2. Integrated Urban Land Use--Transportation Models
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2. Integrated Urban Land Use--Transportation Models |
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This section of the report is devoted to a review of operational integrated urban land use-transportation--models, that is, models which have been empirically applied in either a research or actual planning context within the past decade. The term "integrated" implies a feedback mechanism of the type shown in Fig. 2, between the transportation system and the rest of the urban land use system. Here the "land use" system supplies the transportation system with estimates of the location and volume of travel generators. "Land use" is a general term here, covering both the types and intensities of activities taking place at specific urban sites as well as the physical area of land and any built structures used in support of such activities. This involves modeling the demand for employment, residential, shopping, and other activities at different sites, and then translating and possibly constraining these demands on the basis of appropriate physical or artificial (i.e., planner-imposed) land utilization rates. The more ambitious models also include the simulation of housing stocks and floor space requirements for industrial buildings. Within some models this also means simulation of pricing effects on, in particular, residential choice. A further extension in a limited number of modeling systems is a linked simulation of demographic change, allowing the urban area's population to evolve along with the evolution of the physical city within which it lives and works. Wegener (1994) refers to these types of model as "integrated urban models," although the interaction between transportation and other land uses remains their key trait.
The spatial distributions of residents and workers are assumed to create the major demands for travel which drive development of the transportation system. The "transportation" system in Fig. 2 represents both the physical infrastructure and services provided by the different travel modes, either separately or in combination, as well as these demands, now translated into mode-specific vehicular and nonvehicular trips, for either passenger or freight movement. This interplay between travel demand and supply resolves itself within the typical transportation model into a series of single-purpose and single-destination trips which together form the on-the-road traffic volumes of interest to an environmental analysis of fuel use and mobile source emissions.
The origin-to-destination travel costs resulting from this interplay between transportation demand and supply can be fed back into the residential and employment activity location models, where they are used to allocate the area's residents and workers to specific urban zones within the land use model. This allows transportation system changes to affect land utilization, which in turn feeds back its effects in the form of new levels (and locations) of traffic generation. The notion of locational accessibility here plays a central role in all currently operational models. As an integral component of such accessibility, travel cost changes become part of the mechanism used to reallocate labor, residents, retail and service activities, and when modeled, freight flows between spatially separated land uses.
In terms of an urban dynamic, most models employ static-recursive approaches to multiyear forecasting or (more realistically) scenario generation. That is, cross-sectional representations of the urban system are moved forward through a series of discrete time intervals. However, both the operational details and level of sophistication imposed on this dynamic vary considerably across existing models. This is the topic for Sect.2.5 below. A common planning horizon for such a single-time-period forecast is 5 years, although intervals from 1 year to as many as 30 years have been used. Forecasting further into the future, an obviously risky business, is accomplished in the more advanced modeling systems by iterating the land use and transportation subsystems through a series of discrete time intervals. In an effort to keep transportation and other urban land uses in some kind of synchronization, both lagged and marginally incremental methods are used to update and to control for selected variables as part of this process.
Figure 2 also shows the location of three types of public policy instruments commonly used to simulate the effects of significant travel reduction strategies: (1) land use controls, (2) fuel pricing policies, and (3) those transportation control measures which impact directly the capacity and level of service of the specific transportation modes.
Table 2 lists the better-known and documented operational models, along with some of their applications to specific urbanized area studies. The table draws heavily on the models reported by the International Study Group on Land Use-Transportation Interaction (ISGLUTI) (Webster, Bly and Paulley, 1988),(2) on the survey of available models by Cambridge Systematics and The Hague Consulting Group (1991), and on the reviews by Berechman and Gordon (1986), Berechman and Small (1988), Mackett (1985), Putman (1983, 1991), and Wegener (1994, 1995b). These sources were supplemented by a further literature search and through contacts with a number of the field's leading model developers.
Among the most recent round of empirically supported U.S. studies of note are those for the Chicago area (Anas and Duann, 1986; Boyce et al., 1992, 1993; Kim, 1989); for the San Francisco Bay Area (Prastacos, 1986a,b; Caindec and Prastacos, 1995); the Puget Sound Region of Washington State (Watterson, 1993); and Portland, Oregon's Land Use, Transportation, and Air Quality (LUTRAQ) study (Cambridge Systematics -- Hague Consulting Group, 1991). The most widespread application of a particular modeling approach in the United States comes out of the extensive model development and calibration efforts of Putman and colleagues (see Putman 1983, 1991) , whose joint implementations of the Disaggregate Residential Allocation Model (DRAM) and the Employment Allocation Model (EMPAL) are currently used in some fourteen of the largest U.S. metropolitan planning agencies (Putman, 1994). During the 1970s and 1980s Putman also developed the Integrated Transportation Land Use Package (ITLUP), linking DRAM and EMPAL with selected components of the traditional four-step transportation planning model, containing submodels to estimate trip distribution, modal choice, and traffic assignment. References to past empirical applications of ITLUP include studies in Kansas City, Washington, D.C., and Houston. The LUTRAQ study also recommended use of an ITLUP-like approach (Cambridge Systematics et al., 1992b). Recently DRAM and EMPAL have been linked to the TRANSPLAN suite of transportation planning models in a 772-zone application to the southern California region, centered on Los Angeles (Putman, 1994).
