Fausto Lo Feudo
email: fausto.lofeudo@inria.fr

Evidences of communicating vessels principle in results of a regional land use and transport integrated modeling application

Keywords: Land Use and Transport Integrated models; Tranus, TOD, modal share, urbanism, urban planning

Evidences of communicating vessels principle in results of a regional land use and transport integrated modeling application

Fausto Lo Feudo

ABSTRACT. This article presents part of results obtained from an integrated land use and transport regional modeling, using the simulation software Tranus. Specifically, this research aimed to analyze effects of a regional Transit Oriented Development plan, applied to the French region of Nord-Pas-de-Calais, with reference to the evolution of modal share between private car and public transport and of residential and activity location dynamics. In particular the model has provided results that show the existence of a system of mutual interdependence in transport modal share evolution. This interaction entails the activation of a substitution effect in transport demand distribution, as a consequence of the application of interventions discouraging car use and reinforcing public transport supply performance. Furthermore we also observed some evidences referable to a process proper of the physical principle of communicating vessels. In particular the increase over simulation times of modal share related to public transport, resulting in the application of TOD policies, produces in some zones of the model, a progressive desaturation and decongestion of the road network and therefore a gradual return of attractiveness for private cars. This phenomenon of communicating vessels related to transport demand evolution, indicates the presence of a permanent state of tension in modal share, depending on some particular factors (segment of demand; temporal and territorial context; structure of transport network) and generally tending to a temporary equilibrium. These results invite therefore to observe how policies that promote and encourage the use of public transport may have, in some particular contexts, controversial effects and sometimes contrary to expectations, especially in the long term. The article explains the principles behind the research that have allowed achieving these results, analyzing causes and consequences related to the observation of the phenomenon of communicating vessels applied to dynamics of mobility and transport. MOTS-CLES : Modèles d'usage du sol et transport, Tranus, TOD, répartition modale, urbanisme, aménagement du territoire.

Land Use and Transport Integrated modeling

Land Use and Transport Integrated (LUTI) modeling intends the ability to model interactions between supply and demand of a transportation system and the socioeconomic functioning of a specific territory. These models are able to simulate regional and urban systems, reproducing economic equilibrium between supply and demand and dynamics of competition related to localization choices of households and activities, depending on certain key factors: accessibility, generalized transport costs, land and housing prices [START_REF] Nguyen-Luong | Les modèles transport-urbanisme: de la théorie à la pratique[END_REF].

Several researchers, including F. [START_REF] Leurent | Les modèles d'usage du sol et transport. où la géographie et l'économie se rejoignent[END_REF], observe that LUTI modeling is a tool that allows answering to typical questions of developers and planners; thanks in particular to its potential and ability in space-time decomposition and in analyzing different behavioral aspects of multiple actors and factors contributing to evolution of territories. This type of modeling can provide a comprehensive and inclusive analysis, particularly during the decision-making process relating to relocation of services, resources or activities, as well as for identification of new spatial development configuration.

Modeling research introduced in this article intends to analyse effects of urban densification and transit oriented policies applied in correspondence of main regional railway corridors and nodes of the study area. In particular such hypotheses, detailed later, have activated an unexpected mechanism of substitution, and subsequently of complementarity among transport demand segments related to private car and public transports. Results show that car has a return of attractiveness caused by reduction of road congestion, produced in turn by an increase in public transport rate of frequentation due to effects of modeling hypothesis. This unexpected substitution effect in favour of car occurred in two zones of the model, in the simulation scenario more favourable to public transport. That situation induced to develop further reflections, more oriented to transport and urban planning strategies, considering how impacts of some transport and land use policies could be diversified considering the short and the long term and controversial if some reciprocal and secondary effects are underestimate during the planning phase.

Results presented in this article confirm LUTI modeling as a proper tool to study complex and articulated territorial dynamics, allowing, as illustrated later, to read and decode different factors that influence inverse relationship between generalized transport cost and demand distribution.

Moreover we are conscious that use of LUTI is still limited and many criticisms are addressed to this modeling technique, especially about its complexity, its low theoretical progress and its character of black box [START_REF] Timmermans | The Saga of Integrated Land Use-Transport Modeling: How Many More Dreams Before We Wake Up? 10th International Conference on Travel Behavior Research[END_REF]. Further limitations are related to the need of a multidisciplinary approach, to the large amount of data required and also to the difficulty in defining automated and standardized calibration and validation methods. Lee (1974) and later Waddel (2011) have described and analyzed main critical elements of LUTI models, as well as their greatest potentialities, as for instance: transparency, understanding, flexibility and uncertainty.

Different authors like

This complexity explains how rare are examples of LUTI models applied to support real decision processes [START_REF] Gayda | Application du logiciel TRANUS au cas de Bruxelles: l'évaluation des mesures d'accompagnement du futur RER de Bruxelles[END_REF]. Otherwise the research project Cities 1 , founded by the French ANR (Agence Nationale de la Recherche), is indeed an example of integration between research, planning and decisional actors, to work on implementation of an operative LUTI model and on development of solid and consistent calibration methods [START_REF] Bonnel | A survey on the calibration and validation of integrated land use and transportation models[END_REF][START_REF] Capelle | Formulating LUTI calibration as an optimization problem: example of Tranus shadow-price estimation[END_REF][START_REF] Prados | Involving endusers in calibration and validation processes: A key factor to favor transfer of integrated models[END_REF]).

LUTI models generally require the definition of population, employment and transport demand categories, of activity sectors and also of land use and housing types. It is also necessary to accurately divide study area in discrete zones, define physical (infrastructure) and operative (services) transport supply and time intervals of simulation.

The scientific literature has a wide number of documents that analyze different LUTI modeling approaches [START_REF] Wilson | Land-use/Transport Interaction Models. Past and Future[END_REF]Wegener, 2004), reviewing their main potentialities, weaknesses and operational characteristics [START_REF] Clement | Schéma Régional des Transports et des Mobilités (SRTM)[END_REF]DETR, 1999;NCHRP, 2002;[START_REF] Timmermans | The Saga of Integrated Land Use-Transport Modeling: How Many More Dreams Before We Wake Up? 10th International Conference on Travel Behavior Research[END_REF]DT, 2005;[START_REF] Hunt | Current operational urban land-use-transport modeling frameworks: A review[END_REF]Zhao and Chung, 2006;[START_REF] Wegener | Overview of land-use transport models[END_REF].

Among them in a report of the British Department of the Environment, Transport and the Regions (DETR, 1999), Simmonds and others proposed a classification of LUTI models in two macros categories: static models (referred to a single point in the time) and quasi-dynamic models (referred to a series of time horizons). This last category is then divided in: Entropy-Based models (in which relations between activities are based on the analogy with Newton's gravitational theory); Spatial-Economics models (based on description of spatial distribution of people and activities) and Activity-Based Models (based on representation of interactions between activities). Following Simmonds classification, the Tranus model, used for this research, belongs to Spatial-Economics models. This type of models articulate micro-economic theories with spatial interaction models and random utility based multi-region input-output models.

Micro-economic theories [START_REF] Thunen | Der Isolierte Staat in Beziehung ant Landswirtschaft and Nationalekomie[END_REF][START_REF] Wingo | Transportation and urban land. Ressource for the future[END_REF][START_REF] Alonso | Location and land use[END_REF] describe land use market with a disaggregated approach, considering a competition between households and firms to consume space, that reaches an equilibrium when land and transport costs maximize utilities for consumers (and benefits for suppliers).

Spatial interaction models [START_REF] Lowry | A Model of Metropolis[END_REF][START_REF] Echenique | Urban Systems: Towards and Explorative Model. WP7. Land Use and Built Form Studies[END_REF][START_REF] Wilson | Urban & Regional Models in Geography & Planning[END_REF] describe location of activities in space and interaction flows, using aggregated discrete categories and assuming similar behaviors and characteristics for members belonging to a same group. Interactions between activities produce flows (of 1. Calibrage et valIdation de modèles Transport -usagE des Sols. passengers or freights) and are proportional to number of activities in a particular zone and inversely proportional to transport network constraints.

