Keywords

1 Introduction

Several works have demonstrated that we are constantly pushing the limits of our daily travel, leading to urban sprawl (Orfeuil, 2000). In France, for example, the population living in urban areas is constantly increasing, estimated by the Banque Mondiale to be 80% of the total population today, compared with only 62% in 1960. At equal cost, with increasingly efficient means of transport, infrastructure, systems, and vehicles, it is possible to live further and further from the city center to seek environmental amenities or access a property. Urban sprawl produces an explosion in commuting, which results in increasing congestion of transport infrastructures, air pollution at peak hours, and a dependency on cars (Newman & Kenworthy, 1998).

Within this perspective, many authors question the fragility of populations living in peri-urban areas and whose transport budgets may be very sensitive to changes in energy costs (Crozet & Joly, 2004). At the same time, scarcity is what is generally observed: scarcity of space, energy, and time. This requires an understanding of residential locations and daily household movements from another perspective: that of travel conditions and planning urban space. Households are living in increasingly tight markets, with a constrained budget for housing, transportation, and heating. As an example, the average property prices in Bordeaux quadrupled between 1998 and today, pushing people further out toward the periphery. Controlling spatial urban growth is clearly becoming a requirement for sustainable development and public policies.

To limit greenhouse gas (GHG) emissions and fulfill France’s international commitments to fight global warming, the government has implemented a series of plans (low-carbon strategy, multiyear energy programs, etc.) and laws such as the adoption of the Climate, Air, and Territorial Energy Plan. Thus, the law on energy transition for green growth requires all regions with more than 20,000 inhabitants to adopt a Climate, Air, and Territorial Energy Plan by December 31, 2018, at the latest, to be renewed every 6 years. The most critical issues regarding energy transition are found in urban areas, where most human activities (social, economic, etc.) are concentrated and consequently generate nearly two-thirds of GHG emissions. Indeed, urban areas raise the question of the most effective policy level at which global and local problems can be addressed with sustainable city policies. A wide part of the problem is felt at the local level (such as congestion and pollution), and many effects exist that have a global nature (such as global warming). Urban areas may be regarded as efficient starting points for sustainability policies because they operate locally with a global advantage (Camagni et al., 1998). Then, sustainable urban areas need to develop strategic tools of an urban sustainability policy such as smart cities.

On the other hand, local authorities have no tools at their disposal, which are capable of assessing the prospective effects of Climate, Air, and Territorial Energy Plans in their regions. While the current diagnosis of GHG emissions is undertaken in a detailed and precise manner per sector (mobility, building, etc.), future forecasts remain based on single-sector approaches that ignore intersectoral interactions (Zerguini & Gaussier, 2020). For example, building a tramway line impacts not only GHG emissions linked to mobility (reduction of emissions through the mechanism wherein travel flows are transferred from cars to public transport) but also impacts GHG emissions linked to urban planning (through the mechanism wherein the urban area of the region is made more accessible by the tramway line).

The MUST-B model addresses this double issue of urban growth and sustainability (Bouanan et al., 2018). It aims to address the growing preoccupations of sustainable urban development, focusing specifically on prospective assessment in the field of transport and land use planning. Many studies have thus confronted the complexity of urban dynamics to provide models that integrate the interactions between transport and urbanization, known by the LUTI acronym, which stands for “Land Use – Transport Interaction.” While the use of LUTI models has been compulsory in the United States for the past 30 years (the ISTEA Act, 1991 and TEA 21 Act, 1998), some local communities in France (Ile-de-France, Lyon, Lille, Grenoble, Besançon) have begun to explore urbanization scenarios in terms of investments and government policies.

The MUST-B model is designed to aid decision-making (helping to define and develop government policies) to guide the “trajectory of an area toward improved sustainability.” Its ambition is to be the simulation model for actions and urban policies that work toward building the city of tomorrow, that is, a smart and sustainable city. According to (Giffinger, 2011), a smart city is a city that performs well in six characteristics (environment, economy, mobility, quality of life, habitat, governance) built on the “smart” combination of endowments and activities of self-decisive, independent, and conscious citizens. The city is a complex system characterized by human–human and human–environment microinteractions; the emergence of unexpected phenomena that arise from the behavior of interdependent units; nonlinear dynamics, which means that it is difficult to predict the output of the system from its inputs; and feedback loops. MUST-B is based on a systemic approach that allows us to take into account all these characteristics of the complexity and functioning of the city system.