| Model | Useful References | Example Urban Studies |
| AMERSFOORT | Floor and de Jong(1981)a | Amersfoort, Utrecht, Netherlands; Leeds, UK |
| BOYCE, ET AL | Boyce, Tatineni & Zhang (1992), | Chicago |
| Boyce, Lupa, Tatineni & He (1993) |  |
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| CALUTAS | Nakamura et al (1983)a | Tokyo, Nagoya, Okayama, Japan |
| CATLAS/NYSIM/METROSIM | Anas (1983b), Anas & Duann (1986), | Chicago, New York |
| Anas ( 1992, 1994) | |
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| DORTMUND | Wegener (1982a,b; 1986, 1995a)a | Dortmund, Germany |
| KIM | Kim (1989) | Chicago |
| ITLUP | Putman (1983, 1991)a | San Francisco, Los Angeles, Houston, Dallas, Portland, Others |
| LILT | Mackett (1983, 1990a, 1991a,b)a | Leeds, England; Dortmund, Germany; Tokyo, Japan |
| MASTER | Mackett (1990b, 1990c) | Leeds, England |
| MEPLAN | Echenique et al (1985)a, | Bilbao, Spain; Sao Paulo, Brazil |
| Hunt & Simmonds (1993), | Santiago, Chile; Naples, Italy; | |
| Hunt (1993, 1994) | Others. | |
| OSAKA | Amano et al (1985)a | Osaka, Japan |
| POLIS | Prastacos (1986a,b), | San Francisco Bay Area. |
| Caindec & Prastacos (1995) | |
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| PSCOG | Watterson (1993) | Puget Sound, Washington. |
| TRANSLOC | Boyce & Lundqvist (1987),a | Stockholm, Sweden |
| Lundqvist (1989) | |
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| TOPAZ | Brotchie et al (1980)a ; | Melbourne, Darwin, Australia; |
| Dickey and Leiner (1983), | Prince William Co. Virginia; | |
| Sharpe (1978, 1980, 1982) | Others | |
| HAMILTON | Anderson, et al (1994); | Hamilton, Canada |
| Kanaroglous, et al (1995) | |
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| TRANUS | de la Barra (1989) | Caracas, La Victoria, Venezuela |
| a indicates participation in the International Study Group on Land Use-Transportation Interaction (ISGLUTI) study; see Webster, Blye, and Paulley (1988). | ||
Building on the CATLAS model of combined residential location, housing and mode choice, the modeling of non-work travel choices and commercial real estate markets in the New York region (the NYSIM model), and the modeling of metropolitan housing market dynamics in a number of US cities (the CHPMM model), Anas and colleagues have developed a highly integrated economic model of transportation and land use called METROSIM. METROSIM (Anas, 1994) consists of 7 sub-models, providing analysis of a region's basic industry, non-basic industry, residential and commercial real estate, vacant land, households, commuting and non-commuting travel and traffic assignment, within a single, jointly solved-for structure that is strongly oriented towards theoretically sound and empirically workable economic relationships.
In the United Kingdom notable efforts to develop land use-transportation models are found in both the theoretical and the empirical work begun by Wilson and colleagues at the University of Leeds (see Wilson et al., 1977, 1981), and carried on by Mackett at the University College, London. Mackett has devoted considerable effort to building and calibrating both the Leeds Integrated Land Use-Transportation modeling package (LILT) (Mackett 1983, 1991a,b) and the MASTER microsimulation-based modeling system (Mackett, 1990b). Echenique and colleagues at the University of Cambridge, and subsequently within the commercial sector, have been especially energetic in developing and applying the MEPLAN modeling system. Their work includes planning applications for the city of Bilbao, Spain, and for the Third World cities of Sao Paulo, Brazil (Echenique, 1985); Caracas, Venezuela (Feo et al., 1975); and central Chile (de la Barra et al., 1975). Hunt and Simmonds (1993) reference 22 different empirical applications of MEPLAN, including a recent study for Naples, Italy (Hunt, 1994). A similar but now separate modeling system, TRANUS, has also been applied to the island of Curacao and the city of La Victoria in Venezuela (de la Barra, 1989), as well as to more idealized simulations of energy and urban form relationships (de la Barra and Rickaby, 1982; Rickaby, 1987, 1991). Johnston (1995) indicates that TRANUS is currently being experimented with in Sacramento, at the University of California at Davis, where it is being examined in conjunction with the California Urban Futures Model, or CUFM (see Landis, 1994).
Pioneering work in the field has also resulted from a long-term involvement in the area by the Commonwealth Scientific and Industrial Research Organization (CSIRO) in Australia, based largely on use of the TOPAZ modeling system (Brotchie, 1969; Brotchie, Dickey, and Sharpe, 1980; Sharpe, 1978, 1980, 1982 and other references therein). As its name implies (Technique for Optimal Placement of Activities in Zones), the approach taken in the TOPAZ model is a normative one, using a very general location-allocation modeling system adaptable to a number of different scales of spatial analysis. In recent work, the object-oriented SUSTAIN model (Roy and Marquez, 1993) is being developed to facilitate more idealized, less idiosyncratic comparisons of different energy-efficient forms of urban transportation infrastructure development.
Other work of interest in Australia includes development of the LAND gaming-simulation model by Young and colleagues at Monash University in Melbourne (Gu et al., 1992), and the proposed PIMMS (Pricing and Investment Model for Multi-Modal Systems) model, described by Hensher et al. (1993) at the University of Sydney.
In Canada, initial progress in the development and empirical application of an integrated land use-transportation model to the Hamilton Consolidated Metropolitan Area is reported by Anderson et al (1994), Kanargolou et al (1995) and Anderson, Kanargolou, and Miller (1994). Here the early focus has been placed on simulating automobile fuel consumption and emissions.
In Japan, integrated urban modeling includes the CALUTAS model (Computer-Aided Land Use Transport Analysis System) (Nakamura et al., 1983) and the Osaka model (Amano et al., 1985). Wegener (1994) briefly references other recent Japanese developments. Other non-U.S. studies include van Est's (1979) modeling of the Eindhoven urban area; Bertuglia et al.'s (1981) modeling of Turin and Rome in Italy; and a number of modeling applications to the city of Stockholm in Sweden, including application of the Transportation and Location, or TRANSLOC, model listed in Table 2 (see Boyce and Ludqvist, 1987, for example).