Random utility theories (Mc Fadden, 1973) and discrete choice models describe the decision chain of demand groups in function of multiple possible interdependent choices (as typically happens in urban and regional systems). Users make their choices influenced by variable costs, supply constraints and elastic demand functions (that describe relationship between demand and supply).

Econometric input-output models are then used to reproduce interaction and relations between activities and the urban and regional territorial structure (de la [START_REF] De La Barra | Integrated land use and transport modeling[END_REF]). In the input/output model [START_REF] Leontief | The Structure on the American Economy 1919-1939[END_REF] regional economy is divided in activity sectors and transport demand is obtained in function of economic relations that occur between activities. Products of an economic sector (outputs) can be used as inputs for another productive sector (induced) or consumed by final demand (which may include population, exports, investments, etc.) [START_REF] Wilson | Urban & Regional Models in Geography & Planning[END_REF]. Inputs are divided in produced inputs and primary inputs, while outputs are divided in intermediate and final demand (de la [START_REF] De La Barra | Integrated land use and transport modeling[END_REF]. Industrial inputs coming from outside the regional economic system represent exogenous inputs (raw material, financial capital, public subsidies, etc.) [START_REF] Wilson | Urban & Regional Models in Geography & Planning[END_REF], while intermediate demand is characterized in a matrix, where each element represents the amount of output from a production sector, demanded by another activity sector. Once completed the iterative calculation and once convergence is achieved, the input/output model provides the amount of regional production required to meet the total consumption demand (de la [START_REF] De La Barra | Integrated land use and transport modeling[END_REF].

The integrated simulation software Tranus

Tranus presents an approach based on the overall equilibrium between supply and demand (of transport, of land and/or housing). It is an aggregated spatial input/output model, based on equilibrium in function of price and time and on a nested logit multinomial model (de la [START_REF] De La Barra | Integrated land use and transport modeling[END_REF]. This model has been select mainly because of its multi-scale potentiality of representation (regional, suburban and urban) of the study area and because it is an open source software, with a direct on-line support by its creators. Other reasons were the Tranus integrated conformation, that doesn't implicate the use of external transport models, as in the case of many others LUTI models, and the presence in the research environment of the author, of researchers with precedent experiences in Tranus modeling. 2 Tranus stands out in particular by its ability to include several theoretical approaches into a single integrated structure, which represents both transport and 2. This work is part of a joint PhD research program in urban and transport planning, which took place at the University of the Sciences and Technologies of Lille 1, in the Laboratory city mobility and transport (LVMT), research unit of the French institute of sciences and technologies for transport, development and networks (IFSTTAR) and in the Department of Territorial Planning of University of Calabria (Italy). land use phenomena. Among the theoretical basis of Tranus we have: the economic based theory of [START_REF] Lowry | A Model of Metropolis[END_REF], which considers that a territorial system develops around a main attractive economic center; the input/output model [START_REF] Leontief | The Structure on the American Economy 1919-1939[END_REF] to define relations between consumption and production; microeconomic theory of random utility of [START_REF] Mcfadden | Conditional logit analysis of qualitative choice behavior[END_REF] to define user behaviors (path choice, modal choice, location choice, etc.) depending on the utility attributed to all available options.

Tranus includes, in fact, a transport sub-model (which simulates generation and distribution of transport demand, modal share and congestion levels), an activity sub-model (which simulates economic interactions between activities and households and location dynamics) and an interface module that allows transforming economic interactions between activities in transport flows.

The activity and land use sub-model is a discrete-economic spatial model and consists in the calculation of total demand, through an input-output matrix, which is then distributed in space according to the principle of utility maximization (considering localization and transport costs). Demand functions define consumption of each economic sector in function of prices and can be elastic for commodities that could be consumed only in their production zone (basically land and housing types) or completely inelastic for other economic sectors. Each activity sector and population category can choose within a range of different location types (Johnston et de la Barra, 1998) and consume production of several productive sectors, previously reported as substitutes (with corresponding preferences and penalties by demand category). The model is therefore able to reproduce the own competition mechanism of real estate market, where, for example, if housing demand increases in a specific area, without available surface for new urbanization, housing and land prices will also increase.

Tranus also represents in detail the transport system, taking into account capacity constraints, congestion and multimodality. Transport demand is distributed over transport network in function of disutilities, which include monetary (price, toll, energy costs, cost of transfer between modes of transport, etc.) and non-monetary factors (value of waiting time, penalties related to each transport category) and travel time is calculated according to a capacities restrictions process (de la Barra, 2013) (where if assigned demand exceeds capacity, then there will be an increase of congestion and thus of travel time). This process is therefore a fundamental characteristic with reference to the substitution and communicating vessels effect observed in the model and described later in this article.

In particular the process of capacity restriction allows to adjust travel times and waiting times as a function of demand/capacity ratio [START_REF] Modelistica | REPORT 466: Desk Reference for Estimating the Indirect Effects of Proposed Transportation Projects[END_REF]. At the end of each iteration demand is assigned to supply and then speed of vehicles is reduced in function of congestion levels, while in accord with queue theory, waiting times for public transport modes are increased as number of boarding units match or exceeds capacity. That is a crucial step that occurs at the end of the decision chain that defines in Tranus land use and transport integration.

The decision chain process starts calculating the cost of travel at a route level, then aggregating it from route level to model level and after to origin-destination level, generating the generalized composite cost of travel (de la [START_REF] De La Barra | Integrated land use and transport modeling[END_REF].

Activity location model is then executed as a function of this generalized composite cost and then potential travel demand is estimated by an elastic trip generation model. Modal choice is then defined as a function of composite costs by mode and assignment probabilities are calculated in function of travel cost at a route level (de la [START_REF] De La Barra | Integrated land use and transport modeling[END_REF]. Finally Capacity restriction step allows to compare demand with supply, adjusting if necessary travel and waiting time that will be considered in next iteration.

The definition of a time lag beetween the location/interaction of activity and the transport chain allows to adapt activity location choices to changes in accessibility, giving an integrated and dynamic structure to the model (de la [START_REF] De La Barra | Integrated land use and transport modeling[END_REF].

For each zone of the model and for each sector, values of production and demand, induced and exogenous, are defined. Exogenous sectors consume only inputs coming from outside the study area, while induced sectors are both consumers and producers and represent sectors induced by the production of exogenous activities.

The mechanism of distribution of households and jobs in space, follows the principle of minimization of generalized cost and thus of maximizing the utility function. The utility function therefore includes both generalized transport costs and location costs. This modeling structure has the ability to reproduce some typical urban cause and effects mechanisms as for example the fact that living in areas with high employment density implies a reduction in transport costs (related to homework trips), while living in low density area implies reduced localization costs but increased transportation costs.

The interface model is finally represented by an input/output matrix, which has the function to manage the interaction between the two sub-models (transport and activity sub-models) and which essentially transforms economic interactions between activities in transport interactions, that is economic flows in transport flows. Then it calculates costs and transport disutilities which will influence the interactions of activity in next simulations, reproducing the feedback loop between transport and land use [START_REF] Wegener | Overview of land-use transport models[END_REF].

The Tranus model for the French region of Nord-Pas-de-Calais

The Tranus model for the French region of Nord-Pas-de-Calais was designed mainly to simulate, analyze and evaluate interaction between transport, activities and residential systems with a multi-scale approach, which includes urban, suburban and regional scales, in different time horizons [START_REF] Feudo | Un scénario tod pour la région nord-pas-de-calais. Enseignements d'une modélisation intégrée transport-usage du sol[END_REF].

In particular, the main objective of this modeling research was to test the application of a regional plan of Transit Oriented Development (TOD) [START_REF] Calthorpe | The Next American Metropolis: Ecology, Community and the American Dream[END_REF][START_REF] Cervero | Transit Metropolis, a Global Inquiry[END_REF][START_REF] Bertolini | Cities on rail. The redevelopment of railway stations and their surroundings[END_REF], with the aim of concentrating future urban development as much as possible near main regional railway corridors and nodes.