It aims to enable the prospective assessment of the impact of its Climate, Air, and Territorial Energy Plan, particularly in the Bordeaux metropolitan area. This is conducted according to actions that can be implemented in the Energy–Climate policy. The MUST-B tool can provide interesting insight to support institutional decision-makers in the Bordeaux area and rise to the challenge of sustainable urbanization.

This chapter first exposes the state of the art of LUTI modeling and the positioning of the MUST-B model in relation to existing LUTI models. It then presents the principles underpinning the development of the MUST-B model and its implementation for a given future time prospect. The third section describes the theoretical and methodological choices made to model the utility function and location mechanisms of households and workplaces, as well as the systemic interactions between households and workplaces. The final part, which presents the implementation of MUST-B in the Bordeaux Urban Area (AUB), highlights the main indicators of the complexity of the urban phenomenon produced by the model.

2 MUST-B: Context and Positioning

There is a wealth of literature on the subject of LUTI models (Wegener, 2004) dating back to the 1950s in the United States, which study the interaction between transport and urban development. It aims to better “open up” the black box of transport – urbanization interactions with the aim of proposing applications in the context of large foreign and French agglomerations. It raises many questions, particularly about the representation and articulation of the systems that make up these models. Wegener (2004) thus identifies approximately 20 models that he compares using an articulated reading grid according to nine characteristics: (1) Their unified or composite structure, developed from hierarchically ordered subsystems, (2) The complete or partial integration of the transport system, (3) The theoretical foundations – auction-based models, expected utility theory, equilibrium, etc., (4) Modeling techniques according to their consideration of space and time, (5) Simulated dynamics, (6) Necessary data, (7) Parameter and validation exercises of the model, (8) Operationality, and (9) Model applicability.

In the MUST-B model, the mechanism of the location choice of the agents (households, firms) is based on the theory of maximizing the utility that this location will provide (Zerguini & Gaussier, 2019). Here, we are interested in the balance between the real estate and the land markets that emerges following the simulation of intra-agent competition (competition between households on residential supply and between workplaces on business premises supply) and interagent competition (competition between households and workplaces on buildable land stock). More generally, MUST-B is founded on a formalized set of principles taking into account the behavior of a large number of urban agents/actors and their mutual interactions: households, businesses, planners, developers, government policies, regulations, etc. To account for the complexity of the urban phenomenon, a multiagent simulation is used wherein most of the mechanisms that govern land use are endogenized, such as how property prices are defined, occupancy of the buildable land stock, and access to jobs and labor.

MUST-B proposes a novel approach in comparison to the numerous previous works on LUTI modeling for the following reasons:

  • Its systemic articulation of the land and real estate markets (planner/developer/occupier – households and workplaces) enables us to consider all interactions between the different urban actors using a countdown mechanism, according to which the land price is deducted from the other costs of an operation and the sale price of real estate.

  • The collaboration of multidisciplinary researchers (in the fields of the economy, urban planning, geography, transport, IT, etc.) enables us to consider the specificities of the different disciplinary fields in relation to the urban phenomenon.

  • The diversity of the project team (researchers and consultants) enables us to develop a tool that is compatible with the requirements of local and operational authorities to conduct research and provide advice.

  • Its multiagent simulation enables us to better understand the complexity of the city system based on individual behaviors. Using computer power, multiagent simulation enables us to model collective behaviors that are not otherwise easily accessible through intuition or analytical calculation (Lemoy et al., 2011).

  • It compares theoretical approaches with operational actors (developers, corporations, etc.), enabling us to validate the modeled mechanisms.

  • It includes social housing, which represents a quarter of the housing stock in France. The modeling of the choice of location in social housing follows the same approach as for private housing (maximization of residential utility), and the price of social housing is indexed to that of private housing resulting from the auction mechanism.

3 Methodology

3.1 Architecture and Operation of the Model

Households compete with each other in real estate and workplaces to occupy buildable land stock.

MUST-B operates like a “four-stage” transport model, in that, for a given time prospect (Bonnel, 2001), the balance results from the confrontation between supply (transport networks) and demand (flow matrix). Thus, MUST-B can be considered a supply-and-demand model wherein spatial entities (land, housing, business premises) interact with social entities (households, institutions).

