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Land-Use Transport Interaction Models

  • Michael WegenerEmail author
Living reference work entry

Abstract

The relationship between urban development and transport is not simple and one way but complex and two way and is closely linked to other urban processes, such as macroeconomic development, interregional migration, demography, household formation, and technological innovation. In this chapter, one segment of this complex relationship is discussed: the two-way interaction between urban land use and transport within urban regions. The chapter looks at integrated models of urban land use and transport, i.e., models that explicitly model the two-way interaction between land use and transport to forecast the likely impacts of land use and transport policies for decision support in urban planning. The discussion starts with a review of the main theories of land-use transport interaction from transport planning, urban economics, and social geography. It then gives a brief overview of selected current operational urban models, thereby distinguishing between spatial-interaction location models and accessibility-based location models, and discusses their advantages and problems. Next, it reports on two important current debates about model design: are equilibrium models or dynamic models preferable, and what is the most appropriate level of spatial resolution and substantive disaggregation? This chapter closes with a reflection of new challenges for integrated urban models likely to come up in the future.

Keywords

Urban land-use transport interaction Land use and transport policies Equilibrium vs Dynamic models Macro vs micro models 

1 Introduction

The history of urban settlements is closely linked to transport. Cities appeared in human history when technological innovation required the spatial division of labor between specialized crafts and agricultural labor and gave rise to urban–rural travel and goods transport. Cities were established at trade routes, ports, or river crossings and became origins and destinations of trade flows. Cities were compact, as all movements were done on foot, until the railway and later the automobile opened the way to today’s sprawling agglomerations.

These brief notes already show that the relationship between urban development and transport is not simple and one way but complex and two way. On the one hand, spatial division of labor, i.e., the separation of locations of human activities in space, requires spatial interaction, i.e., travel and goods transport. On the other hand, the availability of transport infrastructure, such as roads, railways, and airlines, makes locations attractive as residences or business locations and so affects real estate markets and the choice of location of households and firms. Moreover, it becomes clear that the relationship between urban development and transport is closely linked to other urban processes, such as macroeconomic development, interregional migration, demography and household formation, and technological innovation.

In this chapter, one segment of the complex relationship between urban development and transport is discussed: the two-way interaction between urban land use and transport within urban regions. The macroeconomic dimension dealing with growth or decline of whole cities within urban systems is addressed in several other chapters, such as chapters “Interregional Input–Output Models” and “Interregional Trade Models”.

This chapter looks at integrated models of urban land use and transport, i.e., models which explicitly model the two-way interaction between land use and transport to forecast the likely impacts of land-use policies, such as zoning or building density or height constraints, and of transport policies, such as transport infrastructure investments, public transport improvements, or taxes or user charges, for decision support in urban planning. That excludes transport models per se which predict traffic patterns that result from different land-use configurations and land-use change models that predict likely land-use changes that result from a particular transport system, as well as models that deal only with one urban subsystem, such as housing or business location.

The discussion proceeds from a review of the main theoretical approaches of land-use transport models and a brief overview of operational models to current debates and new challenges that are likely to influence future development in this field.

There are in the literature several reviews of integrated land-use transport models, such as Wegener (2004) and Hunt et al. (2005).

2 Theory

Urban land-use transport models originated in the United States in the 1960s as part of the diffusion of operations research and systems theory into all fields of society. The first attempts to model the interaction between land use and transport were initiated by transport planners who felt that predicting future traffic flows without taking account of their impacts on location was inadequate. Hansen (1959) showed for Washington, DC, that locations with good accessibility had a higher chance of being developed, and at a higher density, than remote locations (“how accessibility shapes land use”). The recognition that mobility and location decisions co-determine each other and that therefore transport and land-use planning need to be coordinated led to the notion of the “land-use transport feedback cycle”. The set of relationships implied by this term can be summarized as follows (Wegener and Fürst 1999, see Fig. 1):
  • The distribution of land uses, such as residential, industrial, or commercial, over the urban area determines the locations of households and firms and so the locations of human activities such as living, working, shopping, education, and leisure.

  • The distribution of human activities in space requires spatial interactions or trips in the transport system to overcome the distance between the locations of activities.

  • These spatial interactions are based on decisions of travelers about car availability, number of trips, destination, mode, and route. They result in traffic flows and, in case of congestion, in increased travel times, trip lengths, and travel costs.