For the Middle East, Garnett (1980) reports a planning model and policy application for Tehran, Iran. Martinez (1992a,b) recently calibrated his own version of an integrated land use-transportation model for Santiago, Chile. Finally, Cambridge Systematics and The Hague Consulting Group (1991) also report the existence of two commercially available, ITLUP-like computer packages known as TRACKS and TRANSTEP, with 51 reputedly different applications in Australia and the Far East.
As a set, the models listed above have been empirical by applied to a wide range of policy questions. While the initial reasons for developing the various modeling approaches may have differed, the ISGLUTI study found sufficient similarity across nine of the models reported in Table 1 to carry out a set of common tests. These tests covered the effects on travel choices and land use arrangements from introducing changes in the following variables:
Moving into specific policy impact studies, Mackett (1994) concludes that current models can be particularly useful for analyzing either congestion reduction or energy reduction strategies. (Also considered were safety, the environment, social equity, quality of life, public expenditure and privatization policies.) He lists the following commonly available (if not always popular) public policy instruments as being well suited to analysis with models which integrate transportation planning decisions into a broader and longer-range analysis of land use.
In a research context a handful of past studies have also used such models to look specifically at alternative, if rather abstract, energy-efficient urban futures (see Sharpe, 1978, 1980, 1982; de la Barra and Rickaby, 1982; Rickaby, 1991; Roy and Marquez, 1993). In the United States the 1990 Clean Air Act Amendments and supporting legislation within the 1991 Intermodal Surface Transportation Efficiency Act have caused recent practice to focus on using such models to forecast future levels of urban air quality (see Putman, 1994, using the DRAM/ITLUP modeling approach; and Watterson, 1993, using modified versions of the DRAM and EMPAL models within the Puget Sound Council of Governments model).(3) The spatial as well as temporal extent of such applications also varies, from specific highway or transit corridor analyses to full-scale urban area or complete transit network simulations.
Urban transportation modeling began in earnest in the mid-1950s in the United States (see Weiner, 1992, for historical developments). Since the 1960s most metropolitan areas have used variants of the Urban Transportation Planning System (UTPS) models shown in Fig. 3. This four-step, single-destination, separable-purpose, daily trip-based approach has dominated the transportation modeling literature. This includes its use within the integrated land use-transportation models listed above. It has been used to address a wide range of issues covering the physical, economic, and ( in recent years) energy and environmental impacts of major highway or rapid transit investments. The approach is sequential in order to avoid some very difficult multicollinearity problems found to affect more direct estimation techniques. It is also meant to be iterative in order to bring the transportation costs computed within the trip distribution (= destination), modal choice, and traffic assignment (routing) submodels down to a common set of values.
In this system the urbanized area is first divided up into a set of spatially contiguous traffic-generating and attracting zones. For our largest cities this involves definition of dozens, sometimes hundreds, of zones linked to highway and transit networks containing hundreds, sometimes thousands, of link and node records. The computational process can be started with a simple all-or-nothing assignment of traffic to least-cost interzonal travel paths. This can be done before any actual trip volumes are "loaded " onto the network. Land use, when modeled explicitly, comes into the process through its influence on trip generation rates. Alternatively, daily trip frequencies are estimated directly from zonally based population and employment forecasts. These forecasts are suitably disaggregated by household type or economic sector based on significantly different observed averaged trip rates. The trip generation (and trip attraction) models are usually regression based, or built on category analytic techniques (see Douglas and Lewis, 1970/71; Institute of Traffic Engineers, 1987).
For a set of zone-specific, average daily trip originations, one or more trip distribution models are then used to allocate purpose-specific trips to destinations within the remaining set of urban analysis zones. Within these spatial interaction models the concept of locational accessibility to opportunities plays a central role in the allocation process. If travel is a derived demand, then accessibility is the "good" it provides. Such locational accessibility indices have the form
where Wj = the level of demand, or more generally a measure
of the attractiveness of a potential destination zone j for trips of a
given purpose (e.g., journey to work, shopping); cij = the
cost of travel from the trip's origination zone, i, to destination zone j;
= an economies-of-scale parameter (0 <=
<= 1); and f(.) = a travel mode and distance-based cost decay function,
such as exp(-
.cij). Here
is a distance-based cost sensitivity parameter, which the modeler must
estimate. Within a work trip model, Wj may refer to the number
of jobs available in zone j. More generally, it may be a composite,
multiplicative, or additive index of locational attractiveness. Similarly,
the travel costs cij may be of a composite or a "generalized"
form, typically including both travel time and any fares or other monetary
operating costs incurred during a trip.
The use of spatial interaction models in urban planning studies gained a boost with the elaboration of both entropy maximizing (Wilson, 1967, 1970) and utility maximizing (Neidercorn and Bechdolt, 1969; Golob, Gustafson and Beckmann, 1973) theories, which have provided, respectively, a more robust statistical mechanics/ information theoretic basis and a rational economic basis for spatial interaction theory. Subsequent theoretical efforts to link these two approaches during the 1970s and 1980s have further strengthened the hold of "logit" forms of interaction model on the discipline (see Anas, 1983a; Brotchie et al., 1979; Williams, 1977; Wilson, et al., 1981). Such a logit model can be stated as
where Tij = the number of trips between zones i and j, Oi
= the number of trips generated at location i (for a particular trip
purpose), and vij = a multicriteria value function reflecting
the attractiveness of location j as a destination for such an i-based
trip. By setting each vij = [lnWj-
cij ] we have the following direct connection to Eq.
(1):
This is a popular form of origin, demand or "production"-constrained spatial interaction model, which Wilson (1971) placed within a family of possible models, including destination (supply, "attraction")-constrained as well as demand and supply ("doubly")-constrained forms.(4) The issues of why and when we travel are handled within this framework by incorporating disaggregations by trip purpose and time of day, respectively. This usually leads to separate matrices of zone-to-zone flows coming out of a work trip model and one or more types of nonwork trip (e.g., shopping, social and recreational, school trip) distribution models.