TOD is in fact a model of urban and territorial development which favours mixing and compact urban densification near transit corridors and nodes, giving priority to active modes and public transport. Basically TOD consists in concentrating quality urban development around rail stations or interchange nodes, to encourage use of public transport (Bertolini, and al., on 2009) and with the aim of reducing natural land consumption, urban sprawl and car dependence.

Most important theoretical references of TOD could be found in previous concepts of Garden City (Howard, 1898) and of Linear City (Soria y Mata, 1926), with the intent to adapt these principles to complexity of contemporary cities and to create an alternative to automobility (Urry, 2003), which strongly characterized transport and urban planning in the last decades (F. [START_REF] Feudo | Un scénario tod pour la région nord-pas-de-calais. Enseignements d'une modélisation intégrée transport-usage du sol[END_REF].

The fundamental interest of the model is the analysis of effects of these integrated policies with the aim of resolving some territorial priority issues found in the main regional strategic planning documents (Conseil Régional NPDC, 2013), such as urban sprawl, excessive consumption of natural land and car dependence.

North-Pas-de-Calais is a region well equipped in transports infrastructures and located in a strategic geographical position, between Brussels and Paris. Despite significant regional investments in last years to improve railway network and public transport services, car still results largely predominant in mobility practices (see Figure 1). Most important transport flows are in direction of the metropolitan area of Lille, main regional economic pole, originated mainly from the central urban area and from the urban agglomerations of Valenciennes and Dunkerque. Smaller but not negligible flows occur also among medium urban agglomerations located along the ideal arc, placed at south of Lille (see Figure 2) defined "Arc sud". In that context is evident a greater dynamism of the north part of the region, concerning economic activities and mobility, also influenced by its cross-border nature.

In regional strategic planning documents railway is considered as the element on which to found and build future development, following principles of environmental and energy sustainability, economic growth and quality of life. In this regard, some regional rail corridors have been identified as potentially capable of hosting TOD interventions. Then, on these areas, were simulated, in a time horizon of 16 years (2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017)(2018)(2019)(2020)(2021)(2022)(2023)(2024)(2025), hypothesis of progressive urban densification, improvement of public transport supply quality, as well as the application of policies of integrated public transport ticketing and of discouraging car use.

The main objective was to evaluate effects of these policies on residential and activities location and modal share evolution. [START_REF] Fabre | Pages de Profils n°113: La région Nord-Pas-de-Calais structurée autour de neuf espaces[END_REF].

Structure of the model

For zoning characterization of the Tranus model 16 urban zones were defined, representing main regional cities of Nord-Pas-de-Calais. The agglomeration effect was also considered, grouping each main regional city with most important adjacent peripheral municipalities, following building and morphological continuity.

Metropolitan agglomeration of Lille (Lille Metropole Communauté Urbaine) was instead divided in 21 different zones, related to most representative municipalities. Furthermore 15 zones corresponding to the rest of regional territory were considered, according to institutional limits of main regional employ areas (Zones d'Emplois). Finally were also identified 14 "TOD zones", corresponding to groups of two or more municipalities containing rail stations sufficiently integrated with the surrounding urban fabric (F. [START_REF] Feudo | Un scénario tod pour la région nord-pas-de-calais. Enseignements d'une modélisation intégrée transport-usage du sol[END_REF]. To take account of the crossborder nature of the regional territory of Nord-Pas-de-Calais, 7 external zones were also defined.

The model considers three household categories in function of income levels (high, medium and low income) and two transport categories related to home-work and home-service trips. The whole operative and physical transport supply was loaded in the model and several parameters were defined, characterizing mobility behaviors of each transport demand category. In particular the transport sub-model considers the morning rush hour period (7:00 -9:00 a.m.) and only motorized interzonal trips (internal zonal trips and no-motorized trips are not considered)3 . Furthermore two exogenous activity sectors (industry and construction; agriculture) and two induced activity sectors (public tertiary and service tertiary) were defined, with correspondent number of employs for each zone of the model.

Land use sectors are exclusively related to urbanized land and to empty land for new urbanization, without considering natural land. Seven land use types were considered: residential land; continuous urban dense land or mixed land; collective residential land; isolated residential land; activity land; empty land; TOD land (introduced in the model to represent land with housing density levels of 10% -15% higher than existing residential and mixed land). For each type of land available surfaces were calculated and rental prices par unit of surface were estimated. Three alternative scenarios have been implemented on a time horizon of 16 years, from 2009 (base scenario) until 2025. A trend scenario (scenario A) was implemented assuming any change in transport and land use policies. A TOD scenario (scenario B) was implemented referred to the application of a TOD Regional Plan that provides, in some specific areas (TOD zones), interventions of progressive mixed and multifunctional urban densification and of improving public transport frequencies of service. From this second scenario was also developed a third scenario TOD + scenario (scenario C), which provides in addition to scenario B, some supplementary interventions to discourage car use, such as the introduction of motorway tolls and of an integrated ticketing system between regional rail services and urban and suburban bus services.

Hypothesis of densification applied in scenario B and C, consist specifically of interventions of urban renewal and regeneration (without consuming natural or agricultural areas), transforming progressively part of existing empty and residential land, in mixed, multifunctional and dense land and thus in TOD land.

According to TOD principle, TOD land is in fact characterized by high quality of urban design and high public transport connectivity and accessibility. This quality attributes of TOD urban space were reproduced in Tranus using some parameters called attractors, assuming a gain of attractiveness for areas affected by TOD interventions.

Model results and evidences of the communicating vessels principle

Results of the model, as exposed in detailed in [START_REF] Feudo | Un scénario tod pour la région nord-pas-de-calais. Enseignements d'une modélisation intégrée transport-usage du sol[END_REF], show that without specific actions, an intensification of urban sprawl would be observed, especially in Lille metropolitan area and in urban central area of the region.

In scenario A at 2025 (the last simulation period) most of growth is in fact located in rural zones, perceived more attractive than urban and TOD zones, consequently indicating an intensification of urban sprawl.

Interventions of multifunctional and mixed urban densification following TOD principles, simulated in scenario B, show a reversed trend. Residences and activities, hence households and jobs are mainly located nearby urban and TOD zones, even more distinctly in scenario C, demonstrating an increase of attractiveness of mixed, dense and public transport well-connected areas (see Figure 4). After the introduction of TOD hypothesis, rural and detached land consumption remains almost constant, even decreasing for high income households, in contrast with urban mixed land consumption, that generally increase for all demand sectors. Results related to land prices evolution also show how TOD interventions applied in scenario B and C contribute to improve land values in TOD zones. Transport results also show a positive effect of TOD Regional Plan in increasing modal share for public transport (see Figure 5). In particular results (considering motorized and inter-zonal trips only) show how public transport rates of frequentation redouble in the last time of simulation of scenario C. We also observe that at 2025, the strategic objective, considered in regional transport planning documents (Conseil Régional NPDC, 2013), of doubling number of passengers for regional rail services is reached in scenario B and even exceeded in Scenario C (see Figure 6).

In particular we observe that rail corridors that link Lille metropolitan area to the central urban area of the region (Lens, Douai, Bethune) and to the TOD zone located in the south of Valenciennes (including municipalities of Denain, Somain and Bouchain), give a positive response to TOD interventions. We can argue that the strategic position of these rail corridors, located on the axis Brussels-Lille-Paris, in a large and attractive jobs and residences regional polarity, and affected by important and growing transport flows directed to Lille, promotes a positive response to TOD interventions (see Figure 7).

More attractive and more efficient public transport services, seems to generally increase attractiveness for areas on which were activated TOD interventions.

Analyzing modal share for each single TOD zone, results give a trend that essentially reproduce the total modal share data, with some more favorable effects in zones closeness to rail corridors previously described.

However we observe in two TOD zones (TOD zone of Armentières and TOD zone of Denain, Somain, Bouchain, in the south of Valenciennes), a different trend, with public transport modal share that decreases in the last scenario (the most favorable to public transport) (see Figure 8). [START_REF] Feudo | Un scénario tod pour la région nord-pas-de-calais. Enseignements d'une modélisation intégrée transport-usage du sol[END_REF] Moreover these transport results are associated with a general increase of transport demand in these zones, due to the significant growth of population and employees (especially for tertiary activity sectors) in the last simulation scenario (effects of TOD densification hypothesis) (see Figure 9 and Figure 10). To understand the reason of these unexpected results was analyzed the Tranus output related to evolution of road level of service4 . Results about road network level of service show in fact that in last simulation period of scenario C there is a significant reduction of highway congestion levels and therefore an increase in average speed.