  • Travel times, trip lengths, and travel costs create opportunities for spatial interactions that can be measured as accessibility.

  • The spatial distribution of accessibility influences, among other attractiveness indicators, location decisions of investors and results in changes of the building stock by demolition, upgrading, or new construction.

  • These changes in building supply determine location and relocation decisions of households and firms and thus the distribution of activities in space.
    Fig. 1

    The land-use transport feedback cycle (Wegener and Fürst 1999, 6)

This simple explanation pattern is used in many engineering-based and human-geography urban development theories. These start from origins and destinations, such as workers and workplaces, and from these infer trip volumes that best reproduce observed trip frequency distributions. It had already been observed by Ravenstein (1885) and Zipf (1949) that the frequency of human interactions, such as messages, trips, or migrations between two locations (cities or regions), is proportional to their size but inversely proportional to their distance. The analogy to the law of gravitation in physics is obvious.

The gravity model was the first spatial-interaction model. Its physical analogy has later been replaced by better founded formulations derived from statistical mechanics (Wilson 1967) or information theory (Snickars and Weibull 1977). Only later did it become possible (Anas 1983) to link it via random utility theory (Domencich and McFadden 1975) to psychological models of human decision behavior.

From the spatial-interaction model, it is only a small step to its application as a location model. If it is possible to draw conclusions from the spatial distribution of human activities to the interactions between them, it must also be possible to identify the location of activities giving rise to a certain trip pattern. Wilson (1970) distinguishes four types of urban spatial-interaction location models: unconstrained models, production-constrained models, attraction-constrained models, and doubly constrained models. Unconstrained models deal with households without fixed residence or workplace, production-constrained models with households looking for a job, and attraction-constrained models with households looking for a residence. The doubly constrained model is actually not a location model but the familiar transport model (see chapter “Travel Behavior and Travel Demand”).

To give an example, the production-constrained spatial-interaction model is written as follows:

$$ {T}_{ij}={A}_i{O}_i{D}_j\exp \left(-\beta {c}_{ij}\right) $$
(1)
$$ {A}_i=1/\sum \limits_j{D}_j\exp \left(-\beta {c}_{ij}\right) $$
(2)
$$ {p}_{ij}=\frac{D_j\exp \left(-\beta {c}_{ij}\right)}{\sum \limits_j{D}_j\exp \left(-\beta {c}_{ij}\right)} $$
(3)
where Tij are trips between zone i and zone j, Oi are trips generated by i and Dj trips attracted by j, and cij is the travel time or travel cost, or both, between i and j. The β is a parameter indicating the sensitivity to travel cost; because of its negative sign, more distant destinations are less likely to be selected. Ai is the so-called balancing factor ensuring that total trips equal Oi, and pij is the probability that a trip goes from i to j.

A second set of theories focuses on the economic foundations of land use. A fundamental assumption of all spatial economic theories is that locations with good accessibility are more attractive and have a higher market value than peripheral locations. This assumption goes back to von Thünen (1826) and has since been varied and refined in many ways (see chapter “Classical Contributions: Von Thünen, Weber, Christaller, Lösch”). Probably the most influential example of the latter kind is the model of the urban land market by Alonso (1964). The basic assumption of the Alonso model is that firms and households choose that location at which their bid rent, i.e., the land price they are willing to pay, equals the asking rent of the landlord, so that the land market is in equilibrium. The bid rent of firms results from the cost structure of their production function, i.e., sales price minus production and transport costs plus profit divided by size of land. A firm having a higher added value per unit of land is therefore able to pay a higher price than a firm with less intensive land utilization, everything else being equal. So it is not surprising that, say, jewelers are found in the center, whereas trucking companies have their yards on the periphery. Alonso’s model has been the point of departure for a multitude of urban-economics model approaches. In more advanced variations of the model, restrictive assumptions, such as the monocentric city or perfect competition and complete information, have been relaxed (e.g., Anas 1982).

A third group of theories used in land-use transport models are social theories. In social theories of urban development, the spatial development of cities is the result of individual or collective appropriation of space. Based on an adaptation of evolutionist thoughts from philosophy (Spencer) and biology (Darwin), the Chicago school of urban sociologists interpreted the city as a multispecies ecosystem, in which social and economic groups fight for ecological positions. Appropriation of space takes place in the form of immigration of different ethnic or income groups or tertiary activities into residential neighborhoods, and concepts of animal and plant ecology, such as “invasion,” “succession,” or “dominance,” are used to describe the phases of such displacement.