  • Land occupation by households and workplaces in the different zones of an urban area at a given future time prospect is based on the following process (Fig. 1):

  • Exogenous demand in the future is defined by distinguishing between households (population) and workplaces (employment).

  • At the beginning of the modeling process, agents are arbitrarily assigned to the respective current housing stock, respecting capacity constraints. For this, a procedure is developed in MUST-B, which enables an automatic preassignment of agents in the zones.

  • Households will start by occupying the current housing stock. Once this is saturated, they will occupy the buildable land stock dedicated to housing according to the developer’s profitability conditions. Deciding the location of workplaces follows the same process.

  • When the dedicated buildable land stock is saturated, households and/or workplaces will be located in buildable land stock designated for mixed housing/business premises until this is saturated.

Fig. 1
A path diagram represents a transport model with accessibility associated with households and workplaces. Based on the saturation, current housing stock and current business premises stock lead to the capacity reserve of housing and business premises which further leads to a capacity reserve of both.

Architecture and operating principles of MUST-B

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The MUST-B model is thus able to account for urban sprawl or tightness: apart from the current exogenous stock, supply becomes endogenous, capped by the buildable land stock available, under pressure from demand from agents (households and workplaces) and financial profitability for the developer (countdown mechanism presented in Sect. 3.3).

3.2 Formalization and Implementation of the MUST-B Model

Agent-based modeling is defined as a modeling and simulation technique that works on the level of microunits such as workplaces and households. Each microunit contains several attributes and follows a set of behavioral rules. This technique simulates the decision-making processes of individuals based on the heterogeneous attributes of agents and their interactions with the environment and other agents. The agent-based modeling approach has recently emerged and gained popularity within the scientific community regarding urban planning. These models use agent links (households or workplaces) – the use of land as objects of analysis and simulation – and pay particular attention to the interactions between these “agents.” Agents are defined by several characteristics: they are autonomous, they share an environment through communication and interaction, and they make decisions that link their behavior to the environment. Agents make inductive and dynamic choices that lead them to achieve well-being objectives.

The MUST-B model is implemented in the VLE -Virtual Laboratory Environment (Quesnel et al., 2009). VLE is a platform for multimodeling and simulation of dynamic systems based on discrete event system simulation (DEVS) (Zeigler et al., 2000). VLE enables us to specify complex systems in terms of reactive objects and agents, simulate the system dynamics, and analyze the results of the simulation. The indexes provided also facilitate the development of customized programs. MUST-B was developed using the concept of object-oriented programming, in particular the C++ language.

3.3 The Notion of Equilibrium in MUST-B

MUST-B locates each randomly selected agent. The modeled territory is assumed to be that of a closed city, with a given future time perspective, in which the total number of agents (population, jobs) is fixed in advance. Thus, a large number of selections (several million) are conducted in a simulation to achieve equilibrium. The equilibrium is derived from the simulated dynamics of household and workplace location choices. Equilibrium is considered to be achieved when agents no longer improve the utility they can derive from a new location. This dynamic urban equilibrium, as opposed to the static equilibrium, which can be calculated in urban models, is similar to the Wardrop equilibrium (Wardrop, 1952; Corea & Stier-Moses, 2011) used in traffic flow allocation models. The Wardrop equilibrium is achieved in the allocation of traffic on a road network when no user can change itinerary without compromising their travel time.

In practice, in the MUST-B model, the aggregate utility of a given type of agent (household or workplace) converges toward a U* level after a number I* of iterations (Fig. 2). I* corresponds to more than four million iterations for households, while workplaces require a higher number of iterations.

Fig. 2
A line graph plots aggregated utility versus iterations. The line represents an upward trend and a vertical line meets the curve. It begins from the point I asterisk that is marked on the right of the center on the X-axis.

Evolution of aggregated utility over iterations (MUST-B calculation)

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It can therefore be considered that after a certain number of iterations I*, the aggregate utility of households will no longer increase and that no household can increase its utility by being in a given area without at least decreasing that of another. As with Pareto efficiency, there is nothing to say that all households are satisfied with their location. The same applies to business premises.