The modal choice submodel "splits" these interzonal trip volumes across the most likely travel modes (usually auto versus public rail or bus transit, but with walk, cycle or multimodal trips also possible). The logit is again the most popular form in use. At this step "disaggregate"--that is, individual traveler--response-based multinomial logit models have also become popular in the United States, using McFadden's (1974) maximum likelihood method to include a wide range of explanatory variables as well as multiple travel choices within such model calibration efforts.
A subsequent and now increasingly used theoretical development was the specification of "nested" logit forms, which allow the results from one production-or attraction-constrained logit model to be passed into another in a behaviorally consistent manner (see Williams, 1977; Ben-Akiva and Lerman, 1985). For example, mode m-specific travel (dis)utilities, cijm (i.e., modal travel costs), can be averaged into a destination choice model such as Eq. (2) above, using log-sum or inclusive value terms of the form
where cij* is now the modally averaged
disutility of travel between i and j. Here 
is a calibrated model parameter representing the sensitivity to modal cost
differences in a manner analogous to the way
represents sensitivity to distance-based destination choice in
Eq. (2). Taking such a nesting one stage further, we
can also compute the expected or averaged travel (dis)utility associated
with the set of mode and destination combinations available to a
traveler located in zone i, vi**, using an
inclusive value index of the form
which, in terms of equation (1) above is a log-accessibility measure, and which in economic terms is often interpreted as a locational or consumer's surplus measure associated with zone i (see Williams, 1977; Fisk and Boyce, 1984).
The resulting mode-specific interzonal traffic volumes are then assigned to one or more routes, or paths, by the traffic assignment submodel shown in Fig. 3. This results in a new set of interzonal travel costs which ought to be submitted back to the trip distribution model. The process of model calibration should then be continued by iterating the travel costs within the various mode, destination, and assignment submodels until they converge to a single set of values.
A number of variants on this iterative procedure are now used (see Boyce, Lupa, and Zhang, 1994). At the traffic assignment stage the auto trips and any truck trip matrices that have been generated are converted into passenger car equivalent traffic volumes before being simultaneously loaded onto the highway network. Logits can also be used to select alternative routes and have been incorporated within a number of different assignment methods (see Sheffi, 1985). However, the most commonly referenced assignment model is the capacity-sensitive approach proposed by Wardrop (1952). Under this approach, which is geared to handling the congested conditions experienced during the commute to and from work, urban traffic volumes are distributed such that all multilink routes used between any origin-to-destination pair of traffic zones have the same travel time, while all available but unused routes have a higher travel time. The result is termed a user optimal equilibrium assignment in which no traveler can change his or her route without incurring extra en route delays (Beckmann, McGuire, and Winsten, 1956). Mathematically, this can be stated as
subject to
where Tij is a trip matrix, and we are solving for fa
= the flow of traffic on link a. Here Ca(fa) = the
congestion-sensitive cost of travel along link a, such as a convex
function of the form ca(1+afa)4
for ca = free flow travel time, and a
= a function of the link's design capacity.
The Xijp variables in Eq. (7)
represent the number of trips from origin i to destination j using
multilink route (path) p, and 
ijap
= 1 if link a belongs to route p, and is zero otherwise. Equation
(7) ensures that each link's assigned traffic volume is the sum of
the volumes of each path using it, while Eq. (8)
ensures that all route volumes from a given origin-to-destination sum to
the original number of i-to-j trips input to the algorithm (from the trip
distribution modeling step described above).
Figure 4 shows a simple two-route, two-link example for the type of link speed-volume relationships often used in practice. The area created under these two marginal link travel cost curves is the solution to the objective function given by Eq. (6) above. Efficient computational procedures now exist for solving this and similar capacity-constrained traffic assignment problems for quite large and detailed urban area networks. Recent developments by Janson (1991) and Janson and Southworth (1992) have also extended this sort of equilibrium assignment model into computationally tractable dynamic forms, which may soon allow the analysis of such strategies as staggered work trip departure times and their effects on traffic congestion. Such developments also take us squarely into the realm of Intelligent Transportation Systems (ITS) research, an area currently receiving large amounts of funding from the U.S. Department of Transportation (DOT) in support of the 1991 ISTEA legislation.
Rail transit options are usually modeled over their own, separate network. Where bus transit is a significant alternative, passenger car equivalent (pce) conversion factors can be used to simulate the effects of each bus within the resulting traffic stream, and suitable network coding techniques can handle the presence of bus-only lanes or other forms of high-occupancy vehicle (HOV) facility. A similar pce procedure can also be used to portray the effects of larger trucks in the traffic stream.
Variants on this same four-step transportation system modeling process are often used for both long-term (10-to 30-year) planning, and shorter range (1-to 5-year) transportation system management (TSM) planning (see Yu, 1982, for an overview). In some cases specifically designed variants on the overall modeling approach have been developed to better focus on a particular TSM strategy; these include the Network Performance Evaluation Model developed for the U.S. Department of Energy (DOE) to analyze the energy and environmental impacts of various types of HOV lanes, (see Janson, Zozaya-Gorostiza, and Southworth, 1987).
Fuel use and related mobile-source, pollutant-specific emissions estimates are typically computed using these assignment model-generated traffic volumes and speeds. For this purpose baseline emissions estimates for light-duty motor vehicles (automobiles and light trucks) are generated by the Federal Test Procedure. Under the FTP vehicles go through a series of stops and starts with an average driving speed of 19.6 mph. Emissions rates for vehicles at other speeds are derived by a statistical regression of fuel consumption against average speed for cycles other than the FTP. Speed correction factors (SCFs) for this purpose have been developed by the U.S. Environmental Protection Agency and by the California Department of Transportation.