Social geography theories go beyond the macro perspective of social ecology by referring to age-, gender-, or social-group specific activity patterns which lead to characteristic spatiotemporal behavior and hence to permanent localizations. Action space analyses (e.g., Chapin and Weiss 1968) identify the frequency of performance of activities reconstructed from daily space-time protocols as a function of distance to other activities and draw conclusions from this for the most probable allocation of housing, workplaces, shopping, and recreation facilities or, in other words, for the most likely level of spatial division of labor in cities.

Hägerstrand (1970) made these ideas operational by the introduction of “time budgets,” in which individuals, according to their social role, income, and level of technology (e.g., car ownership), command action spaces of different size and duration subject to three types of constraints: (i) capacity constraints, i.e., personal, nonspatial restrictions on mobility, such as monetary budgets, time budgets, availability of transport modes, and ability to use them; (ii) coupling constraints, i.e., restrictions on the coupling of activities by location and time schedules of facilities and other individuals; and (iii) institutional constraints, i.e., restrictions of access to facilities by public or private regulations such as property, opening hours, entrance fees, or prices. Only locations within the action spaces can be considered as destinations or permanent locations.

On the basis of Hägerstrand’s action space theory, Zahavi (1974) proposed the hypothesis that individuals in their daily mobility decisions do not, as the conventional theory of travel behavior assumes, minimize travel time or travel cost needed to perform a given set of activities but instead maximize activities or opportunities that can be reached within their travel time and money budgets.

3 Operational Models

Lowry’s (1964) Model of Metropolis was the first attempt to quantify the land-use transport feedback cycle in one integrated model. The model consists of two singly constrained spatial-interaction location models, a residential location model and a service and retail employment location model, nested into each other. In modern notation, the two models would be written as

$$ {T}_{ij}=\frac{R_i\exp \left(-\beta {c}_{ij}\right)}{\sum \limits_i{R}_i\exp \left(-\beta {c}_{ij}\right)}{E}_j $$
(4)
$$ {S}_{ij}=\frac{W_j\exp \left(-\beta {c}_{ij}\right)}{\sum \limits_i{W}_j\exp \left(-\beta {c}_{ij}\right)}{P}_i $$
(5)
where Tij are work trips between residential zone i and work zone j and Sij shopping trips between residential zone i to retail facilities in zone j. Ej are workers in j and Pi population in i to be distributed, and Ri are dwellings in i and Wj shopping facilities in j used as destinations in the two spatial-interaction models, and cij is the travel time between i and j. In the first iteration, only work trips to the workplaces of basic industries, i.e., industries exporting to other regions and not serving the local population, are modeled. The two spatial-interaction location models are linked by assumptions about how many people are supported by one worker and how many retail employees are supported by one resident. In each subsequent iteration, workers and residents are updated until they no longer change, i.e., until the system is in equilibrium.

The Lowry model stimulated a large number of increasingly complex land-use transport models in the USA and not much later also in Europe. Many of these early models were not successful because of unexpected difficulties of data collection and calibration and the still imperfect computer technology of the time. More important, however, was that the models were mainly oriented toward urban growth and the efficiency of the transport system and had nothing to say about the ethnic and social conflicts arising in US cities at that time. Moreover, the models were committed to the paradigm of synoptic rationalism in planning theory, which was increasingly replaced by incremental, participatory forms of planning. In his “Requiem for Large Scale Models,” Lee (1973) accused the models of “seven sins”: hypercomprehensiveness, grossness, mechanicalness, expensiveness, hungriness, wrongheadedness, and complicatedness.

But many of the technical problems of the early models were solved by better data availability and faster computers. The spatial and substantial resolution of the models was increased, and they were based on better theories, such as bid-rent theory, discrete choice theory, and user equilibrium in transport networks (see chapter “Network Equilibrium Models for Urban Transport”). In addition, better visualization techniques made the results of the models better understood by citizens and policy makers. A new generation of models paid more attention to aspects of social equity.