If we consider the specific case of the TOD zone of Armentières, we can say that the gradual reduction of road congestion of highway A25 (consequently to increased public transport rate of frequentation), added to the high level of road accessibility and connectivity of this zone (that represents a strategic access point to Lille agglomeration), induced on this specific highway section, in scenario C, an initial increase of public transport rate of frequentation (simulation periods 2013, 2017, 2021) and then a return of attractiveness for private car (simulation period of 2025).

The same mechanism can be found in correspondence of the TOD zone located in the south of Valenciennes, where in scenario C the A2 highway section that connects Valenciennes to Cambrai, becomes completely decongested and characterized by the maximum level of service (level A). Also in this TOD zone private car became more attractive in the simulation scenario C, the most favorable to public transport (see Figure 11 and Figure 12).

Basically TOD hypothesis applied to our study area, leading gradually to a significant reduction of traffic congestion, bring cars in the last simulation time to regain attractiveness (especially in two TOD zones particularly well-connected to highway network), hence to the activation of an initial substitution effect between private car and public transport demand (generalized in the entire study area), followed by a re-equilibration, that we define as a communicating vessels effect, in favor of private car. This situation is however quite limited, because in all other zones of the model public transport modal share generally grows in TOD scenarios, even if there is a general improvement of traffic conditions and road levels of service. TOD zones of Armentières and in the south of Valenciennes are very well road-connected, with high level of commuter flows directed to Lille agglomeration and dramatically affected by road congestion in the base time period (2009), in particular during rush hours. These two zones seem therefore incorporate many of different conditions that influence the activation of substitution and communicating vessels effects, applied to mobility and transport dynamics [START_REF] Bovy | Substitution of travel demand between car and public transport: a challenge to policy makers, Ministry of Transport and Public Works, Traffic and Transport Research Division[END_REF].

Further considerations about the sequence of substitution and communicating vessels effects

In accord with theory of demand, a change in price or in transport costs (in Tranus generalized transport costs include monetary costs and perceived travel and waiting time (Modelistica, 2103)), keeping constant utility, will cause an increase of consumption, therefore there is an inverse relationship between transport cost and demand.

This inverse relationship produces an income and a substitution effect. Income effect means that lower prices allow users to have the same consumption level with less expenditure [START_REF] Button | A Dictionary of Transport Analysis[END_REF]. Moreover if consumption of two goods (or services) increases as income rises, these are normal goods, while if consumption of one within two goods decreases as income rises, hence this is an inferior good. Furthermore according to cross elasticity of demand, if ratio between changes in demanded quantity of a good (or service) B and changes in price of a good (or service) A is positive, goods are substitutes, otherwise are complementary. Furthermore cross elasticity is zero when two goods or services are not related and the substitution effect increases proportionally in function of number of available substitutes (choice options) for consumers [START_REF] Fouquet | Trends in Income and Price Elasticities of Transport Demand (1850-2010[END_REF].

Results of the model show the activation of a substitution effect related to distribution of transport demand between private car and public transport. In two particular zones, according to theory of demand, was observed that during the first three simulation periods (2013,2017,2021), generalized transport costs for private car increased, due to strong road congestion, while demand for public transport increased, thanks also to TOD interventions (population and activity densification; improvement of public transport frequencies), hence activating a substitution effect.

In the last simulation period (2025), highway congestion levels resulted significantly reduced, while despite an increasing demand for public transport, generalized transport costs for private car decreased, hence public transport and private car became complementary.

Following the substitution effect, reduction in traffic congestion levels restores a comparative advantage for cars versus public transport, leading to the activation of a communicating vessels effect. This trend indicates how transport demand progressively level off, following a temporary and instable equilibrium, influenced among others by demand behaviors and by physical and operative constraints of infrastructure and transport services.

The model essentially provides an empirical confirmation of the existence of a substitution effect between private cars and public transport and of a communicating vessels effect that attenuates this substitution effect. This sequence of substitution and communicating vessels effects, takes place in particular time intervals and conditions and the same factors that determine the activation of substitution effect also influence timing of activation of communicating vessels effect.

Therefore results show the existence of a permanent state of tension in modal share that in the short term induces to consider private car and public transport as substitutes, while in the long term as complementary. In the short term high levels of road congestion (high private car transport costs) associated with increased public transport frequencies, induce to lower private car demand and higher public transport demand (behaving as substitutes). In the long term high rates of public transport use induce lower road congestion levels (lower private car transport costs), thus higher private car demand (behaving as complementary).

Other authors affirm that the substitution effect between private car and public transport occurs only in some specific situations, depending on trip purpose, traveled distance and segments of transport demand.

In particular Baanderr et al. (2011) affirms that, as confirmed by results of the Tranus model, substitution effects happen only in presence of severe congestion, in areas close to large urban centers and in reference to more stable transport demand segments, as house -school and home -work trips. [START_REF] Bovy | Substitution of travel demand between car and public transport: a challenge to policy makers, Ministry of Transport and Public Works, Traffic and Transport Research Division[END_REF] also affirms that some particular transport demand segments related to public transport and private car cannot overlap and therefore cannot be included in the substitution effect and thus in the communicating vessels effect. Some examples of these limitations are the fact that private car is available 24 hours a day while public transport services are available only in service hours, and the fact that public transport services are more accessible in urban areas instead of rural areas [START_REF] Bovy | Substitution of travel demand between car and public transport: a challenge to policy makers, Ministry of Transport and Public Works, Traffic and Transport Research Division[END_REF].

These considerations are a further confirmation of the validity of Tranus model results, which mainly considers home -work trips during morning rush hours. [START_REF] Bovy | Substitution of travel demand between car and public transport: a challenge to policy makers, Ministry of Transport and Public Works, Traffic and Transport Research Division[END_REF] in fact also affirms that other trip purposes, so-called chains of displacements (which includes various types of activities before reaching final destination), are not included in the substitution and communicating vessels effects between public transport and private car. Baanderr et al. (2011) also sustains that activation of communicating vessels effect can be observed only in situations where car and public transport are strongly competitive, providing a further explanation of why return of attractiveness for private car has not occurred in other zones of the model, affected by low congestion and more distant from urban areas. Anyway these considerations cannot prevent to suppose that communicating vessels effect could also happens in other zones of the model, but with different temporalities, that go beyond the simulation period.

A this regard is important to precise that if we can observe a sort of "temporal dynamics" in the context of the modeling exercise presented in this article, that is essentially related to the succession of multiple states of equilibrium, temporary (because they relate to specific time intervals) and interdependent (because each is influenced by the previous equilibrium generated by the model). Anyway the controversy over differences in potentiality, consistency and reliability between static and dynamic LUTI models goes beyond the intentions of this article.

The model for the French region of Nord-Pas-de-Calais considers five times of simulation, with intervals of four years (from 2009 to 2025); in line therefore with Tranus characteristics identified by N. [START_REF] Coulombel | Modélisation du marché du logement dans deux modèles d'interaction transport-urbanisme, TRANUS and URBANISM[END_REF], which makes it particularly suitable to simulate long-term process. The succession of several equilibrium states, relating to different time simulations, gives the appearance of a temporal evolution in model results. A level of evolution that is enough to read a temporal cause and effect dynamic in the process of interaction between supply and demand of transport.

The five times of simulation allow comparing short and long term effects (24 years can be considered as long term compared to phenomena analyzed in that model), in terms of evolution of transport demand modal share. On the other hand it is clear that other more specific events, such as for example rate of frequentation of a specific bus stop, would be more difficult to analyze considering given zoning and model structure.

It is also clear that, as explained in paragraph 2 of this article, the calculation process of Tranus related to capacity restrictions, have a considerable impact on the nature and evolution of obtained results.

