1An established formal theory of sustainable urban mobility does not exist. Researchers on the subject agree, nevertheless, on two major points (Newman and Kenworthy 1998, Litman 1999, Gilbert 2000, Nicolas et al. 2001). First of all, a systemic view of the city-transportation-environment interaction is necessary: urban mobility problems must be studied within their complex interactions. Secondly, local concerns have to be integrated with the contribution of the city to global and intergenerational problems.
2The debate is still open on a “positive” theory of the city-transportation-environment interaction (why things happen). As for a “normative” theory of this interaction (how it should be) we are still at an early stage. Observed patterns of urban mobility are often considered unsustainable. But we don’t know what a city with a sustainable mobility system should look like. Is the city with a sustainable mobility system dense? What is the role of the car within a sustainable urban mobility system? What makes cities less sustainable, a rapid road network or a congested one?
3In this paper, we will not propose a new theory of sustainable urban mobility systems. Rather, we will draw on the principles of wider urban sustainability (Camagni 1996) to derive an operational approach to sustainable urban mobility. It is increasingly apparent that the urban mobility system plays an important role in achieving the city’s wider sustainability objectives (Newman and Kennworthy 1998, Kennworthy and Laube 2002, Williams et al. 2000, Camagni et al. 2002). The main issues are the interaction between urban structure and the urban mobility system and the resulting performance of the system in terms of produced service, resource consumption and externalities. We will focus our attention on the final performance of the mobility system, without imposing particular conditions on the underlying system characteristics (urban structure, transportation offer, modal split, etc.). A mobility system contributing to urban sustainability probably should:
be energy saving
pollute as little as possible
save economic resources
be time-efficient for its users
allow high accessibility within the city for economic and social interaction.
4From an economic point of view, the accessibility necessary for individuals and firms could be assured only by cars. A principle of social equity with respect to non-motorised citizens (Gilbert 2000) imposes high accessibility to be possible through urban transit, too. Non-motorized citizens are always the weakest (children, the elderly, women within poorer households, newly immigrated city dwellers, etc.) and constitute more than 50% of the population even in the most heavily motorised cities.
5These objectives only describe the final outputs of the system and we don’t know its features. Our investigation can be seen as an inverse problem. We want to develop a model of the city-transportation-environment interaction (why things happen) and, by imposing the achievement of the objectives (how things should be), we want to identify the features of the system achieving these objectives.
6In order to develop our model, we considered data from seventy-five world cities, mainly within highly developed countries (Europe, North America, Australia, Wealthy Eastern Asian countries) but also from the Southern Mediterranean Coast and from emerging countries in South-Eastern Asia.
7The cities of our analysis are listed in Table 1. They include 44 cities from Europe and the Southern Mediterranean Coast, 20 cities from the New Worlds (North America and Australia) and 11 cities from Eastern Asia. They are all big cities (from 500 000 to 2 million inhabitants) or very big cities (over 2 million) normally defined at the level of urban agglomerations.
8The variables considered, which constitute the elements of the model, are thirty-eight indicators of the city-transportation-environment interaction. Indicators are synthetic parameters describing the average situation of the city with respect to a particular element of the mobility system. The selected indicators are listed in Table 2, along with the labels used in the model and with the units of measurement. They include three indicators of the socio-economic condition of the city, five indicators of urban structure, seven indicators of transportation offer, five indicators of daily mobility demand, six indicators of traffic flow and eleven indicators of externalities and costs. A final indicator was used to assure that the slightly different definitions of cities with respect to the urban agglomeration had no influence on the resulting model.
9The main source of data is the Millennium Cities Database (UITP-ISTP 2001) developed by the UITP in Brusselsand by the team of Peter Newman and Jeffrey Kenworthy at the Murdoch University, Australia. The data are normally from 1995-96. The database, made of the selected thirty-eight indicators and evaluated for the seventy-five world cities, is not complete as 1.2% of the 2850 numerical values are missing.