The 1990s brought a revival in the development of urban land-use transport models. New environmental legislation in the USA required that cities applying for federal funds for transport investments demonstrate the likely impacts of their projects on land use. This had the effect that virtually all major metropolitan areas in the USA maintained an integrated land-use transport model. In Europe, the European Commission initiated a large research program The City of Tomorrow, in which integrated land-use transport models were applied in several research projects (Marshall and Banister 2007). Several integrated land-use transport models were applied in a growing number of metropolitan areas. New developments in data availability brought about by geographical information systems (GIS) and further advances in computer technology have removed former technical barriers.

It is impossible to present here all operational integrated land-use transport models existing in the world today. Instead a classification of models by the way they implement the feedback from transport to land use is proposed using a few examples, recognizing that in each group, there exists a great variety of approaches.

3.1 Spatial-Interaction Location Models

Spatial-interaction locations models retain the original Lowry concept by modeling the location of human activities as destinations of trips using the production-constrained spatial-interaction model. The most prominent urban model of this kind was the MEPLAN model developed by Echenique (1985). Current examples of operational models are TRANUS (de la Barra 1989) and PECAS (Hunt and Abraham 2005). These models use a multi-industry, multiregional input–output framework (see chapter “Interregional Input–Output Models”) to predict the locations of production and consumption in the urban region, where households of different types are treated as industries producing labor and consuming commodities. By iterating between the land-use parts and the transport parts of the models, general equilibrium between transport costs (including congestion) and land and commodity prices is achieved. The core equation of MEPLAN is

$$ {X}_{ir s}={X}_{ir}\, {A}_{ir}\, \mathrm{f}\left({c}_{ir}+{g}_{ir s}\right)\, {Z}_{is} $$
(6)
where Xirs are deliveries of industry i from region r to region s, Xir is the supply of goods of industry i in r and Zir the demand for such products in s, and cir are unit production costs of such products in r and girs their unit transport costs from r to s. Air is the balancing factor as in Eq. (1) ensuring that total trade flows from region r equal production in r.

The great advantage of spatial-interaction location models is their firm foundation in economic theory with respect to production and consumption. One possible criticism is that households are treated as industries producing labor and consuming commodities, with the consequence that residential location solely depends on workplace location, as if workers decided where to live on their way back from work.

In his most recent model RELU-TRAN, Anas reverses the causal direction of the input–output framework by modeling the location choice of consumers (households), producers (firms), landlords, and developers separately by utility functions for households which include the costs of budget-constrained trips and production functions for firms including interindustry links as generated by the transport part of the model. As in the input–output models, by iterating between the land-use and transport parts of the model, general equilibrium between land use and transport is achieved (Anas and Liu 2007). In PECAS the spatial-interaction part represents a short-term equilibrium and is complemented by a parcel-based model of actions of developers (Hunt and Abraham 2005).

3.2 Accessibility-Based Location Models

The second group of land-use transport models predicts not actual spatial interactions but the opportunity for spatial interactions at potential locations. The indicator of opportunity for spatial interactions is called accessibility. Accessibility indicators can take a wide range of forms, from simple accessibility indicators, such as distance to the nearest bus station or motorway exit, to complex indicators measuring the ease of reaching all destinations of interest. The most frequently used complex accessibility indicator is potential accessibility or the total of all destinations of interest weighted by an inverse function of the effort to reach them measured in time or cost or a combination of both as “generalized cost”:

$$ {A}_i={\sum \limits}_j{D}_{j\, }\exp \left(-\beta {c}_{ij}\right) $$
(7)
where Ai is the potential accessibility of zone i with respect to destinations of interest Dj and cij is the generalized costs of travel between i and j. The inverse similarity with the balancing factor of Eq. (2) is obvious.

Examples of operational accessibility-based location models in use today are IRPUD (Wegener 1982, 2018), RURBAN (Miyamoto and Kitazume 1989; Miyamoto and Udomsri 1996, Miyamoto et al. 2007), MUSSA (Martinez 1996, 2018), DELTA (Simmonds 1999), and UrbanSim (Waddell 2002). These models predict location choices of households and firms with discrete choice models using multi-attribute utility functions in which accessibility indicators are combined with other attributes of potential locations to indicate their attractiveness from the point of view of households looking for a residential location or firms looking for a business location. In that respect, these models build on the bid-rent approach of Alonso (1964), although equilibrium between asking rents and bid rents on the land market is achieved only in RURBAN, MUSSA and DELTA, whereas IRPUD keeps land prices fixed during a simulation period and defer the price response of landlords to the next simulation period.