Analyzing these results from a point of view more oriented to strategic and operative planning, we can also observe that factors and conditions necessary to the activation of the sequence of substitution and communicating vessels effects, can alternatively favors private car or public transport and in some situations cancel or notably downsize effects of policies and actions encouraging public transport use (Baanders et al. 2011). This is also the case of this model where return of attractiveness for private car occurs exactly in the simulation period where most favorable policies to public transport use are applied. Therefore observed communicating vessels effect, invites to consider public transport as not necessarily competitive and alternative to private car, but rather as complementary, in particular in the case of long term TOD plans.

This necessarily implies the need to consider, in the phase of strategic planning, all possible unexpected reciprocal effects that some transport and land use planning policies can arise. In the phase of operative planning the main need is instead of providing a continuous action of observation, control and adaptation of implemented policies, to well manage modal share evolution.

In particular planners have to consider the tendency of transport demand to be distributed following multiple temporary and instable equilibriums, which in turn are influenced by transport costs, user's perceptions and behaviors and by planning actions.

Conclusions

Model results show the ability of a TOD intervention extended to the entire region of Nord-Pas-de-Calais, to limit or at least moderate urban sprawl, promote urban development along main corridors of the regional rail network and increase use of public transport. However were observed unexpected results, related to return of attractiveness of private cars as a result of highway congestion reduction in two TOD zones of the model, in the last simulation scenario (more favorable to public transport).

A phenomenon that should be explained through the activation of a substitution effect followed by a communicating vessels effect, which influenced transport demand distribution between private car and public transport, depending on travel costs and congestion levels, following a principle of succession between multiple temporary and instable states of equilibrium.

Furthermore the fact that these effects do not appear in other zones of the model, indicates that the sequence of substitution and communicating vessels effects occurs only in some specific contexts and time intervals, depending on particular conditions (stable demand segments; strong competition between car and public transport; high levels of congestion; proximity to attractive urban agglomerations).

In particular results show the existence of a permanent and instable state of tension in modal share that induces to consider private car and public transport as substitutes in the short term and as complementary in the long term.

Figure 1 .

 1 Figure 1. Modal share and public transport modal share in the study area in the base scenario (2010). (Conseil Régional NPDC, 2010).

Figure 2 .

 2 Figure 2. Structuration et interconnexions en Nord-Pas-de-Calais[START_REF] Fabre | Pages de Profils n°113: La région Nord-Pas-de-Calais structurée autour de neuf espaces[END_REF].

Figure 3 .

 3 Figure 3. Interactions between sectors in the Tranus model for North-Pas-de-Calais.

Figure 4 .

 4 Figure 4. Evolution of population and employment in the study area.

Figure 5 .

 5 Figure 5. Evolution of transport demand modal share between car and public transport. (F[START_REF] Feudo | Un scénario tod pour la région nord-pas-de-calais. Enseignements d'une modélisation intégrée transport-usage du sol[END_REF]

Figure 7 .

 7 Figure 7. Evolution of railway services rate of frequentation. (F.[START_REF] Feudo | Un scénario tod pour la région nord-pas-de-calais. Enseignements d'une modélisation intégrée transport-usage du sol[END_REF]

Figure 9 .

 9 Figure 9. Population growth in two TOD zones at 2025, by simulation scenario.

Figure 10 .

 10 Figure 10. Employment growth in two TOD zones at 2025, by simulation scenario.

Figure 11 .Figure 12 .

 1112 Figure 11. Evolution of road network level of services at 2009 in the base scenari..[START_REF] Feudo | Un scénario tod pour la région nord-pas-de-calais. Enseignements d'une modélisation intégrée transport-usage du sol[END_REF]

  Substitution effect favors private car or public transport, depending on modeling assumptions and on different simulation scenarios, demonstrating a greater A25 SCENARIO C -2025 A2 sensitivity to some specific factors: households and activities location trends, levels of congestion, speed and travel time, frequencies of public transport services.

Internal zonal trips cannot be simulated in Tranus, therefore in the model are simulated only inter-zonal trips and bike and pedestrian trips related to transfers between transport modes and connections to zone centroids. That is actually an unfavourable condition to evaluate and verify expected effects of TOD hypothesis; because normally the most important positive impacts of TOD mixed densification interventions are related to proximity and not motorized mobility.

Level of service (LOS) is a qualitative measure used to analyse the quality of traffic service. LOS standards are defined in the Highway Capacity Manual (HCM), published by the Transportation Research Board (TRB) and in the Geometric Design of Highways and Streets, published by AASHTO (American Association of State Highway and Transportation Officials), using letters A through F, with A being the best and F being the worst.


Jean Patrick

Mfoulou Olugu
email: mfuluolugu@yahoo.fr

URBAN FORM, MOBILITY BEHAVIOR AND DYSFUNCTION OF TRANSPORT SUPPLY: THE CASE OF YAOUNDÉ *

Keywords: urban form, urban mobility, transport supply, agglomeration in Africa, Yaoundé

The objective of this chapter is to assess the relationship between urban form, mobility behavior, and dysfunction of transport supply in a large African city with high urban growth like Yaoundé in Cameroon. Specifically, the chapter aims at assessing the influence of urban, mobility, and socio-economic characteristics of an origin area on the mobility choice of individuals. Using field data collected by the urban community of Yaoundé in 2010 and statistical tools such as multinomial logits, results show that urban form characteristics, such as human and establishment densities, accessibility, and origindestination distances influence the choices of individual mobility. The urban form of major cities in Africa, due to a very high urban growth uncontrolled by the local authorities, plays a negative role on the operations of urban transport service in Africa because it promotes an artisanal supply characterized by a low capacity and reduces the efficiency and competitiveness of mass public transportation, which is cheaper. Based on results of this study, recommendations are: controlling urban sprawl, easing of accessibility to public transport, and developing an efficient and competitive mass transportation.

INTRODUCTION

Urban mobility is currently becoming an important concern of developing countries with the principal challenge being the reduction of artisanal supply characterized by a low capacity and the increase of efficiency and competitiveness of mass public transportation. In Africa where the households' motorization rate is still weak, the main issue appears to be adequate public transportation. The authorities have neglected urban growth and management as a potential means to solve mobility problems. The topic is that current and urban growth affects all sphere of the economy (agriculture, welfare, health, pollution, among others). According to [START_REF] Zhao | Car use, commuting and urban form in a rapidly growing city: Evidence from Beijing[END_REF], urban transport and ways of reducing travel needs in cities must contribute towards achieving carbon reduction targets. The role of developing countries, where urban transport is still done as business as usual, is crucial in achieving this target.

In October 2015, The Africa Sustainable Transport Forum (ASTF) implemented with the support of UNEP 1 , the World Bank, the SSATP 2 program and UN-Habitat 3 , outlined a harmonized roadmap for achieving sustainable transport in Africa where mass transit system, vehicle emission, and energy efficiency are among some of the priority areas. The ASTF 4 agenda focused on challenges in terms of day-to-day realities of sustainable transport in Africa and discussed solutions in the context of green growth and emissions reductions. Prior to the ASTF roadmap, matters of urban mobility were not given full consideration by the authorities adopting the "business as usual" approach (small cars, normal vehicles, traffic jam, high cost, and high number of road fatalities in town) to resolve negative externalities. The underlining observation that tackling urban sprawl and mobility behaviors appears to be the main goal to achieve sustainable transport systems and is particularly evident in large African cities like the metropolitan city of Yaoundé in Cameroon.

The urban structure of Yaoundé is similar to the structure of large agglomerations in Sub-Saharan Africa. The spatial growth is a result of an uncontrolled expansion by the Government. It is characterized by a horizontal, anarchic, and uncontrolled spread creating a functional differentiation of space and forcing to travel long distances, particularly on commuter routes that have only one limited access way to the center. The urbanized area of Yaoundé organizes around the center that is very sparsely inhabited, mostly reserved to activities, and constituting the oldest nucleus whose first developments date back to the early 60s. This scheme reduces the efficiency and competitiveness of mass transportation, with a very strong complementarity of small carriers to craft practices.