3.4 Theoretical Principles and Modeling

3.4.1 Utility Functions

The proposed approach consists of developing a residential utility function that integrates household behaviors into their residential location choices. This enables households to be assigned to the different residential options according to an auction procedure. The residential utility function reflects the economic well-being that the household can derive from a given location and type of housing. It depends on several parameters relating to housing and space, such as the accessibility and reputation of the zone, the surface area of the housing, or the price of real estate.

The utility function of household h residing in zone z can be expressed as follows:

$$ {U}_{\mathrm{h},\mathrm{z}}={\alpha}_{1_{\mathrm{h}}}{\mathrm{AC}}_{\mathrm{z}}+{\alpha}_{2_{\mathrm{h}}}{\mathrm{NO}}_{\mathrm{z}}+{\alpha}_{3_{\mathrm{h}}}{\mathrm{SA}}_{\mathrm{h}}-{\mathrm{EB}}_{\mathrm{z}}\times {\mathrm{SA}}_{\mathrm{h}}-{P}_{\mathrm{z}}^l\times {\mathrm{SA}}_{\mathrm{h}} $$
(1)

where:

  • AC: Accessibility of the zone under consideration (reflecting access to employment)

  • NO: Notoriety of the zone under consideration (reflecting the image and amenity of a zone that can be qualified by various parameters such as the atmosphere, style, specificity, and diversity of the businesses that are present)

  • SA: Surface area of the desired housing

  • EB: Energy bill per m2 of the zone in question

  • P: Price per m2 of housing in the area under consideration (reflecting the energy costs related to the use of the housing such as heating, air conditioning, lighting, etc.)

  • αi: Parameters to be estimated according to the household’s socioprofessional category (SPC)

To take the heterogeneity of households within the same category (size × SPC) into account, a statistical distribution is introduced within each category. This distribution concerns the αi parameters of the residential utility function. The statistical distribution used is the normal distribution of the mean of the value of αi, and the standard deviation is assumed to be 10% of the mean.

The proposed method for simulating workplace location choices is similar to that of households. It consists of developing a job location function that integrates the behavior of companies in the location choices of their workplaces and enables jobs to be assigned to the premises according to an auction procedure. This function reflects the utility that the company can derive from a given location and type of premises. This depends on several parameters, such as the accessibility and reputation (image) of the zone, the surface area of the premises, property prices, taxes, financial assistance, etc. In the same way, as for a household, the company will seek to acquire the premises that it considers the most useful for its business, taking the size of the workplace into account.

The utility function of workplace w (characterized by its size and its sector of activity) located in zone z can be expressed in this way:

$$ {U}_{\mathrm{w},\mathrm{z}}=\left({\lambda}_{1_{\mathrm{w}}}{\mathrm{AC}}_{\mathrm{z}}+{\lambda}_{2_{\mathrm{w}}}{\mathrm{NO}}_{\mathrm{z}}+{\lambda}_{3_{\mathrm{w}}}{\mathrm{RW}}_{\mathrm{z}}-{\mathrm{TD}}_{\mathrm{z}}\times {\mathrm{SA}}_{\mathrm{w}\mathrm{a}}-{P}_{\mathrm{z}}^w\times {\mathrm{SA}}_{\mathrm{w}\mathrm{a}}\right)\times {S}_{\mathrm{w}} $$
(2)

where:

  • AC: Accessibility of the zone under consideration (i.e., access to labor)

  • NO: Notoriety of the zone under consideration (i.e., the image and specificity of a zone)

  • SAea: Surface area of a job per type of business activity

  • RW: Ratio of workplaces operating the same business activity as the premises under consideration out of all of the premises present in the zone (i.e., agglomeration effects)

  • TD: Level of taxes and duties in the zone under consideration

  • P: Price per m2 of business premises in the zone under consideration

  • Sw: Size of the workplace

  • λi: Parameters to be estimated according to the business activity of the premises

3.4.2 Location Selection Mechanism

The mechanism for choosing the location of households is the same as that of workplaces: it is based on maximizing the utility of a location for the agent (household/workplace).

The assignment of agents to the different zones that make up the agglomeration is based on an auction mechanism for the acquisition of housing/business premises. The principle is that each agent will locate itself in a given zone, seeking to maximize their utility. The bid made by the agent (candidate wishing to move) is composed of the price of their current zone and the “monetarized” gain of the utility provided by their potential move.