Table 1 : The seventy-five world cities of the database.
Table 2 : The thirty-eight indicators of the database (the labels of the variables are in French).
10In order do develop a systemic model of the city-transportation-environment interaction, we opted for the technique of Bayesian networks. At the frontier between multivariate statistics and artificial intelligence, Bayesian networks owe their success both to the increasing availability of computing power and to newly developed algorithms making them finally computationally treatable.
11Bayesian networks are graphical models of causal knowledge in an uncertain context (Pearl 2000, Jensen 2001, Becker and Naim 1999). They are a relatively new and powerful tool of knowledge representation, manipulation and discovery, whose capabilities are just beginning to be applied in urban studies (Waddel 2001, Fusco 2003a, 2003b). A Bayesian network couples a graphical formalism with a mathematical one. Graphically, it is made up of circles (representing variables) and directed arcs (representing causal links among them). The resulting directed graph (Figure 1) constitutes the network structure and represents qualitative information on causality among variables. The structure of a Bayesian Network cannot contain loops. Only directed acyclic graphs (DAG) are possible network structures.
Figure 1 : The structure of a simple Bayesian network of five variables.
12The causal graph is a representation of causal knowledge within a probabilistic framework. Every circle represents a stochastic variable, which can be described through a probability function (eventually a probability table in the case of discrete variables, as in Figure 2). The numeric values of the probability function (or table) constitute the network parameters. The parameters and the structure are tightly linked. The joint probability distribution of the network factorizes according to the structure of the underlying graph. The conditional probability function (or table) of every node depends only on the values of its parent nodes and the total probability of the network is thus obtained as the product of the conditional probabilities of each node given its parents. For the network shown in Figure 1, we have:
13P(A, B, C, D, E) = P(A) P(B|A) P(C|B) P(D|A,B) P(E|D)
14where P(B|A) indicates the conditional probability of B, given A.
Figure 2 : The conditional probability table associated with variable B.
15Figure 2 is a conditional probability table, illustrating P(B|A) in the case of discrete variables with only three values (Low-Medium-High). The table must be read by line: if A is Low, then B has probability 0.7 of being Low, 0.2 of being Medium and 0.1 of being High. This probabilistic approach to causality is particularly suited for representing links among territorial variables.
16Figure 3 schematically illustrates the process of creating and using a Bayesian network. The diagram has a double starting point. On the one hand, we have the domain expert, who we will be asked to formalise his knowledge of the system in a very simple way. In particular, he will highlight the key variables and rank them in a causal hierarchy (this ranking of the variables will be used to restrict the search for the most probable network among a subset of possible ones). On the other hand, we have a database where the variables have been measured for several records serving as examples. The database can include missing values, as is the case for our application.
17Powerful generating algorithms (like the K2 algorithm developed by Cooper and Hersovits, 1992) are able to determine the most probable structure and parameters explaining the data, while being compatible with the assigned causal hierarchy. The result is a Bayesian network representing a possible causal model among the system variables. New data can be used for incremental learning of parameters and structure.
18The debate is open on how to interpret the directed links generated by algorithms from observational data (Druzdzel et Simon 1993, Lauritzen 2001). Not every automatically produced Bayesian network can be considered to be a causal Bayesian network and the very concept of causality is the object of debate (Pearl 2000). These interesting debates go beyond the scope of this paper. We will thus use the terms "cause" and "effect" in a rather informal way in the following pages. The "causal" model generated from data has a heuristic value, and a verification phase should be carried out in order to ascertain the causal content of the links found among the variables.
19Aware of these considerations, the Bayesian network generated can finally be exploited for its inferential capabilities. Knowing the values of selected variables, we can infer the probability distributions for the values of the remaining variables. Bayesian networks are extremely flexible in use: within the inference process there is no need to specify inputs and outputs of the model. We can infer "effects" from "causes", "causes" from "effects"; and, much more generally, any group of elements from any other subset. In our application, we went through all the phases of this scheme, except for the incremental learning phase.
