed framework can also be used as simulation tool for the estimation of secondary induced traffic impacts.

Most urban models accept the assumptions of the Markov processes: the state and location of each urban object at time step t+1 are defined by its state, location and environmental conditions at t. This assumption is not at all evident, just because the city is developed by humans who have memory and might implement long-term development plans, and, thus demands confirmations. The Markov nature of developers’ behavior is investigated on the base of laboratory experiments, in which 30 participants were asked to construct a ‘city’ on the floor of a hall; each participant had to use the same set of mock-up buildings. Each mock-up established was represented as a feature of GIS layer, and its urban function, given by the participant, was recorded. The analysis of participants’ behavior reveals that the relation between the urban pattern on the step t of the experiment and the decision regarding the urban function and location of the mock-up at t+1 is very close to assumed by the Markov theory. Based on the experimental results, spatially explicit model of participants’ behavior was further constructed. The comparison between the experimental and the model patters, in their dynamics, clearly favor the idea of a shared Markov process as the basis for representing human urban development behavior. In the same time, with the increase in city complexity, the spectrum of participants’ behavior becomes wider that that of the model and some participants tends to deviate from it This experiment is a preliminary yet important step towards the experimental study of decision-making behavior among real developers and planners, which provide the basis for description of the real-world urban dynamics.

Self-organization is not only a feature of urban evolution, but also found within urban environments. Here, we will focus on three aspects: (i) spatiotemporal patterns in pedestrian flows and their implications for optimized pedestrian facilities, (ii) trail formation of pedestrians and their consequences for improved way systems, and (iii) a self-organization approach to an adaptive control of traffic lights. This chapter will discuss the problems, modelling concepts, results, and solutions, while the mathematical formulation and analysis of the models is presented elsewhere.

Design involves assembling parts into whole to satisfy specified relationships. Binary relations between pairs of elements are not rich enough to represent the generality of this. Powerful though they are, graphs and networks must be extended to multidimensional networks to represent the many subtleties of complex systems. These structures underlie a natural theory of multilevel systems that has within it a kind of structural time defined by multidimensional events. Slow changing relational structure is discriminated from fast moving events captured by patterns of numbers. It will shown that the former acts as a kind of multilevel multidimensional backcloth for the multilevel multidimensional dynamic traffic of the latter. The theory will be illustrated by examples.

The aim of the research is to investigate land use transformations in a territorial area of Albania, analyzing the connections existing between the deep political and socio-economical changes. The tools we adopted, from the field of the KDS, is able to produce IF/THEN type rules, in which the “IF” part describes the observed state, and the “THEN” part identifies the transition to another state. The application included different phases:

This paper focuses on two interrelated properties of the agent-base (AB) and cellular automata (CA) urban simulation models currently employed in the study cities: The global urban structures that emerge out of their dynamics plays no role in the dynamics itself and, agents’ behavior as postulated in these models disregards the basic principles of human cognition, behavior and action as revealed by cognitive science. These two properties are interrelated because empirical and theoretical studies in cognitive science indicate that agents’ behavior in cities is strongly influenced by the global structure of cities. The paper elaborates on the deep roots of these properties, identifies some of the major problems they entail, and suggests a structural-cognitive approach to urban simulation models.

Following a first attempt presented as the SIMPOP model (a multi-agents systems whose prototype is described in Bura et al. 1996), our aim is to develop a generic model for simulating the evolution of systems of towns and cities, using the SWARM simulation platform. The scientific issue is: to understand how cities that are interconnected through material and immaterial networks co-evolve, within an environment where social and economic innovation continuously emerge, while maintaining at a macro-geographical scale functional, hierarchic and spatial differentiation which evolve at a much slower pace.

The SIMPOP2 model is designed for testing hypothesis about the general processes of urbanisation and interactions between towns and cities. The objective is to identify and order the rules and parameters that have produced a variety of configuration at the level of the systems of cities, according mainly to the changing conditions of spatial interaction: communication means, transportation speed, range of trading activities, proximity networks and long distance connectivity. Three main varieties of urban systems that have had different histories of urbanisation and conditions of circulation will be investigated: developed countries with old settlement systems, developed countries of much more recent urbanisation, and developing countries. A first generic version of the model includes the minimal rules that seem necessary for reproducing the emergence and evolution of any system of cities, whereas three different scenarios will be constructed for simulating the characteristic features of the three main variations.

There are many evidences for a great return of large-scale urban models. Nevertheless this revival could be a true renaissance, only if the modellers will win seven challenges, in dealing with changes in urban phenomena, in urban theories, in planning theories and practices, in modelling activity, in types of models and in technical aspect of modelling. The supreme challenge, however, in building good urban models will be to join scientific and classical cultures.

A multi-agents simulation model for the development of a poli-nucleated urban area is presented. This model, CityDev, is based on agents, goods and markets. Each agent (family, industrial firm, commercial firm, service firm, or developer) produces goods (labor, buildings, consumption goods) by using other goods and exchanges the goods in the markets. Each agent needs a building where to live or work, hence the urban fabric is produced and transformed as the result of the co-evolution of the economic and spatial systems. The model is applied to Florence (Italy) and its main feature — the interactivity via Internet is shown. In fact web users can direct during the simulation the agents generated by the simulator as well as the new agents established by themselves. In conclusion the basic characteristics of a multiagents method are highlighted: the comprehensive character of an agent based simulation, the ability to interact with human users, and the validation based both on observed data and on a direct interaction with real actors.

We present a mathematical model for urban systems based on a continuous valued cellular automaton. In the modelling we have an urban system, described through a specification cell by cell of built volumes and surfaces for different land uses and a system of agents interacting with the urban system and governed by fuzzy decision processes depending on the configuration of the urban system. For developers e.g. a point in the decision space specifies the cell and a set of continuous parameters describing the building quantitatively (e.g. surface and volume). 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. Computer simulations on an artificial case with detailed real characteristics are presented.

In this contribution, I address the function of multiplicative stochastic processes in modelling the occurrence of power-law city size distributions. As an explanation of the result of Zipf’s rank analysis, Simon’s model is presented in a mathematically elementary way, with a thorough discussion of the involved hypotheses. Emphasis is put on the flexibility of the model, as to its possible extensions and the relaxation of some strong assumptions. I point out some open problems regarding the prediction of the detailed shape of Zipf’s rank plots, which may be tackled by means of such extensions.