However, these emissions outputs, and the traffic volumes themselves, are usually aggregated or averaged over one or more traffic analysis zones for the purposes of computing emissions on a wider regional or "gridded" basis (see Quint and Loudon, 1994; Outwater and Loudon, 1994). Currently, there is a good deal of uncertainty surrounding the accuracy of emissions calculations for carbon monoxide (CO), hydrocarbons (HC), and oxides of nitrogen (NOX) and, in particular, their relationship to actual traffic conditions (see Guensler, 1993; Bae, 1993). Nor were the traffic volumes and speeds from static traffic assignment models meant to handle such details. While detailed traffic simulation programs based on individual vehicle movements are now also in use, it has been only recently, and in a research context, that this sort of detailed traffic flow modeling has been tied directly to emissions estimation (see Matzoros and Van Vliet, 1992a,b), and little testing of its accuracy has been carried out.
For the purposes of estimating areawide CO2 emissions, which are highly correlated with total fuel used, less concern for such accuracy may be warranted. Unlike the CAAA-controlled pollutants, which are by volume comparatively marginal engine emissions, CO2 emissions are highly correlated with fuel used and associated, congestion-conditioned vehicle miles traveled (VMT). Nor need we be concerned within such an analysis of greenhouse gas buildup with such location-specific issues as the health effects of CO hotspots.
Urban land use modeling also began in the 1950s, again in the United States (see Batty, 1980, who dates such efforts from 1958). Most of today's operational land use-transportation models derive from ideas and model forms introduced into the wider literature during the 1960s and 1970s. There is now an extensive literature dealing with the theoretical and methodological as well as operational aspects of such models. The discussion presented below draws on the historical and technical accounts and efforts at synthesis described in, among others, Anas (1984), Batty and Hutchinson (1983), Berechman and Gordon (1986), Berechman and Small (1988), Bertuglia et al. (1987), Echenique and Williams (1980), Echenique (1985), Kim (1989), MacGill and Wilson (1979), Mackett (1985, 1994), Putman (1983, 1991, 1994), Transportation Research Board (1990), Wegener (1994, 1995b), Wilson (1987), and Wilson et al. (1977, 1981).
Figure 5 shows the basic idea behind linking a land use model to the four-step transportation planning model described above. As noted in this figure, a number of modeling systems use the spatial interaction formulas at the heart of their residential and employment location submodels to replace (obviate the need for) a separate set of trip-based distribution models. The ITLUP model can be used to generate such trip distributions within the DRAM submodel. The MEPLAN and TRANUS models generate all of their inter-zonal flow matrices as a series of "trades" within the land use modeling system. Within a number of operational models, including the MEPLAN and Kim models described later in this review, the urban system is modeled as a series of markets, with emphasis placed on clearing a transportation market and one or more other land use markets, by solving endogenously for a suitable set of spatially varying market prices; which include travel costs and site rents. Within the less inclusive models, such as ITLUP, which avoid endogenous modeling of nontransportation price mechanisms, an equilibrium between the transportation system's demands and supplies can also be brought about; this also stabilizes the parameters within the residential and employment activity location submodels. Such considerations of equilibrium in urban evolution quickly take us into the area of temporal dynamics. Within the ITLUP, MEPLAN, and Dortmund models described in some detail below, lagged effects play an important role in linking different submodels within the transportation and land use systems both across as well as within a single time period (see Sect. 2.5, below).
While operational transportation planning models have tended to be built around the above four-step approach, once we link these developments to urban land use models a good deal more variety is evident. At least five significantly different theoretical and/or methodological approaches have combined to produce the current state of best practice among such extended and "integrated" modeling systems. Each of these approaches--the Lowry model, normative and mathematical programming developments, spatial input-output analysis, urban economics, and microanalytical simulation--is reviewed briefly below.
In the discussion of each of these approaches a model from Table 2 has been selected for detailed presentation, as a means of demonstrating how such developments translate into current modeling practice. The reader should note, however, that the assignment of a model below to a particular approach is somewhat arbitrary. The order of presentation was selected to show how current models have brought developments from a number of the above discussed advances into their frameworks. A significant feature of model advances over the past 30 years has been the gradual incorporation and unification of different theories and methods within individual modeling frameworks. The purpose of the following descriptions is not to fully elaborate on any single modeling system but to use specific models to elaborate on key areas of development. In selecting examples for presentation there is also a strong bias towards U.S.-based modeling efforts. For a complete list of a model's current functionality the reader should see the references cited in the text.
Most operational urban land use models today, and all of those discussed below, can trace their beginnings to Lowry's (1964) "Model of Metropolis" for the city of Pittsburgh. The original Lowry model incorporates the spatial distribution of population, employment, retailing (the entire service, or "non-basic," sector), and land use within a compact iterative procedure requiring only nine equations and three inequalities. In essence, the approach consists of linking together two spatial interaction models. One of these models allocates workers to a predefined set of land use zones on the basis of exogenously supplied basic employment levels (i.e., employment in manufacturing and primary industries). The dependent families of these workers are then defined using a suitable activity ratio (the ratio of total regional population to total regional employment). These workers and their families demand services, and these demands are met by means of a second spatial interaction model which allocates this service supply, in the form of "nonbasic" employment, across the same spatial zoning system. Iteration is required to then bring the resulting residential and nonbasic employment activity allocation models into line with each other. To generate estimates of either land area occupied or floor space used within each zone a two-stage process is required. First, the residential and employment activity levels are allocated across the set of available zones, then suitable activity-to-floor space rates are assigned, with checks to ensure that the physical limits and any planning restrictions on the space within a zone are not violated.