In Yaoundé, mobility problems have worsened since the shutdown of the Public Urban Transport Company (SOTUC) in late 1990s. Despite the entry into operation in 2006 of the "Lebus" public transport company, daily mobility remains mainly by taxis of small capacity (61%). Their operation is characterized by frequent stops and disordered, significant negative externalities, and high costs beared by users [START_REF] Mfoulou | Structure urbaine et mobilité à Yaoundé[END_REF]. In order to meet the demand center-periphery, minibuses realize up to 9% of trips to remote areas of the city center. In areas where the road is particularly in bad conditions, motorcycles, of which the share is estimated at 3% and the number is rapidly and steadily emerging, are used. Despite these initiatives, the issue of mobility still arises with a great acuity.

Law n°2004/003 of April 21, 2004 governing town planning in Cameroon defines the Urbanism Plan as an urban planning document that sets guidelines for the urban land, general densification of soils, and programming equipment. The Master Urban Plan was developed around four objectives for transforming the city of Yaoundé: (i) a more radiant city; (ii) a more welcoming and pleasant city; (iii) a restructured and rebalanced city; and (iv) a more accessible city. But, despite the existence of urbanization and development schemes to facilitate the management of urban space and mobility of citizens, there is an increasing proliferation of new neighborhoods at the periphery of the city or spontaneous ones that accentuates the dysfunction of the transport offer.

Urban development raises many reflections on its consequences and on actions to be taken. Should we react to urban sprawl? If yes how? Should we let the pretext that these are the preferences of individuals? Challenges of sustainable development have revived these discussions and a planner or a local decision-maker must be brought to the question of the effects of planning choices on mobility behavior? Or specifically, what are the consequences of a poorly planned urbanization development on mobility choices and costs? In the current context of reflection on "the city," these issues need to be asked. But, there is still a very little literature on this topic in Africa. The little knowledge about this area remains very inadequate to inform effectively decisions on urban planning. The objective of this chapter is to evaluate factors that drive urban economic agents to prefer a mode of mobility capabilities such as a small taxi or a motobike that accentuates the dysfunction of the offer in Yaoundé. Specifically, it assesses the impact of urban factors on the choice and costs of mobility in Yaoundé.

URBAN STRUCTURE AND CHARACTERISTICS OF MOBILITY IN YAOUNDÉ

The urban structure of the city of Yaoundé is characterized by a horizontal expansion and a functional differentiation in the utilization of the urban space. We also observe low levels of public infrastructural services in peripheries. Likewise, demographic and spatial growth is anarchic and uncontrolled due a lack of accessibility and an inappropriate road network [START_REF] Mfoulou | Structure urbaine et mobilité à Yaoundé[END_REF][START_REF] Ongolo | Suburbanization and Inequality in Transport Mobility in Yaoundé (Cameroon): Drawing Public Policy for African Cities. GDN Project on Urbanization and Development -Francophone Africa Project[END_REF]. According to the IMF5 (2004) and the Cameroon Poverty Reduction Strategy paper, urban sprawl in Cameroon has accelerated over the past 20 years with an average growth rate between 6 and 7%. More recently, the 2009 Growth and Employment Strategy Document of the Government of Cameroon recognizes that both urban and suburban towns and cities are likely to growth. The document also identifies, among others, the need to rehabilitate urban infrastructure and to manage better urban sprawl. For the city of Yaoundé, the urban surface area quadrupled between 1980 and 2001 from less than 4,000 hectares to 16,000 hectares. In 2010, the surface area of the Yaoundé Urban Council (CUY) was approximately of 30,000 hectares (CUY 2010). The increase in the urban surface area has affected mobility patterns in Yaoundé [START_REF] Mfoulou | Structure urbaine et mobilité à Yaoundé[END_REF][START_REF] Ongolo | Sources of inequality in the cost of transport mobility in the city of Yaoundé, Cameroon[END_REF]. Urbanization in Yaoundé is organized around the center that is very few inhabited, mostly reserved to administrative and commercial activities, and constitutes the oldest nucleus whose first developments date back to the early 1960s. The center contains most of the administrative and commercial structures of the country. As it appears in Figure 1 above, almost all official bodies are contained in the central zone. The center is the main attraction of the city. Although local administrative delegations cover the whole city, they have a smaller workforce than central delegations. The commercial center meanwhile focuses on many services such as banks, insurance, and formal trade. It should be noted that some services are spread throughout the city and especially near housing areas. This is particularly the case of bakeries and gas stations. Industrial activities, although scattered throughout the city, are largely located in the South, stretching along the center and periphery. In the city center, the presence of formal activities generates an informal sector: small sellers, restoration, various repairs, etc., and major markets. Generally, the central administrative fabric is characterized by concentrated constructions, but having a low coefficient of footprint (approximately 30%).

The localization of basic services in the city of Yaoundé is dependent on the level of services provided. Indeed, most public schools, better known for their qualities, are situated in the central area or the inner suburbs of the center, while private schools created more recently are built near popular suburbs. High schools also have a greater tendency to concentrate near the city center, on the contrary primary schools are scattered throughout the city. Likewise, a part from the complex of the General Hospital is located within or close to the city center. The "Lebus" company operates on 6 out of the 13 lines of the network defined by the former SOTUC operator. As illustrated in Figure 2, the whole city traffic converges towards the city center.

Source: CUY (2010). Saturation of the central place then leads migrants still many to turn to the periphery in the search of new constructible land; hence, the city explodes and spreads. Districts created consolidate themselves in an urban disorder. These neighborhoods are characterized by a lack of equipment and accessibility. There are about 60 people per hectare. In 2010, the annual production of informal dwellings in Yaoundé was estimated at about 115,000 units, broken down into 2,500 modern structures and 8,500 informal structures (CUY 2010). The management of roads faces recurring blockages due to the urban configuration of the city. The realization of roads (paved or not) involves more expropriations and maintenance difficulties. Several mobility problems actually appear in Yaoundé: the public road network is not adapted to the high proportion of walking; the railway is not structured to favor urban mobility; over 74% of vehicles registered under small capacity have over 15 years of age; and the supply of "Lebus" transportation is inadequate and ineffective. The Yaoundé's urban form results, as a consequence, in an increase in distance, travel time and modes of transportation based on small capacity vehicles. The 2010 Urban Displacement Plan estimated that small capacity vehicles with up to five seats perform over 86% of the daily traffic volume of Yaoundé. Only 2% of vehicles are minibuses (9 to 12 seats) and buses with over 30 seats. The report also indicates a high level of congestion during peak hours.

The hourly traffic represents on average 4% of daily traffic. The morning rush hour is between 7 a.m. and 8 a.m. and concentrates transit transport for professional and educational reasons and the evening rush hour is between 5 to 7 p.m. and conrresponds to 7% of the total traffic. The traffic between 10 p.m. and 6 a.m. represents 7.5% of the total (see Figure 3).

Following road network surveys of the city at peak hours, it appears that heavy traffic in Yaoundé reaches a floor of 810 vehicles and a ceiling of 3530 vehicles during a rush hour on relevant roads. This leads to congestion and persistent traffic jams that lengthen travel time, thus promoting increased energy consumption and the emission of exhaust gases. The average travel time recorded in surveys is of 29 minutes. For a round trip, it is about 60 minutes. As against bus users for which the average travel time is of 60 minutes, this timeframe is clearly an obstacle to the use of this type of transportation. However, the congestion of certain channels may increase the travel time from 150 to 200%. It was possible to differentiate movements on the movement pattern. The choice was made based on the suggestion of Wiel (2002) of distinguishing between recurring and regular movements that correspond to stress mobility (pattern 1: home-to-work, home-to-school and education) and more occasional trips, which are the responsibility of a selected mobility (pattern 2: leisure, shopping, etc.). Table 2 below provides a breakdown of the top 10 reasons, identified during our investigations, for which people move in Yaoundé. They represent 71% of all possible reasons. The motive for which one goes from home to work is the most important, those related to visits, shops, and schools follow from far enough. The ensuing effect of urban sprawl of Yaoundé has been an increase in distance travelled; time for transportation, and fuel consumption leading to greenhouse gas emissions. Likewise, Yaoundé has witnessed an increase in the number and types of vehicles. The 2010 Urban Displacement Plan, using an origin/destination matrix and the gradient method, estimated that vehicles with at most five seats carry out more than 50% of the daily volume of traffic in Yaoundé. Only 9% of these vehicles are minibuses (9 to 12 places) and 3% buses with more than 30 seats. This report also indicates that the average rate of congestion during peak hours is of 0.3 with about 14 kilometres of saturated roads, that is about 5% of the total distance. The Yaoundé Urban Council has recently indicated that since 2010 these figures have worsened because of the disappearance of the transport supply by buses and urban sprawl. The graphics below simulate car traffic for 2010 and 2030 in the city of Yaoundé using the Unit Passenger Car (UPC).