20The thirty-eight indicators of transportation, environment and urbanism have been used to generate a probabilistic model of the city-transportation-environment interaction in the form of a Bayesian network. In this application, both the parameters and the structure of the network were generated from the data using the K2 algorithm implemented with a greedy strategy, in the working environment of Bayesware Discoverer® (Bayesware 2000). K2 generates the network with the highest posterior probability under the constraints of the assumed causal hierarchy. The algorithm sequentially evaluates all possible links towards each variable starting from the lowest in the causal hierarchy. Links are added only if they increase the total posterior probability (i.e. the probability knowing the data) of the network and if they don't introduce loops in the graph. The greedy strategy simplifies the generation process and avoids the creation of loops, by assuming that possible parents for a given variable are only those preceding it in the causal hierarchy.
21Using different hypotheses on the possible hierarchies among the variables, we generated several Bayesian networks for the selected thirty-eight variables. In this paper we will use only the most pertinent network produced,presenting the highest log-likelihood (the statistical parameter used to characterize its posterior probability). The causal hierarchy used to generate this network is shown in Table 3.
Table 3 – The causal hierarchy among the 38 variables, used to generate the Bayesian network (the names of the variables are in French).
22The main assumptions underlying this ranking of the variables can be summarized as follows:
Socio-economic factors and urban structure parameters are considered exogenous to the urban mobility system. They are, therefore, at the top of the causal hierarchy.
With the exception of vehicle ownership, the parameters describing the offer of urban transportation (both in terms of infrastructure and service) are susceptible of depending on socio-economic factors and urban structure.
The parameters of the performance of the transportation networks (average speed and accessibility) are the next variables in the causal hierarchy.
Vehicle ownership and parameters of mobility demand are susceptible of depending on the combination of the preceding elements (socio-economic factors, urban structure, transportation offer, speed, accessibility).
The parameters of the actual traffic flows on the transportation system are to be found in a lower hierarchical position.
Finally, at the end of the causal hierarchy, consumption of resources and environmental externalities are a possible result of all the elements mentioned above.
23Globally, this causal hierarchy gives the greatest importance to the role played by urban structure. Apart from the socio-economic factors, urban structure is conceived as the element capable of determining, in the last instance, the functioning of the whole system and is independent from the dynamics of urban mobility.
- 1 In the case of variables having only three values, the conditional probability table of a node wit (...)
24Using the data of the seventy-five world cities and the hierarchy of Table 3, we generated the network, whose structure is shown in Figure 4. This network is also the result of several limitations we imposed on the generating algorithm. In order to obtain a sufficiently robust network from such a small data set (only 75 cities) we discretized continuous variables in only three values (low – medium – high). We also imposed a maximum of two parents for each node. This was done because the learning algorithms need a database which is as complete as possible (i.e. a database where all combinations of values of the conditional probability table are observed at least once) in order to perform a correct network generation (Becker et Naïm 1999).1
25The produced Bayesian network is globally well-connected (only four elements could not be linked). The analysis of this network in terms of causality has been fully discussed in other works (Fusco 2003b). Despite a few inconsistencies and the necessary approximations introduced by the discretization process, we can consider that the Bayesian network represented in Figure 4 constitutes a good "causal" explanation of the system variables.
26The Bayesian model provides a positive framework of the city-transportation-environment interaction. The model is a simplification of reality, but through it we can clearly identify the key-links among the indicators of this complex interaction. In the following section, we will use the Bayesian model to explore the characteristics of the city with sustainable mobility. With this objective, we will exploit the inferential capability of Bayesian networks in order to simulate the model's behaviour under unobserved conditions.
Figure 4 : The Bayesian network of the urban mobility system.