In the United States the most used successors to Lowry's model are the Disaggregate Residential Allocation Model (DRAM) and the Employment Allocation Model (EMPAL) as developed by Putman and colleagues (see Putman, 1983, 1991). Both are now in use in a number of U.S. cities (a recent count was 14; Putman, 1994). On the basis of empirical testing Putman (1983, Ch.7) specified DRAM to have the form
where Nin = the number of type n residents in
zone i; fn(cij) = a cost of travel function for
type n residents moving from i to j ( = cij
n.exp[-n.cij],
where n
and n
are parameters to be estimated); Ejk = the amount
of employment in sector k in zone j; akn = a regionwide
coefficient relating the number of type k employees to type n households;
and Win = a composite measure of the
attractiveness of zone i to employees from residential group n, and given
as
and where Liu = the area of vacant, developable land in zone i; xi = the proportion of developable land in zone i which has already been developed; Lir = the area of residential land in zone i; and qn, rn, sn and bn are parameters to be estimated.
A similar level of elaboration has gone into development of a number of service employment location models. Putman (1983) provides the following formula for EMPAL:
where EjtR refers to the amount of retail employment in sector R in time period t in zone j; Pit-1 is the total population in zone i in prior time period t 1, and Wjt-1R is the attractiveness of zone j for sector R activity in period t 1. This is also a composite index of the form
for Ejt-1* = total employment in zone j in prior
period t 1; Lj = the total land area of zone j; and
and
are parameters to be estimated. Finally, the "balancing term" Ait-1R
in Eq.(12) has the form
which is interpreted within this and most spatial interaction models as the inverse of a spatial accessibility index of the Hansen type (Hansen, 1959) (recall Eq. 1).
Putman (1994) discusses the recent experience of regional and metropolitan planning agencies with these iteratively linked models, which require an additional subroutine or submodel to translate their activity allocations into suitable zonal land utilization rates. He notes that income group quartile and quintile disaggregations (the latter matching trip generation model groupings) are most common within DRAM; but that ethnicity may be at least as useful a component in residence selection within some of our larger cities. He also discusses possible lagged variable forms of DRAM as a means for improving next period forecasts of zonal populations by income group (Eq. 10 above). Similarly, within EMPAL a number of employment sectors may be defined, for example, based on Standard Industrial Classification (SIC) groupings.
The first operational and truly "Integrated" Transportation Land-Use Package (ITLUP) in the United States appears also to have been developed by Putman (see Putman, 1983, 1991) to provide a feedback mechanism between DRAM, EMPAL, and the mode split and traffic assignment components of the UTPS model described in Sect. 2.3. First EMPAL allocates employment across analysis zones in the forecast time period (period t) using prior period (t-1) accessibility, population, and employment totals. A typical sectoral breakdown might be two industrial (heavy and light), one basic nonindustrial, and one nonbasic (e.g., retail) sector (Webster et al., 1988). These are typically 5-year forecasts. DRAM next forecasts the future allocation of households using prior period (t-1) locational accessibilities but also using the forecast period t distribution of zonal employment.
A third submodel, actually within DRAM and termed LANCON, calculates land consumption in the forecast period by combining base year data with a forecast based on multiple regression. DRAM also contains the system's trip distribution models, by converting the housing allocation probabilities into vehicle trips using region-specific vehicle utilization rates. Three trip matrices are produced: home-to-work, home-to-shop, and work-to-shop trips. The home-to-work trip matrices are then split into private and public vehicular modes using a multinomial logit model, and private trips are allocated to the highway network using one of at least four available types of capacity-constrained traffic assignment (see Putman, 1983, 1991). Travel cost changes are fed back into the residential and employment allocation models, which in turn--and subject to suitable physical capacity or other planning constraints on zonal land use--will then generate new interaction matrices as a result of revised locational accessibility measures.
Over the years Putman and colleagues have explored a number of variations on this static-recursive approach to forecasting (Putman, 1983, 1984, 1991). Miller (1990) also describes a number of different approaches to this recursive modeling process and provides a matrix formulation for ITLUP which mirrors Garin's (1966) matrix formulation of the original Lowry model.
In a recent study for PSCOG, Watterson (1993) also describes the results of linking modified versions of DRAM and EMPAL (see Watterson, 1990) to the widely used UTPS software. This study is notable for its use of widely available modeling packages, as well as an interesting description of their application to a highly visible public planning study, beset with real-world problems and deadlines. The process of generating alternative scenarios used was, however, a much simpler one: first set basic employment levels, then for the year 2020 create a baseline set of travel costs and run DRAM and EMPAL, then create scenario-specific sets of transportation system improvements for 2020, rerun DRAM and EMPAL, and then rerun the UTPS travel models. Scenario-specific results are then compared to the 2020 baseline model run. That is, a series of alternative 30-year scenarios (1990-2020) are generated within a single feedback loop. Attention was given to environmental concerns, including the simulation of regionwide mobile source emissions estimates. Scenarios developed included application of a wide range of TCM strategies to different forms of polynucleated urban development.
An advantage of the DRAM/EMPAL-based approaches is their basis in generally available data sources. This emphasis also translates into a weakness of the approach: the absence of any mechanism for simulating the land market clearing process underlying multiyear infrastructure change. Clearly, more comprehensive simulation of the land market requires additional data that is generally difficult to collect, notably data on the pricing of land, housing, and other forms of development. An unresolved issue is how effectively we can generate multiyear land use-transportation plans without incorporation of such additional details.
A second and equally consistent line of advance has resulted from a normative approach; reflecting a long held interest within the planning profession for best possible solutions. Emphasis on prediction of future outcomes, or indeed the replication of current or past ones, is replaced here by efforts to define, or to "design," more efficient urban futures. This viewpoint brings with it at least three advantages: (1) it can make use of generally simpler mathematical forms that are readily tied to theories of system efficiency, cost minimization, or net gain; and therefore (2) it avoids the need to account for a wide range of empirically observed idiosyncrasies, while (3) using mathematical programming frameworks to state the urban land use-transportation problem as a single, if rather complex, mathematical formulation.