Source: CUY (2010).

METHODOLOGY

We consider that the location of subsystems (urban form) and social relationships (socioeconomic characteristics) are inputs in mutual interactions and the choice of the transport system are outputs. It is essential to take into account these interactions to determine what proportion of mobility is explained by characteristics of households and by the urban form. The answer to this question will help us to legitimize or not urban development measures whose the aim is to control the growth of small capacity vehicles (taxis and motorcycle) in Yaoundé. We proceed at the individual level integrating simultaneously explanatory variables in our models relating to characteristics of individuals and the urban form.

Experience shows that individuals with identical characteristics, placed in the same context may not be asked to perform the same choice of mode of transport (Bonne 2004). An individual usually performs the choice that maximizes his utility, but it is imperfectly known (Ben-Akiva and Lerman 1985). Models used in this approach are based on logit formulations. Assuming that an individual i has m comprehensive alternatives to make a choice of transport modes, then the utility from choosing the alternative j (j = 1,…, m) can be represented as follows:

(1) where U ij represents the utility derived by a consumer when choosing the mode j, x' ij is the matrix of explanatory variables, ε ij is unobserved, and β is the vector of model parameters. The utility (U ij ) of the consumer i after choosing the mode of transport j is not observed. Only the mode of transport is observed. Thus, the consumer i chooses the mode of transport j if it gives to him a maximum utility or if he acquires from it the maximum satisfaction.

(2)

For the choice of transport mode (y i ) by the consumer i, it follows that:

(3) With and P(y i = j) ≥ 0 (m being the number of transport modes available). This probability depends on the value of the utility of the transport mode with respect to the alternatives. The distribution function of a logistic law can be presented as follows:

(4)

To take account of random disturbances, the estimation of model parameters β is made by using the maximum likelihood.

(5)

The interpretation of estimated parameters of a logit model requires caution. Indeed, estimated parameters only provide information on the positive (β > 0) or negative (β < 0) impact of independent variables. Thus, the quantification of the impact of each variable on the probability P(y i = j) will proceed by calculating of the marginal effects. The marginal effects of a change in an exogenous variable x i k , ∀k = 1,...,K, (K being individuals' characteristics) on the probability that the consumer chooses the j th mode, ∀j = 1,...,m, are defined by: where β j k is the k th component of β j associated with the explanatory variable x i k and P ij = P(y i = j) and δ ij is the effect of a unit change in an independent variable on the probability that the consumer i uses the alternative j. Three types of statistical tests are used to validate the quality of the model and often give similar results: the likelihood ratio test (Likelihood ratio), the score test (Score), and the Wald test (Wald). These tests follow the same principle. Generally, they compare the information provided by the reference model, that is to say the one containing the explanatory variables and the information provided by a simplified model. Estimates of the multinomial logit model are generated by: (7) where y i represents the mobility choice. A total of five modes are possible: (1) Motorcycle;

ij ij ij x U ε β + = ' ( ) im i i ij u u u Max U ,..., , 2 1 = ) ' ;...; ' ; ' ( ) ' ( )) ,..., , ( ( ) ( 2 2 1 1 2 1 im im i i i i ij ij im i i ij i x x x Max x P u u u Max U P j y P ε β ε β ε β ε β + + + = + = = = = ∑ = = = m j i j y P 1 1 ) ( i i i x x x i i r i e e e x F y P P ' ' ' 1 1 1 ) ( ) 1 ( β β β β - + = + = = = =           + = = = ∑ ∑ ∑ ∑∑ ≠ ≠ = = = = = 3 1 ' ' 1 1 1 1 1 ln )] ( ln
(2) Personal car; (3) Taxi; (4) Bus and Minibus; and (5) others. CL(VA) is a linear combination of independent variables. Source: Author: PDU data (2010).

) (

1 k z K z iz k j ij k i ij ij P P x P β β δ ∑ - = ∂ ∂ = = i i VA CL -P P y ε + =         = ) ( (choice) 1 choice) ( ln
Data come from surveys conducted by CUY as part of the development of the Urban Transport Plan (PDU). These surveys focused on the identification of vehicles, the estimation of traffic volumes, and the analysis of the main crossing points, patterns, origins, and destinations of trips. Surveys were designed to measure and define the structure of traffic in Yaoundé and the type of vehicle to obtain information required for the analysis of traffic problems and to provide a better future traffic in the city. Surveys also helped to better understand motives and means used for traveling within the city. The Origin/Destination investigations performed in same places as traffic counts; 34 points were identified. They were carried out in a continuous manner between 6 a.m. and 10 p.m. Table 3 below shows all variables used to estimate the influence of the urban form on mobility choices. A total of 16,205 to 17,950 individuals were selected to have a consistent sample.

RESULTS

The attitude of the consumer in choosing a mode of transport depends on several factors. The first step to access a transport is to join the road. Accessibility to public transportation seems to be the first significant factor of transport mobility choices. It appears that accessibility to public transit significantly and negatively influences the use of the motorbike and taxi. Contrariwise, this influence is positive on the use of bus. The less the consumer has access to public transportation, the more he uses a motorbike or a taxi. In most cases, the less fortunate urban dwellers use both modes of mobility: first, they use the motorbike to get until the paved road and after they take a taxi. At the opposite, the wealthy city dwellers use their personal car and are generally localized in areas accessible by car. The density of the area of origin significantly influences all choices of mobility, but in different directions. For the motobike, the effect is positive, the more areas are densely populated, the more urban mobility choices deals with motorcycle. Supply and demand for mobility by motorcycle usually abound in popular neighborhoods with high population density. This observation is justified by the fact that the motobike is accessible to all and from door-to-door. But, the density also encourages other mobility choices as bus and minibus. Generally, densely populated areas have a very high demand for mobility and justifies the availability of public transportation. These areas are also those where supply for bus and minibus is also available. In reality, it was old neighborhoods of the city of Yaoundé that benefited public amenities before the crisis years of 1980-1990. The population density has a negative influence on the choice of taxi. In fact, in densely populated areas, citizens less prefer this choice because of its strong capability at generating congestion. The motobike is then chosen in those areas due to its speed and cost, but less for comfort and safety. This mode is typically used for very short origin-destination distances in less accessible areas.

Consumer attitudes concerning transportation also depend on the desired pattern regaring means of transport. The reason of the positive impact of all mobility modes with a marked significance for taxi and personal car is that urban dwellers choose less the motobike to reach their workplace. Note that, this mode is usually used to reach the place where it is possble to take a taxi, a bus line, or the nearest Minibus. Moreover, it is also important to point out that this mode of mobility has no access to the city center or administrative center where most jobs are located. The time variable has a significant influence on the choice of the motobike and the personnel car. This observation is justified, because the choice of the motorcycle is generally a mandatory choice. When facing the dysfunction of the transport supply, the consumer has no alternate offers of transportation. In the case of the personal car, the consumer is generally indifferent to other optional offers since he has his own car. It makes use of the latter regardless the type of travel.

The individual cost of mobility influences negatively and significantly the choice of the motobike. This means that this mode become more popular and is more used. However, the cost of mobility influences positively and significantly the use of bus and minibus. In fact, bus and minibus are not effective and competitive modes. Already, availability is limited to some coverage lines, which do not allow serving the vast majority of the population, usually located on the periphery. The likelihood that an increase in the original density influences the choice of an urban mobility is of 45% (with an elasticity of 1.23), a higher proportion than for all other variables. To influence mobility choices in favor of collective modes, public facilities must move towards urban densification policies. Beyond the urban densification policies, the accessibility to transport infrastructure affects positively mobility choices with a probability of 25%.