As an example of accessibility-based location choice, the allocation of housing demand to vacant residential land by a multinomial logit model in the IRPUD model is shown (Wegener 2018):

$$ {C}_{kli}\left(t,t+1\right)=\frac{L_{kli}\, \exp \left[{\beta}_k\, {u}_{kli}(t)\right]}{\sum \limits_{il}{L}_{kli}\, \exp \left[{\beta}_k\, {u}_{kli}(t)\right]}\quad {C}_k\left(t,t+1\right) $$
(8)
where Ck(t, t + 1) are new dwellings of type k developers plan to build in the whole region between time t and t + 1, Ckli(t, t + 1) are dwellings of that type that will be built on land-use category l in zone i in that period, and Lkli is the capacity of vacant land for such dwellings given zoning and building density and height constraints. The parameters βk indicate the selectivity of developers with respect to the attractiveness ukli(t) of land-use category l in zone i for dwellings of housing type k:
$$ {u}_{kl i}(t)={\left[{u}_{ki}(t)\right]}^{v_k}{\left[{u}_{kl}(t)\right]}^{w_k}{\left[u\left({c}_{kl i}\right)(t)\right]}^{1-{v}_k-{w}_k} $$
(9)
where uki(t) is the attractiveness of zone i as a location for housing type k, ukl(t) is the attractiveness of land-use category l for housing type k, and u(ckli)(t) is the attractiveness of the land price of land use category l in zone i in relation to the expected rent or price of the dwelling. The vk, wk, and 1−vkwk are multiplicative weights adding up to unity. The zonal attractiveness uki(t) is multi-attribute and contains, besides other indicators of neighborhood quality, one or more types of accessibility indicators.

The advantage of accessibility-based location models is that by inserting different types of accessibility indicators into the utility functions of different types of locators, the great diversity of accessibility needs reflecting different lifestyles and preferences of households and different communication and transport needs of firms can be considered. Their disadvantage is that the actual travel and transport behavior, and hence actual travel times and transport cost, become known only in the next iteration of the associated transport model, but this may be acceptable because they change over time only gradually. The separation of the land-use and transport parts of the model by the accessibility interface makes it easier to develop custom-tailored submodels of the location behavior of individual groups of actors, such as households looking for a dwelling, landlords looking for a tenant, developers considering upgrading of their housing stock or looking for vacant land for new residential buildings, or firms looking for vacant floorspace or for land to build new floorspace.

This has important implications for the software organization of the models. While spatial-interaction location models as described in the previous section tend to be “unified,” i.e., to consist of one single complex algorithm designed to achieve general equilibrium, the accessibility-based models described in this section tend to be “composite,” i.e., to consist of several interlinked modules each serving a specific purpose, modeling the behavior of a particular group of actors and using the accessibility indicators most appropriate for that. Several accessibility-based LUTI models, such as RURBAN, MUSSA, DELTA and UrbanSim, originally did not contain transport submodels but were linked to existing transport models, and recently transport submodels were developed for DELTA and UrbanSim.

4 Current Debates

The urban models sketched so far represent the main model types coexisting until the end of the 1990s. However, from then on, the urban modeling scene has become increasingly fragmented along two dividing lines. The first divide runs between equilibrium modeling approaches and models that attempt to capture the dynamics of urban processes. The second more recent divide runs between aggregate macro-analytic approaches and new microscopic agent-based models.

4.1 Equilibrium or Dynamics

The first urban models were static equilibrium models, such as the Lowry model which generated an “instant metropolis” at a point in time in the future. This tradition was maintained and is still strong in urban-economics models based on the notion that all markets, including urban housing, real estate, and transport markets, tend to move toward equilibrium between demand and supply and that therefore the equilibrium state is the most appropriate guidance for urban planning.

In contrast to this view, a different movement in urban modeling has become more interested in the adjustment processes going on in cities that may lead to equilibrium but more frequently do not. The proponents of this movement, influenced by systems theory and complexity theory, argue that cities have evolved over a long time and display a strong inertia which resists sudden changes toward a desired optimum or equilibrium (see chapter “Spatial Dynamics and Space-Time Data Analysis”). Following this view, urban change processes can be classified as slow, medium speed, and fast (Wegener et al. 1986):
  • Slow Processes: Construction. Urban transport, communications, and utility networks are the most permanent elements of the physical structure of cities. The land-use distribution is equally stable; it changes only incrementally. Buildings have a life-span of up to 100 years and take several years from planning to completion.