27In this section, we will identify the features of the urban mobility system achieving sustainability objectives. From the desired performance of a sustainable urban mobility system, we can derive objectives for eight of the thirty-four elements of the network:
28Accessibility: - Road accessibility to jobs must be high
29 - Public transportation accessibility to jobs must be high
30Economic costs: - Mobility costs (as a percentage of the city GDP) must be low
31Security: - Road mortality must be low
32Energy: - Energy consumption must be low
33Air pollution: - Pollutant emission per capita must be low
34 - Pollutant emission per urban hectare must be low
35Time consumption: - Time consumption by motorised trips must be low
36The realization of these objectives provides a minimal set of normative elements for the urban mobility system. More precisely, we ask the city with sustainable urban mobility to be ranked in the best group of cities for every sustainability objective. It appears to be a pragmatic and realistic requirement. Still, no real city is able to attain the eight objectives simultaneously. The city with sustainable mobility is a utopian city, in the etymological sense (that is, it is to be found nowhere).
37Having determined the minimal requirements for the performance of the sustainable mobility system, the Bayesian model can be used to solve the inverse problem. The process of determining the features of the city with sustainable urban mobility is the following (Figure 5). We enter the desired values for sustainability objectives as elements of certain knowledge in the Bayesian network. The network calculates the conditional probabilities of the remaining variables under the assumption that the sustainability objectives are achieved. We will finally select the most probable values for the different elements in order to identify the ideal profile of the city with sustainable mobility.
Figure 5 : Inferring the characteristics of the city with sustainable urban mobility.
38The simulations with the Bayesian network revealed that the sustainability objectives are partially conflicting objectives. We can distinguish two groups of objectives.
39The first group is energy consumption, pollution per capita, security, economic costs and accessibilities. The city attaining the six first objectives is a very dense city, with a high use of transit, little offer of urban freeways, low volumes of traffic per capita, and a congested road network. This city does not attain the remaining objectives of time consumption and pollutant emission density
40The city attaining the latter two objectives is a low-density city, with car-based mobility, a good offer of urban freeways and high traffic volumes in a fast road network. This city does not attain the six remaining objectives. Most crucially, this city provides very low levels of accessibility both by car and by transit. Evidently, the presence of a network of urban freeways allows a redistribution of activities in a wider urban space. The road network is faster, but fewer jobs are to be reached in less than 30 minutes.
41Now, what happens if we impose the realization of all eight objectives to the Bayesian network? What will be the most probable characteristics of the city with a sustainable mobility system?
42The conceptual model of Figure 6 summarizes the functioning of the sustainable mobility system achieving the eight objectives as it is inferred by the Bayesian network. The reader should be aware that the diagram in Figure 6 is not a Bayesian network. It is simply a qualitative causal graph that we use in order to oversee the relationships among phenomena resulting in sustainable urban mobility (according to the results produced by the Bayesian network).
Figure 6 : Conceptual model of the sustainable urban mobility system.
43The city with a sustainable mobility system is most probably a dense or medium dense city, offering few urban freeways and a very effective transit system. High transit accessibility, shorter distances between possible destinations and high user costs of car trips keep mobility multimodal, thus limiting costs and mortality. That is, the city with a sustainable mobility system is not a car-free city. No big world city could renounce to the contribution of private motor vehicles in the functioning of their mobility system. But car use is limited by the use of transit and non-motorised modes (walking and cycling).
44The dense city reduces the volume of trips (multipurpose trips are easier) and limits the speed of the road network. While time consumption is kept low, high density and reduced speed result in shorter and fewer trips. This, combined with the use of transit, keeps traffic flows per capita low, and reduces energy consumption and pollutant emissions.
45As Rolf Monheim points out (1997), the sustainable city is a city reducing the volume of mobility: mobility should be considered an input and not an output of urban welfare. An efficient system would limit its inputs. But we arrived to Monheim’s conclusion only indirectly, inferring the most probable characteristics of a system achieving a limited set of sustainability objectives.