The size of the trip also has a high probability (22%) on the choice of a mode of mobility and elasticity of 1.02. An increase in the size of travel affects consumer choices, but that choice is at the detriment of the collective mode because the sign of the effect is negative. This argument militates in favor of a reorganization of collective modes, in particular transportation by bus and minibus. But, with limited park and lines that are tens of kilometers from each other, bus frequencies are very low. Low frequencies are partly due to traffic congestion during peak hours that greatly affects the speed of the bus. According to data from a performance audit report carried out by the Government in 2010, bus traffic decreased from 8.7 million passengers in 2008 to 5,700,000 in 2009; a drop of 35% in a year. In 2010, the bus operator continues to lose traffic. In May 2010, he recorded a total traffic of 379,000 passengers, against about 437,000 for the month of May 2009, a decrease of 13%. The analysis of data of the company on traffic at the beginning of June shows that daily traffic by bus in the city is about 14,000 passengers, i.e., 500 passengers per bus. The huge demand for this mode of mobility let us suggest as a recommendation the reorganization of this service towards greater competitiveness and efficiency; this being only possible through a reorganization of the urban space and the creation of poles of urban concentration where collective modes can grow at the expense of individual modes.

CONCLUSION

The main objective of this research was to assess and analyze the impact of the urban form of mobility in the city of Yaoundé in Cameroon. Specifically, it proved important to assess and analyze the impact of the urban form on consumer choices. The approach has mobilized logit econometric techniques. Data were collected by means of surveys organized by CUY in 2010 as part of the development of the PDU. The following results were obtained: urban density has a significant and very strong influence on the choice of mobility by individuals living in Yaoundé. The high popuation density promotes the use of public transit and therefore reduces the cost of mobility. Beyond the density, availability also plays a decisive role on the choice of the type of mobility. Other variables such as motifs of destinations are equally critical to influence the choices of a type of mobility, but with a very low probability and a lower elasticity. Results also confirm that the population density is inversely correlated with the use of the car and is positively associated with the use of soft modes as motobikes. For a dual effect on the level of congestion and accessibility, options in areas with high population can be shuttles and alternative modes of transport to the car, while it increases the cost of the mobility of transport in low population density areas.

  Legend: Ministries Embassies and Consulates Delegations and City councils. Source: CUY (2010).

Figure 1 .

 1 Figure 1. Localization of Ministries, Embassies, Consulates, Delegations, City councils (Top) and Banks (Bottom) in Yaoundé.

Figure 2 .

 2 Figure 2. Lines operated by Lebus.

Figure 3 .

 3 Figure 3. Distribution of hourly traffic in Yaoundé.

Figure 4 .

 4 Figure 4. Simulation of car traffic for 2010 and 2030 in the city of Yaoundé using the Unit Passenger Car (UPC).

Table 1 . Distribution of traffic by type of vehicle in Yaoundé

 1

	No Type of vehicle	Number of vehicles counted	% total Distance in kilometers
	1	Motorcycles	133,163	6.10	3,703.43
	2	Personal cars	823,540	37.80	49,205.88
	3	Taxis	1,065,938	48.80	86,725.17
	4	Minibus	41,578	1.90	4,094.06
	5	Bus	4,366	0.20	7,188.73
	6	Vans	80,771	3.70	4,065.54
	7	Trucks 2 Es	13,098	0.60	495.97
	8	S + Truck	8,732	0.40	80.56
	9	Trailers	7,448	0.30	40.42
	10 Others	4,366	0.20	30.25
		TOTAL	2,183,000	100%	522269.58
	Source: Author: PDU data (2010).

Source: PDU data (2010).

Table 2 . Key reasons for traveling from the origin to destination

 2

	Reasons for traveling	Number of trips	%
	Home-to-work	8,292	47%
	Leisure	3,471	19%
	Home-to-school and education	3,285	18%
	Shopping	2,907	16%
	Total	17,955	100%
	Source: Author: PDU data (2010).

Table 3 . Variables and descriptive statistics

 3

	Variables	Mean	Std. Dev.	Min	Max
	V1: Type of vehicle	12.82	0.916	1	5
	V2: Distance (kilometres from origin to destination)	19.54	22.26	0.5	51.29
	V3: Time (time from origin to destination)	0.83	5. 19	0.03	6.60
	V4: Speed	26.00	20.78	0.15	120.08
	V5: Time of access to public transportation	24.40	21.12	2	70
	V6: Distance covered using a taxi in km	4.65	9.14	1	21
	V7: Distance covered using a bus in km	12.17	3.61	7	28
	V8: Distance covered using a motorcycle in km	2.90	1.15	1	8
	V9: Distance covered using a minibus in km)	11.96	3.64	3	59
	V10: Distance covered using other types of vehicle in km	29.71	17.53	0	18
	V11: Population density	26.00	20.78	15	320.08
	(Number of inhabitants per hectare)
	V12: Density of establishments	14.18	3.00	8	22.25
	(Number of establishments per hectare)
	V13: Distance from the city centre in km	15.66	22.85	0	23.06
	V14: Ratio employment to population in %	6.55	14.84	0.13	964.67
	V15: Reason of the destination: 1. home-to-work and 0.	0.52	0.42	0	1
	and education
	V16: Cost	135.38	36.49	113.67 511.07
	(fuel consumed to cover distance origin to destination)				6
	V17: Number number of travelers in the vehicle	4.05	77.10	1	80

Table 4 . Determinants of mobility choice in Yaoundé

 4

	Variables	Motocycle Taxis	Bus&minibus Others
	V11: Population density at the origin	0.985***	-0.321***	0.524***	-0.564***
	V5: Time of access to public	-0.290***	-0.058***	0.096**	-0.013
	transportation
	V15: Reason of the destination	0.314*	0.113***	0.054**	0.065
	V17: Number of travelers in the vehicle	0.324***	0.272***	-0.429***	-0.401***
	V2: Distance	0.009***	0.014***	-0.033**	0.019
	(kilometres from origin to destination)
	V3: Time (time from origin to	0.636***	0.065***	0.041***	0.070
	destination)
	V4: Speed	0.011***	0.003**	0.001	-0.013
	V16: Cost (fuel consumed to cover	-0.000***	0.014***	0.016**	0.010*
	distance ²origin to destination)
	Intercept	-0.142	0.569**	-0.974***	-0.647***
	Notes: Number of obs = 16,204; LR chi2 (70) = 5,828.31; Prob > chi2 = 0.0000; LnLikelihood =-14886.867;
	Pseudo R2 = 0.1637; legend: * p < 0.05; ** p < 0.01; *** p < 0.001.
	Reference Mode: Personal car.
	Source: Author: PDU data (2010).

Table 5 . Marginal effects and elasticity's mobility choices in Yaoundé

 5

	Variables	Marginal effects (dy/dx)	Elasticities (ey/ex)
	V11: Population density at the origin	.457 (.032)	.237 (.876)
	V5: Time of access to public transportation	.265 (.042)	-.930 (.137)
	V15: Reason of the destination	.200 (.040)	-.722 (.209)
	V17: Number of travelers in the vehicle	-.220 (.016)	.027 (.074)
	V2: Distance (kilometres from origin to destination)	.049 (.017)	.597 (.196)
	V3: Time (time from origin to destination)	.058 (.001)	.225 (.063)
	V4: Speed	.016 (.009)	.981 (.596)
	V16: Cost (fuel consumed to cover distance origin to	.056 (.506)	.194 (.551)
	destination)
	V11: Population density at the origin	-.010 (.036)	.108 (.163)
	Notes: Expression 1 (dy/dx): Number of observations=16,207; Expression 2 (ey/ex):
	Number of obs =16,207.
	Source: Author: PDU data (2010).

IMF: International Monetary Fund.

* This work was funded by the Africa Economic Research Consortium (AERC) to whom I offer my heartfelt thanks. Nations Environment Programme. 2 SSATP: Africa Transport Policy Program. 3 UN-Habitat: United Nations Human Settlments Programme. 4 ASTF: Africa Sustainable Transport Forum.