Concretely, at iterationFootnote 1 n of the simulation, the bid that agent a will make to move into zone j depends on the price of housing in his home zone i at iteration n − 1 and on the difference in utilities between zones i and j at iteration n − 1. This is expressed as follows:

$$ {\pi}_{j,n}^a={P}_{i,n-1}+\varepsilon \left({U}_{j,n-1}^a-{U}_{i,n-1}^a\right) $$
(3)

where ε, the amplitude of the auction, determines the utility gain transformed into a price added to the initial price in their current zone.

With the above mechanism (3), the simulated prices of the different zones will increase as they attract an ever-increasing number of agents. To simulate the inverse mechanism of price decline or stability, it is assumed that the agent can renounce moving if they obtain a reduction in the price of real estate in their home zone i. The auction that the agent makes to remain in their home zone is expressed as (4):

$$ {\pi}_{i,n}^a=\left(1-\beta \right){P}_{i,n-1} $$
(4)

Agent a chooses to be located in the zone where they derive the most utility (Fig. 3).

Fig. 3
A schematic of 2 blocks within a shaded circle read zone i and zone j, respectively. An arrow links zone j to a in zone i and loops back to a.

Arbitrating the location of an agent. (Authors’ graphic)

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If \( U\left({\pi}_{j,n}^a\right)>U\left({\pi}_{i,n}^a\right) \), the agent has chosen to be located in zone j; otherwise, they will remain in zone i.

In the case where the utility of going to zone j is greater than that obtained in zone i and zone j is already saturated (zone j has reached its total capacity), then agent a is relocated in any case to zone j, and it is the agent that derives the least utility in zone j, which is relocated to a randomly selected destination, zone k (Fig. 4).

Fig. 4
3 blocks within a shaded circle read zone i, zone k, and zone j, respectively. An arrow labeled a prime links zone j to zone k. Zone J is striped.

In the event that zone j is saturated. (Authors’ graphic)

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At the end of the location process for the randomly chosen agent assigned to a zone, the zone’s price is updated and calibrated with the auction made by the last agent. Thus, at each iteration, there is necessarily a zone that will be subjected to a price modification, upward or downward.

Equilibrium is attained when, for a given type of agent, the level of utility is the same wherever they are located. The agent cannot improve its utility by changing the zone.

3.4.3 Procedure for the Endogenous Offer (Developer)

For a future time prospect, the MUST-B model locates homes and workplaces in a zone, having knowledge of their current respective land stocks. Once each of these current land stocks is saturated, they will begin allocating to the buildable land stock (land that can be built on in accordance with regulations). Consumption of the buildable land stock is activated by the countdown mechanism:, i.e., the price of land is deducted from all other costs of a real estate transaction. When developers wish to know the maximum price available to buy land and initiate a real estate program, they will deduct from the expected sales figure the costs of construction, financial costs, fees, taxes, and margin (Vilmin, 2015). The only item that ultimately determines the decision to invest and the profitability of the project is the land, given that the margin conditions the bank’s ability to obtain loans and guarantees. The difference between expected revenues and expenses, therefore, corresponds to the maximum land charge that the developer can incur. The endogenous capacity mechanism will therefore be activated with the confrontation between property prices and land charges.

Decisional Investment Mechanism

Therefore, for 1 m2:

  • π: Price of the auction made by the agent at iteration n (in relation to the transferable surface)

  • CL: Cost of land (in relation to the buildable surface area)

  • p: Weighting of the cost of land in the price of real estate (p = CL/π)

  • CC: Cost of construction

  • M: Developer’s margin

  • CP: Cost of production (land cost + construction cost + margin)

We obtain:

$$ {C}_{\mathrm{P}}={C}_{\mathrm{L}}+{C}_{\mathrm{C}}+M $$
(5)
$$ {C}_{\mathrm{P}}= p\pi +{C}_{\mathrm{C}}+x{C}_{\mathrm{P}} $$
(6)

We can deduce that:

$$ {C}_{\mathrm{P}}=\frac{p\pi +{C}_{\mathrm{C}}}{1-x} $$
(7)

The developer’s profitability condition is expressed as follows:

$$ \pi >{C}_{\mathrm{R}} $$
(8)

We finally obtain:

$$ \pi >\frac{C_{\mathrm{C}}}{1-x-p} $$
(9)

As illustrated in Fig. 5, the mechanism for occupying the buildable land stock of a zone is conditioned by a double constraint: the saturation of the current land stock and the expected profitability for the developer to build in this zone (Eq. 9).