From early beginnings in the use of linear programming models of residential location (see Herbert and Stevens, 1960; Harris, 1965), in which the "bid-rent function" (see Sect. 2.4.4 below) made its operational appearance, an important step forward came with the recognition that spatial interaction models could also be written as convex programming problems which could themselves be embedded within activity-allocation modeling frameworks (see Wilson et al., 1981, for an extensive technical treatment; also Erlander, 1977.)
The resulting urban "location-allocation models" usually take the form of convex mathematical programs subject to a set of linear planning constraints. For example, an interesting rearrangement of Eq. (1), using the logit/entropy maximizing form of travel cost function, gives
A theorem for embedding interaction models within mathematical programs (see Wilson et al., 1981, Sect. 7.2.3) then allows the following mathematical program to be formed, in which the maximization is now based on the selection of suitable values for both the volume of flows {Sij} and the size of activity centers {Wj}:
subject to
[which is a restatement of Eq. (2)] , and
Coelho and Wilson (1976) show how to remove the nonlinearities in the constraint set (17) to form the following mathematical program:
which can be stated more generally as
Maximize Z = Net Locational Benefits + Spatial Entropy
subject to the constraint (18) on the overall supply of floor space (in their example, shopping floorspace), and to the following origin-zone-specific activity constraints:
The entropy term (Sij ln Sij ) here reflects
recognition of the systemwide level of spatial dispersion associated with
destination choice. That is, not always the nearest (or largest) activity
center will be chosen. Again
reflects a travel distance decay effect, while
,
with values between 0.0 and 1.0, ameliorates the effects of spatial
concentration of activities on this destination choice. Model calibration
requires that we find suitable values for the parameters
and ; a
procedure for which a number of numerical analysis techniques (e.g.,
Newton-Raphson, linear interpolation) are in general use.
These and related discoveries led researchers in a number of countries to use the mathematical programming approach to pursue alternative formulations of interrelated facility location-allocation problems. This includes the prolific work in the United Kingdom by Wilson and colleagues ( MacGill and Wilson, 1979; Wilson et al. 1977, 1981; see also the review by Wilson, 1987), in Italy, by Leonardi (1979) and Bertuglia and Leonardi (1980); in Sweden (see Boyce and Lundqvist, 1987), in Australia (see Brotchie, et al., 1980; Sharpe, 1978, 1980, 1982, using the TOPAZ model), and in Canada (Los, 1979). Similar efforts are well represented in the United States. The mathematical model proposed by Boyce and Southworth (1979), for example, embeds each of Wilson's singly constrained, doubly constrained , and unconstrained spatial interaction models within a single programming framework which recognizes different population subgroups on the basis of the temporal stability in their residence and/or employment location. Boyce and Southworth's "quasi-dynamic" formulation also incorporates traffic route assignment and mode split within a single optimization framework. The incorporation of further components of the residential, employment, and travel choice decisions within a single jointly optimized modeling framework has been extensively studied in recent years by Boyce and colleagues in Illinois, working with Chicago area data (see Boyce 1988; Boyce et al., 1983, 1992, 1993). Two related mathematical programming-based models to have been applied empirically within the United States are Kim's Chicago area model (Kim, 1989), used in a research context and Prastaco's POLIS model (Prastacos, 1986a,b; Caindec and Prastacos, 1995) now used in actual planning practice.
Within the United States a combined land use-transportation model built around a single mathematical programming formulation has recently been applied within the San Francisco Bay Area. This follows a long tradition of land use-transportation modeling which began in the Bay Area in the early 1960s with a Lowry-derived approach, leading to a system of two interactively operating models known as the Base Employment Model (BEMOD) and the Projective Land Use Model (PLUM) (see Goldner, 1983, for a retrospective summary of these early efforts). During the 1980s the Association of Bay Area Governments (ABAG) again developed a modeling system for the region. This model is known as the Projective Optimization Land Use System, or POLIS. Both the mathematical and algorithmic details of POLIS, as well as a description of the model calibration efforts, are described by Prastacos (1986a,b), and more recently by Caindec and Prastacos (1995).
POLIS incorporates a number of the theoretical developments introduced throughout Sect. 2 of this review. The model can be stated as a single mathematical program which seeks to maximize jointly the locational surplus associated with multimodal travel to work, retail, and local service sector travel, and, significantly and jointly, the agglomeration benefits accruing to basic-sector employers (Prastacos, 1986a):
where
n
= the exponent of this agglomeration function (a model parameter to be
estimated), 
Ein
= the number of additional jobs in basic employment sector n (n
Kbas) to be located in zone j,w,
ks
and
spatial interaction and modal split submodel parameters to be estimatedThe term Hi
refers to the number of new households locating in zone i. Its inclusion
in Eq. (21) is made clear below.
The joint objective function given in Eq. 21 incorporates two spatial entropy terms, two travel cost terms (both for work and service-sector trips, respectively), and a term which adjusts the zonal distribution of basic employment within the region. This is maximized subject to a significant number of linear constraints. These include the usual non-negativity constraints on all flow and stock variables as well as constraints to ensure consistency between the flows (work trips, dollars of retail and service expenditures) generated by the model and the number of workers and households in each zone. They also include a set of linear planning constraints which both ensure consistency between the amount of residential and industrial land available in each zone and the additional amount of new housing and new employment assigned to those zones by the model. Finally, zonal totals for households and jobs are reconciled with county-wide sectoral as well as spatial totals in a manner that reflects the spatial agglomeration economies of basic sector activity at this more macro-spatial level. For example, the allocation of new households to zone i is subject to the following constraint:
where Hi,lb = a lower bound on Hi, the number of houses in zone i; Vi = the vacant residential land in zone i; and dih = the average density of residential development allowed in zone i. For policy analyses the value assigned to dih could be used in selected zones to reflect nonmarket (e.g., government-owned) land use or other zoning constraints.