46The city with sustainable mobility is finally compatible with every socioeconomic context (in terms of GDP per capita, old/young ratio and average household size). It is nevertheless slightly more probable that the old/young ratio is high. Effective transit systems, with dedicated infrastructures, tend to be more probable in cities with an aging population as seniors press local authorities to offer more comfortable and reliable alternatives to car trips.
47Globally, the conclusions that we can draw on the features of the sustainable mobility system inferred through the Bayesian network, agree with the analysis of the ISTP researchers on the fundamental role of urban density and transit infrastructure to achieve more sustainable urban mobility (Newman and Kenworthy 1998, Kenworthy and Laube 2002).
48To verify that the features of a sustainable urban mobility system are the same in cities with different socioeconomic conditions, we carried out Bayesian simulations imposing further elements of knowledge to the network. We studied the two extreme cases: the relatively poor city with a young population and larger households (a city still completing its demographic transition), and the relatively richer city with an aging population and smaller households. Bayesian simulations show that:
The rich and demographically mature city achieving the sustainability objectives must face a few elements more favourable to car use. Daily mobility is almost surely medium, household motorisation is probably medium and the user cost of a car trip is probably low. In order to counterbalance these elements, the transit system is more effective than in the general case. Transit infrastructure offer per inhabitant is higher and denser, and it is more probable that transit service per capita is high. Globally, the city responds with better public transportation offer to counter conditions which are generally more favourable to car use.
The poorer city in demographic transition faces the danger of being under-equipped. Motorisation is very low, as are the offers of urban freeways and of transit infrastructures. The city is almost certainly very dense and has high traffic density, but it has to avoid congestion: the road network can be slow, but motorised trips cannot be time-consuming. Globally, the characteristics of the poor city attaining the sustainability objectives constitute a series of constraints which are hard to respect. The city has to avoid congestion though being in a situation of poor infrastructure equipment and in the impossibility of giving up the contribution of private motorised mobility. The poorer city in demographic transition has fewer degrees of freedom in order to achieve sustainable urban mobility.
49Knowing the most probable characteristics of the city with sustainable mobility, we can evaluate real cities on all elements of their urban mobility system and not just on the realization of the few sustainability objectives. In particular, we can compare every city with the sustainability profile inferred from the Bayesian network in order to understand which weaknesses prevent them from achieving the sustainability objectives (Figure 7).
50A simple and aggregate way of evaluating the distance of real cities from the inferred sustainability profile is to sum the differences found on every indicator. This way of proceeding is not the only one. Other distance definitions, such as the Chi-square metric, could be used to give more accurate results.
Figure 7 : Evaluating the profile of a real city with respect to the inferred sustainability profile.
51Using the distances from the desired sustainability profile, we could produce an overall ranking of world cities. The cartographic representation of this ranking gives a remarkable geography of the sustainability of mobility systems. In the map of Figure 8, cities are grouped in six distance classes from the sustainability profile.
52No city has distance “zero” from the sustainability profile (we already knew that as no city could attain the eight sustainability objectives at the same time). The cities which are closest to the desired sustainability characteristics are either in Central Europe (Berlin, Vienna) or in affluent countries of the Far East (Japanese cities, Hong Kong, Singapore). Remarkably, the Mediterranean port-city of Barcelona is also a member of this small virtuous group.
53A bit further away from the sustainability profile, we find other cities from Central Europe and the Far East, but also other European cities and, particularly, the capital cities of North-Western Europe. Nevertheless, most European and Southern Mediterranean cities are even further from the sustainability profile (with distances between 15 and 25).
Figure 8 : Overall distance of world cities from the inferred sustainability profile.
54Within the Mediterranean basin, the situations differ considerably. Some cities are very far from the sustainability profile (Rome, Marseille, Athens, Casablanca, Nice). Barcelona has one of the most sustainable mobility systems and even Cairo shows a relatively positive standing. Other cities (like Genoa, Tunis and Tel-Aviv) present a more intermediate situation. The good standing of Barcelona is very important in a geographic area known to be particularly problematic for urban mobility.