Fig. 5
3 line graphs plot prices of real estate and production costs, occupation of current land stock in the zone, and occupation of buildable land stock in the zone versus iterations. Points I 1 to 4 are marked on the x-axis. The graphs represent varying trends.

Occupation of buildable land stock. (Authors graphic)

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From Fig. 5, we can identify four configurations:

  1. 1.

    Between the beginning of the simulation and iteration I1, the agents are located in the current zone.

  2. 2.

    Between iteration I1 and iteration I2, the agents are located in the buildable land stock because, on the one hand, the current land stock under consideration is saturated and, on the other hand, the price of the property enables the developer to gain a profit (auction is higher than cost price).

  3. 3.

    Between iteration I2 and iteration I3, the zone is still considered saturated, but the buildable land stock is not mobilized because the developer’s condition of profitability is not fulfilled within this interval.

  4. 4.

    Between iteration I3 and iteration I4, the agents are located in the buildable land stock as the profitability condition is fulfilled once again.

  5. 5.

    From iteration I4, the zone is considered definitively saturated (the capacities of the current zone and buildable land stock being full).

Process of Spatial Occupation of the Buildable Land Stock

Thus:

  • IS: the inhabitable surface area of the real estate sought by the agent (real estate demand)

  • BF: Building footprint

  • GS: Ground surface area of the land used

  • NFmax: Maximal number of floors allowed in the zone

  • k1: add-on factor (k1 > 1) of the occupied surface area taking external walls of the building into account

  • k2: add-on factor (k2 > 1) taking into account networks (road, water, sanitation, street lighting, etc.) and urban planning easements (view, right of way, etc.)

The building footprint satisfying real estate demand IS is expressed as:

$$ \mathrm{BF}={k}_1\times \frac{\mathrm{IS}}{{\mathrm{NF}}_{\mathrm{max}}} $$
(10)

The ground surface area of land consumed by this real estate demand is equal to:

$$ \mathrm{GS}={k}_2\times \mathrm{BF} $$
(11)

We finally obtain:

$$ \mathrm{GS}=\frac{k_1\times {k}_2}{{\mathrm{NF}}_{\mathrm{max}}}\times \mathrm{IS} $$
(12)

Each time an agent (household or workplace) is located in this zone, the ground surface area consumed by this demand is subtracted from the buildable land stock surface until the total consumption of the buildable land stock surface area of the zone in question is attained (see Fig. 6).

Fig. 6
A schematic that displays the rectangular area of ground surface consumed and the real estate's inhabitable surface. The consumed ground surface area consists of 7 cubic and cuboid blocks and occupies up the majority of the area.

Process for the occupation of buildable land stock

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3.4.4 Mechanism of Endogenous Accessibility

Households and premises interact via the accessibility variable (see Fig. 1). Indeed, household accessibility must take into account not only transport supply but also the location of workplaces (employment opportunities). On the other hand, the accessibility of workplaces must take into account transport supply and household location (labor force). There is then feedback between the two types of agents in the system (Fig. 7).

Fig. 7
A conceptual framework explains how population location interacts with the location of jobs through accessibility to employment. The location of jobs interacts with population location via employment opportunities.

Interactions between households and workplaces

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The accessibility of a zone consists of two components: an exogenous component that reflects the performance of the transport network (speed and capacity) serving the zone in question and an endogenous component that reflects the spatial distribution of the population and jobs that evolve during the simulation.

At this stage of development of MUST-B, two simplifying hypotheses are made on how to take accessibility into account:

  • The accessibility of households is reduced solely to access jobs, while there are other dimensions such as access to services, equipment, shops, schools, etc. These elements, which are present in the utility function of households, do not contribute to the calculation of endogenous accessibility.

  • It is assumed that accessibility linked to the performance of transport networks is completely exogenous, whereas part of this component could be endogenized by taking transport network congestion resulting from the attractiveness of certain zones at certain times into account during the simulation.