  • Medium-Speed Processes: Economic, Demographic, and Technological Change. The most significant kind of economic change are changes in the number and sectoral composition of employment. Demographic changes affect population through births, ageing, and death and households through household formation and dissolution. Technological change affects all aspects of urban life, in particular transport and communication. These changes do not affect the physical structure of the city but the way it is used.

  • Fast Processes: Mobility. There are even more rapid processes that are planned and completed in less than a year’s time. They refer to the mobility of people, goods, and information within and between given buildings and communication facilities. These changes range from job relocations and residential moves to the daily pattern of trips and messages.

The advocates of dynamic models argue that in order to make realistic forecasts, it is necessary to explicitly take account of the different speeds of processes. In particular, they criticize the implicit assumption of spatial-interaction location models that households and firms are perfectly elastic in their location behavior and change to the equilibrium spatial configuration as if there were no transaction costs of moving.

In contrast, dynamic urban models make the evolution of the urban system through time explicit. Early dynamic urban models (Harris and Wilson 1978; Allen et al. 1981) treated time as a continuum. Today the most common form are recursive or quasi-dynamic models in which the end state of one simulation period serves as the initial state of the subsequent period. The length of the simulation period, usually 1 year, is the implicit time lag of the model, as changes occurring in one simulation period affect other changes only in the next simulation period. By using results from earlier simulation periods, the modeler can implement longer delays and feedbacks. For instance, if it is assumed that it typically takes 3 years to plan and build a house, a delay of 3 years between residential investment decisions and the new dwellings appearing on the market would be appropriate. Similar delays between investment decision and completion allow to model the typical cycles of over- and undersupply of office space.

Most current dynamic urban models are composite models, i.e., operate with a combination of custom-tailored submodels for different urban change processes. By selecting the sequence in which these submodels are processed during a simulation period, the modeler can give certain processes priority access to scarce resources. It is no coincidence that most dynamic land-use models are accessibility-based location models, i.e., use accessibility indicators as link between transport and land use and so take advantage of the possibility to select different types of accessibility for different types of development.

Most existing equilibrium urban models, however, are unified, i.e., apply one algorithm to all its parts, such as spatial-interaction location in the case of MEPLAN, TRANUS, and PECAS, or bid-rent location in the case of MUSSA, because they aim at general equilibrium between supply and demand, which is easier to achieve in a unified model. However, the growing success of dynamic or quasi-dynamic models has had its effects on equilibrium models. Some spatial-interaction location models, such as MEPLAN and PECAS, have been made recursive, i.e., they are processed not only for a distant target year but for years in between and have been complemented by developer submodels producing residential, commercial, and industrial floorspace that serve as constraints for the allocation of households and economic activity in the equilibration of the subsequent simulation period (Echenique et al. 2013; Jin et al. 2013).

4.2 Macro or Micro

The second major divide appearing in the urban modeling scene concerns the debate about the most appropriate level of spatial and substantive disaggregation.

The first urban models were zone-based like the travel models of the time, as the data required by both types of models were available only for relatively large statistical areas. However, in the 1990s, the growth in computing power and the availability of GIS-based disaggregate data fuelled by non-modeling applications, such as data capture, mapping, spatial analysis, and visualization, has had its impact on urban modeling. New modeling techniques, such as cellular automata (CA) and agent-based models developed and applied in the environmental sciences, were proposed for modeling land-use changes of high-resolution grid cells (see chapter “Cellular Automata and Agent-Based Models”). In transport planning, activity-based models modeling no longer trips but activity-related multi-stop tours have become the state of the art (see chapter “Activity-Based Analysis”). The impact of these developments on urban modeling has been a massive and still continuing trend toward disaggregation to the individual level or microsimulation.

There are important conceptual reasons for microsimulation, such as improved theories and growing knowledge about human cognition, preferences, behavior under uncertainty and constraints, and interactions between individuals in households, groups, and social networks (see chapter “Social Network Analysis”), a growing potential for individualization, the choice of diversified lifestyles and hence mobility and location patterns. Disaggregate models of individual behavior are better suited to capture this heterogeneity.