55At the other extreme of the ranking of world cities, with distances comprised between 35 and 38, we find almost all the American cities along with Calgary and Melbourne. The other Canadian and Australian cities are a bit closer to the sustainability profile. The only exception is Toronto, showing a distance comparable to that of many European cities.
56What kind of cities are the Central European and the East Asian cities which are closest to the to the sustainability profile?
57They are medium to very dense cities, with extremely effective transit systems playing a fundamental role within the system, and with a precise willingness to limit car use. Each city presents specific problems which need to be addressed. Nevertheless, it is clear that they can foresee policies for more sustainable mobility starting from very favourable situations.
58On the contrary, highly car-dependent American cities are particularly far from the sustainability profile. In order to get closer to it, the Bayesian network suggests that they should completely revise their approach to city and transportation planning. Urban sprawl must be stopped in order to attain densities compatible with an efficient transit system and multimodal mobility. Priority should be given to transit infrastructures over urban motorways. The reduction of generated traffic should replace the continuous adaptation of the city to growing automobile flows.
59These indications also hold true for the European, Canadian and Australian cities which are also very distant from the sustainability profile. For New World cities, Toronto represents a good intermediate objective, an indication which emerged already from the first international comparisons done by Newman and Kenworthy (1989).
60In conclusion, through Bayesian networks, we were able to explore the features of the city with a sustainable urban mobility system. These characteristics cannot be directly observed. They were inferred imposing the achievement of a small set of sustainability objectives, which turned out to be partially contradictory among them.
61The city with a sustainable mobility system is most probably a dense city with highly efficient transit and multimodal mobility. It produces high levels of accessibility without relying on a fast road network. Mobility volumes (both in terms of trips per capita and of travelled distances) are medium or low.
62The achievement of sustainability objectives for urban mobility is probably compatible with all socioeconomic contexts. Nevertheless, rich and demographically mature cities must face more pressure for car use; poorer cities in demographic transition have to cope with even more contradictions, resulting in fewer degrees of freedom for their sustainability agendas.
63By measuring the distance of world cities to the inferred sustainability profile, we derived an interesting geography of the sustainability of mobility systems. The cities closest to the sustainability profile are in Central Europe and in affluent countries of the Far East. Car-dependent American cities are the farthest from the desired sustainability profile.
64This work constitutes a prototypical application of the Bayesian networks techniques for modelling the city-transportation-environment interaction. It obviously presents several limitations which should be highlighted.
65First of all, the proposed Bayesian model oversimplifies several aspects of the city-transportation-environment interaction. This is the result of the limitation imposed on the network generation. It is not a limit of Bayesian modelling but a constraint imposed by the exiguity of our database. On the contrary, a clear limit of Bayesian modelling is the impossibility to represent feedbacks within a single network.
66Secondly, the generation of Bayesian networks is sensitive to the modeller’s hypotheses entered in the form of a causal hierarchy among variables. The hypotheses underlying the Bayesian model used in this article conceive urban structure as the element capable of determining the functioning of the urban mobility system. In a wider study (Fusco 2003b) we explored networks generated from different hypotheses. In particular, we assumed that the urban structure can be a result of the transportation system. We could thus produce slightly different networks. The results in terms of the urban sustainability profile were, nevertheless, sufficiently close to the ones obtained through the network used in this article.
67Finally, our analysis remains at a very strategic level. Cities are observed as a whole. More detailed analyses are needed at the infra-urban scale to study the interplay of urban structure, transportation offer and mobility demand.
68Globally, Bayesian networks are a powerful and versatile modelling technique, which can be used to create probable "causal" models from data and to perform simulations of systems functioning in an uncertain context. The use of Bayesian networks to model the city-transportation-environment interaction and to explore the characteristics of a sustainable mobility system proves to be extremely interesting and opens the way to further applications.