The determination of accessibility for both types of agents (households and workplaces) is based on the following approach:

  • Determination of the matrix of generalized costs of interzone travel for PV (private vehicle) and PT (public transport) modes of travel

  • Determination of accessibility vectors for PV and PT modes of transport

  • Aggregation of all modes into a single accessibility vector

Generalized Cost of Travel

The generalized cost of traveling by private vehicle (PV) between zones i and j is expressed as follows:

$$ {C}_{ij}^{\mathrm{PV}}={V}_t\times t{t}_{ij}^{\mathrm{PV}}+\left(\mathrm{CF}+\mathrm{CK}\right)\times {d}_{ij}^{\mathrm{PV}}+{C}_j^{\mathrm{Park}} $$
(13)

where:

  • Vt: Value of time (€/h)

  • \( t{t}_{ij}^{\mathrm{PV}} \): Travel time via PV between zones i and j (h)

  • \( {d}_{ij}^{\mathrm{PV}} \): Distance covered in PV between zones i and j (km)

  • CF: Cost per kilometer of fuel (€/km)

  • CK: Cost per kilometer of vehicle use excluding fuel (€/km)

  • \( {C}_j^{\mathrm{Park}} \): Cost of parking in zone j (€)

The generalized cost of using public transport (PT) between zones i and j is expressed as

$$ {C}_{ij}^{\mathrm{PT}}={V}_t\times t{t}_{ij}^{\mathrm{PT}}+{T}^{\mathrm{PT}}+\eta \times {C}_{ij}^{\mathrm{MC}} $$
(14)

where:

  • \( t{t}_{ij}^{\mathrm{PT}} \): Journey time on public transport between zones i and j (h)

  • T PT: Tariff per trip on public transport

  • \( {N}_{ij}^{\mathrm{MC}} \): Number of mode changes during the trip

  • η: Parameter to be estimated

Accessibility per Mode of Transport

The accessibility provided for household h in zone i at iteration n, composed of an exogenous part (first term of the equation) and an endogenous part (second term of the equation), is expressed as:

$$ {\mathrm{AC}}_{i,n}^{\mathrm{h},\mathrm{PV}}=\theta \sum \limits_j{e}^{-{C}_{ij}^{\mathrm{PV}}}+\mu \sum \limits_j\sum \limits_k\frac{s^k{w}_{j,n-1}^k}{{\left({C}_{ij}^{\mathrm{PV}}\right)}^2} $$
(15)
$$ {\mathrm{AC}}_{i,n}^{\mathrm{h},\mathrm{PT}}=\theta \sum \limits_j{e}^{-{C}_{ij}^{\mathrm{PT}}}+\mu \sum \limits_j\sum \limits_k\frac{s^k{w}_{j,n-1}^k}{{\left({C}_{ij}^{\mathrm{PT}}\right)}^2} $$
(16)

The accessibility provided for workplaces w in zone i at iteration n, composed of an exogenous and an endogenous part, is expressed as:

$$ {\mathrm{AC}}_{i,n}^{\mathrm{w},\mathrm{PV}}={\theta}^{\prime}\sum \limits_j{e}^{-{C}_{ij}^{\mathrm{PV}}}+{\mu}^{\prime}\sum \limits_j\sum \limits_k\frac{s^l{h}_{j,n-1}^l}{{\left({C}_{ij}^{\mathrm{PV}}\right)}^2} $$
(17)
$$ {\mathrm{AC}}_{i,n}^{\mathrm{w},\mathrm{PT}}={\theta}^{\prime}\sum \limits_j{e}^{-{C}_{ij}^{\mathrm{PT}}}+{\mu}^{\prime}\sum \limits_j\sum \limits_k\frac{s^l{h}_{j,n-1}^l}{{\left({C}_{ij}^{\mathrm{PT}}\right)}^2} $$
(18)

where:

  • sl: Size of household (number of people)

  • \( {h}_{i,n-1}^l \): Number of tl sized households in zone i at iteration n − 1

  • tk: Size of the workplace (number of jobs)

  • \( {w}_{j,n-1}^k \): Number of workplaces of tk size in zone j at iteration n − 1