Microsimulation was first used in the social sciences by Orcutt et al. (1961). Early applications with a spatial dimension covered a wide range of processes, such as spatial diffusion and urban expansion (see chapter “Spatial Microsimulation”). Since the 1980s, several microsimulation models of urban land use and transport have been developed, such as the pioneering ILUTE (Salvini and Miller 2005). Stimulated by the technical and conceptual advances discussed above, agent-based microsimulation urban models are proliferating all over the world, including microsimulation versions of originally aggregate models, such as IRPUD, DELTA, and UrbanSim.

However, not all disaggregate urban modeling projects have been successful (see, for instance, Wagner and Wegener 2007; Nguyen-Luong 2008). Many large modeling projects had to reduce their too ambitious targets. The reasons for these failures are partly practical, such as large data requirements and long computing times, but partly also conceptual.

The most important conceptual problem is the lack of stability of microsimulation models due to stochastic variation. Stochastic variation, also called microsimulation or Monte Carlo error, is the variation in model results between simulation runs with different random number seeds (see chapter “Spatial Microsimulation”). In agent-based models of choice behavior, the magnitude of stochastic variation is a function of the ratio between the number of choices and the number of alternatives and the selectivity of the choosing agents (the β parameter in the equations of this chapter). The stochastic variation is small when a large number of agents with clear preferences choose between few alternatives, e.g., travel modes. It is large when a small number of agents with less pronounced preferences choose between a large number of alternatives, e.g., locations, such as grid cells, parcels, or zones, as in the case of residential or business location. In that case, the stochastic noise may be larger than the differences between competing planning alternatives under investigation, and the results may convey an illusionary sense of precision (Wegener 2011).

There are several ways to overcome this dilemma, such as averaging the results to a higher spatial level or to artificially increasing the number of choices in the model. The most frequently recommended method is to run the model several times and to average across the results of the different runs, something rarely done because of the already long computation times of microsimulation models.

In conclusion, the microsimulation community has yet to find a proper answer to the stochastic variation problem. The optimum level of disaggregation may not be the most disaggregate one. What is needed is a theory of multilevel urban models to identify the appropriate level of conceptual, spatial, and temporal resolution for each modeling task.

5 Future Challenges

The world is changing fast, and so are the problems of urban planning. The first land-use transport models were growth-oriented and mainly addressed technical problems, such as the reduction of urban sprawl and traffic congestion. The second generation of models increasingly considered equity aspects, such as social and ethnic segregation, accessibility of public facilities, and distributive issues, such as who gains and who loses if certain policies are implemented. Today the third generation of models tries to take account of the observed individualization of lifestyles and preferences by ever greater spatial, temporal, and substantial disaggregation.

However, today new challenges are becoming visible that cannot be handled by many of the urban land-use transport models existing today.

The first challenge is to extend the models from land-use transport interaction models to land-use transport environment models. Today only few urban models are linked to environmental models to show the impacts of planning policies on greenhouse gas emissions, air quality, traffic noise, and open space (Lautso et al. 2004). As environmental submodels predicting air quality or noise propagation require high-resolution grid cell data, this model extension may give a new twist to the macro versus micro debate toward multilevel models using different spatial levels with different resolutions and upward and downward feedbacks. Even fewer models are able to model the reverse relationship, the impact of environmental quality, such as air quality or traffic noise, on location.

The second challenge is the transition from population growth to population decline already observed and foreseeable in many European cities. With small population decline and moderate economic growth, there is still demand for new housing because of decreasing household size and increasing floorspace per capita. The same is true for work places due to growing floorspace demand per worker. However, if the losses of population and employment become larger than the growth in floorspace demand per capita or per worker, the task is no longer the allocation of growth but the management of decline by new types of policies, such as rehabilitation of neighborhoods, upgrading of rundown housing, or conversion or demolition of derelict or vacant buildings. Only few current urban models are able to handle this.

The third and greatest challenge arises from the possibility of future energy crises and the requirements of climate protection. Both causes are likely to make mobility significantly more expensive. For model design, it does not matter whether car trips become more expensive through higher prices of fossil fuels on the world market or through government policies to meet greenhouse gas reduction targets. What matters is that these targets cannot be achieved without rigorous changes in the framework conditions of land use and transport in urban areas, in particular without significant increases in the price of fossil fuels.