  • θ, θ′, μ and μ′: Factors to estimate

Aggregated Accessibility

To estimate the all-mode accessibility of a given zone, the accessibility of each mode is weighted by its modal share (MS) according to the following expressions:

$$ {\mathrm{AC}}_{i,n+1}^{\mathrm{h}}={\mathrm{PM}}_{i,n}^{\mathrm{PV}}\times {\mathrm{AC}}_{i,n}^{\mathrm{h},\mathrm{PV}}+{\mathrm{PM}}_{i,n}^{\mathrm{PT}}\times {\mathrm{AC}}_{i,n}^{\mathrm{h},\mathrm{PT}} $$
(19)
$$ {\mathrm{AC}}_{i,n+1}^{\mathrm{w}}={\mathrm{PM}}_{i,n}^{\mathrm{PV}}\times {\mathrm{AC}}_{i,n}^{\mathrm{w},\mathrm{PV}}+{\mathrm{PM}}_{i,n}^{\mathrm{PT}}\times {\mathrm{AC}}_{i,n}^{\mathrm{w},\mathrm{PT}} $$
(20)

Modal shares are estimated during the simulation using a sequential approach: generation, distribution, and modal choice. The generation and distribution steps are based on a gravity model and the location of households and workplaces. The modal choice step is based on a logit model and the generalized costs of the two competing modes (PV and PT).

4 MUST-B: Indicators of the Complexity of the Urban Phenomenon

The simulation of a governmental policy can be undertaken using several indicators that are determined in the MUST-B model.

4.1 Indicators Linked to Urban Planning

The occupation of the space following a simulation is characterized by defining the following for each zone:

  • Number of accommodations/households/population

  • Number of workplaces/jobs

  • Social diversity and segregation

  • Functional diversity

  • Price of residential property

  • Price of land property for business activities

  • Price of land property

These indicators are output data calculated directly in the MUST-B model.

4.2 Sustainability Indicators

Following a simulation, the effects of an urban policy on sustainable development are estimated according to a definition for each zone in terms of:

  • Energy consumption (home-work mobility, accommodation)

  • GHG emissions (home-work mobility, accommodation)

  • Artificialization of the land (built land/total surface of the zone ratio)

This last indicator can be directly calculated, whereas the two former indicators require prior calculations, such as the number of kilometers in question or the surface areas of the accommodation occupied according to the degree of emission and energy consumption.

5 Conclusion

The aim of the MUST-B model is to simulate the choice of location of households and firms. It is based on an auction mechanism that enables us, according to different timeframes, to model the competition between agents (households and firms) in the real estate market (existing property holdings: residential, tertiary, and industrial) and on the land market (reserves of buildable land stock).

The multidisciplinary approach to the design and development of MUST-B is a unique and defining characteristic wherein the collaboration of multidisciplinary researchers (from the fields of economics, urban planning, geography, transport, computer science, etc.) The specificities of the different disciplines could be considered in combination with the urban phenomenon, and the multiagent simulation enabled us to model the complexity of the city system from individual behaviors.

Today, MUST-B is an operational tool to support decision-making for urban development planning, integrating the effects of the different sectors of the city (mobility, accommodation, economic activities, etc.) on the climate and atmospheric pollution. Indeed, MUST-B is designed to assist decision-making (helping to define and develop government policies) to guide the trajectory of a region toward increased sustainability.

Simulation using MUST-B, therefore, enables us to assess certain effects of urban policies and actions that communities can undertake, as well as assist them in prioritizing these actions according to their financial resources and objectives and to articulate them in coherent local policies in favor of ecological transition. The MUST-B model can thus significantly contribute to identifying the conditions and levers for action that help to lead to a sustainable territory. For instance, MUST-B is a way to address the foresight exercise at the urban area scale: it makes it possible to test the spatial impact of the development of road, residential, and firm activities. It enlightens different aspects of urban sustainability, such as economic, social, and environmental criteria. It is a way to have a smart perspective on urban planning.

However, some limitations and paths of progression can be noted in the MUST-B model. The first concerns the calibration of the parameters and the validation of the model in relation to the real data and observations of the territory under consideration. For the model to be valid, it must reconstruct for each zone the location of households and jobs as well as the price of residential real estate and that of economic activities. However, the calibration of the model depends on the territories and on their capacity to keep information in the long term to reconstitute it within the framework of the simulations. The second progression of the model consists of integrating the evolution of the behavior of the agents in the mechanism of choice of location of new variables such as, for example, “connectivity to the Internet” in the utility function of households and companies. Indeed, since the crisis induced by the COVID-19 pandemic and the strengthening of telework, high-speed internet connections have become a decisive criterion in the attractiveness of territories for households and firms.