Most current urban models are not prepared for this. Many of them are not able to model transport policies, such as carbon taxes, emissions trading, road pricing, or alternative vehicles and fuels, or land-use policies, such as strict development controls, improvement of the energy efficiency of buildings, or decentralized energy generation. Even fewer models are able to identify population groups or neighborhoods most affected by such policies or possible problems with access to basic services, such as schools or health facilities, or participation in social and cultural life in low-density suburban or rural areas.

Many current transport models cannot correctly predict the impacts of substantial fuel price increases. Many do not consider travel costs in modeling car ownership, trip generation, trip distribution, and modal choice. Many do not forecast induced or suppressed trips. Many use price elasticities estimated in times of cheap energy. Many do not consider household budgets for housing and travel.

Action space theory with explicit travel time and travel cost budgets permits to predict what will happen if speed and cost of travel are changed by environment-oriented planning policies. Acceleration and cost reduction in transport lead to more, faster, and longer trips; speed limits and higher costs to fewer, slower, and shorter trips. In the long run, this has effects on the spatial structure. Longer trips make more dispersed locations and a higher degree of spatial division of labor possible; shorter trips require a better spatial coordination of locations. However, making travel slower and more expensive does not necessarily lead to a reconcentration of land uses back to the historical city center. In many urban regions, population has already decentralized so much that further deconcentration of employment would be more effective in achieving shorter trips than reconcentration of population.

That plausible forecasts of the impacts of substantial energy price increases can be made with land-use transport models based on action space theory was demonstrated by the results of the EU project Scenarios for the Transport System and Energy Supply and their Potential Effects (STEPs). They show that with appropriate combinations of transport and land-use policies, significant reductions in greenhouse gas emissions can be achieved without unacceptable loss of quality of life (Fiorello et al. 2006). More research on urban models and climate change is going on world-wide.

6 Conclusions

After half a century of development, there exists today a broad spectrum of mathematical models to predict the spatial evolution of cities subject to exogenous trends and land-use and transport policies. These models build on a range of theories from transport planning, urban economics, and social geography to explain the complex two-way interaction between urban land use and transport, i.e., the location of households and firms and the resulting mobility patterns in urban regions subject to concurrent economic, demographic, and technological developments. Stimulated by advances in data availability, theory development and computing technology, these models have reached an impressive level of sophistication and operational applicability.

However, the urban modeling field has recently become divided into camps with different modeling philosophies. In particular, two dividing lines are becoming visible: One is the divide between equilibrium approaches which assume that cities are essentially markets moving toward equilibrium between demand and supply and dynamic approaches focusing on adjustment processes of different speeds. The other is the divide between macro approaches dealing with statistical aggregates at the level of zones and micro approaches modeling individual households and firms at the level of grid cells or parcels. In each of the two debates, the advantages and disadvantages of the competing approaches are obvious, but what is missing is an open and honest assessment of their relevance for the validity and robustness of the results of the models. Collaborative research projects in which different models are applied to identical problems and their results compared by meta-analyses are still the exception.

A second issue regarding the future of urban models is the new challenges for urban planning. The growing importance of environmental impacts of land-use and transport policies has not yet fully been embraced by most urban models. Neither has the transition from population growth to population decline already observed or foreseeable in many cities, a great challenge for some models originally designed for allocating growth. But the greatest challenge for urban models will be how to cope with the combined effects of future energy scarcity and the imperatives of climate change. During and after the energy transition, energy for transport and building heating will no longer be abundant and cheap but scarce and expensive. This will have fundamental consequences for mobility and location. Land-use transport models which are calibrated on a purely statistical basis on behavior observed in times of cheap energy and do not consider the costs of travel and location in relation to household income cannot adequately forecast these consequences. To deal with significantly rising energy costs, land-use transport models must consider the basic needs of households which can be assumed to remain relatively constant over time, such as shelter and security at home, accessibility of work, education, retail and necessary services, and the constraints on housing and travel expenditures by disposable household incomes.

To avoid the danger that the models, as in the 1970s, are again rejected by the planning practice, they must give up some long-standing traditions and be prepared to adopt new modeling principles: less extrapolation of past trends but more openness to fundamental change, less reliance on observed behavior but more theory on needs, less consideration of preferences and choices but more taking account of constraints, and less effort on detail but more focus on basic essentials.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Spiekermann & Wegener, Urban and Regional ResearchDortmundGermany

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