Both residential attraction factors, Wi, and retail and service sector attraction factors, Wjk used in these entropy-maximizing spatial interaction models are themselves composite indices. Wi has the form
where qi = the ratio of median household income to median price of housing in zone i (interpreted as a housing affordability index). The Wjk have the form
where Lj = total available land in zone j, Yj = nonresidential developed land in j, Ejk = the employment total in sector k in zone j, and Ej* is the summation of employment in j over all k sectors. Finally, the gjk are accessibility indices of the now familiar form
Within POLIS this index represents the propensity of local service
sectors to locate near new population centers, using in this instance the
number of new houses built in zone i in the prior period (t 1),
Hi,t-1,
to reflect such opportunities.
The zonal agglomeration factors, fin, are of considerable interest since they extend the approach beyond the basic Lowry framework to provide a linkage between traditionally accessibility-determined nonbasic activity and traditionally exogenously determined (and incrementally projected) basic economic activity. Despite extensive early recognition of the importance of agglomeration economies in the growth of urban systems, as Berechman and Small (1988) note, little has been done to bring such effects into operational models.
Lacking any data below the county level against which to construct such functions, they are estimated by factoring the base year zonal employment totals in sector n, Ein, to be consistent with both county-wide and regional employment totals and recent rates of growth. These county and sector-specific employment levels are themselves estimated as functions of prior period employment levels in both basic and nonbasic sectors. For example, for the manufacturing sector, n = 1, this equation has the general lagged, linear form
where 
= a regression coefficients, co refers to county values and * to
regionwide values, and n = 4 refers to the nonbasic "services"
sector. That is, period t manufacturing employment within each county is a
function of prior period employment in the sector, the overall growth in
the sector regionally within the current period, and the current level of
employment in services within the county. A similar regression model was
also created to estimate the amount of "transportation, and finance,
insurance, and real estate" activity within each county in time
period t, and which in this instance also brought in the nonbasic retail
as well as services sector. There is an implicit assumption being made
here that changes in basic employment are a function of macrospatial
effects which cut across county boundaries. To render the agglomeration
potentials zone-specific POLIS defines fin as
follows:
where the changes in employment variables, (represented by
E,)
denote changes in the previous time period.
As Prastacos (1986b) points out, however, using equations such as
(29) in longer-term forecasting may produce erroneous
results, since the coefficients should not remain constant if the model is
indeed expected to capture the shifts in locational patterns. He proposes
either the use of relaxed versions of these regressions or derivation of
confidence intervals for each of the
parameters; a significant extra modeling burden. We return to this topic
of urban agglomeration tendencies in Sect.
3 of the review.
Prastacos (1986b) describes the practical implementation of this model for the Bay Area, including a discussion of data sources and the multistep procedure required for model calibration. The nine county San Francisco Bay Area, which includes some 5.2 million residents, was divided into 107 planning and traffic zones. Two basic economic sectors (manufacturing; transportation and finance, insurance and real estate) were modeled, as were a single "retail" and a single "services" sector, using selected SIC codes. Employment in the primary sectors of agriculture and mining are also allocated to zones by POLIS, using base year conditions and land availability to determine these natural-resource-constrained activities.
Two transportation modes are modeled, termed private and public.
Calibration consists of choosing values for the parameters
w,
sk,
, and
n.
This is accomplished by first calibrating the spatial interaction
submodels to obtain the work and retail travel flows, Tijm and
Sijk, by matching the entropy levels in both
model-generated work and service trip matrices to "observed"
data. In the case of the work trip model this process also requires
iteration with a logistic modal split model, so that not only is
calibrated but it is also used to weight the resulting work trip
destination model's bimodal (private and public) i-to-j cost matrix
[recall Eq. (4) above]. A single
s
is calibrated to both service and retail sectors. Once suitable mode and
spatial interaction model parameters are found, a separate calibration
stage uses these best-guess values to search for suitable
n
values which would reflect existing spatial (zonal) agglomeration of
activities in the two basic sectors. This calibration process is the
reverse of that used in most previous models, which typically have begun
with the calibration of the parameters affecting activity location
decisions, followed by calibration of the travel behavior parameters.
POLIS represents an ambitious attempt to bring a range of planning constraints as well as a concern for spatial agglomeration economies into a practical land use modeling process within the context of consumer surplus, utility, and entropy maximization theory. The approach also demonstrates the viability of using methodological advances in nonlinear programming coupled with the application of a number of useful numerical analysis routines. Caindec and Prastacos (1995) describe the most recent empirical application of the latest version of POLIS to the Bay Area, including a detailed description of a slightly modified mathematical model and the associated calibration exercise. This technical report also overviews the use of POLIS as one step in a four-tiered modeling process used by ABAG. A detailed description of this process, as applied in the Projections 92 project, is provided by Brady and McBride (1992). The process consists of using ABAG's Regional Economic-Demographic System (REDS), a dynamic input-output (I-O) model (see Sect. 2.4.3 below) which estimates regional population and employment totals in 38 different industrial sectors to feed data to the County Employment Forecasting System (CEFS) model (Caindec, 1994). CEFS in turn uses multivariate regression and historical data to estimate job growth for 32 industrial sectors within each of the nine Bay Area counties. These growth trends are then used as inputs to POLIS, which forecasts the distributions of future population, housing, and employment among 114 Bay Area analysis zones. Finally, these POLIS-generated forecasts are used within the Subarea Projections Model (SAM) ( see Yang, 1993) to allocate employment (by three "basic" and three "local serving" SIC categories), population, number of households, land use, and forecast household income and its distributions across the region's 1,209 census tracts.(5) SAM then uses a series of incremental formulas based on combinations of base year activity levels and survey-based "development potentials," the latter defined in terms of acreage, housing units, and employment opportunities.
As described by Brady and McBride (1992), this four-tier spatially hierarchical modeling process uses historical data from 1980 and 1990 to generate inputs to a series of forecasts for the years 1995, 2000, 2005, and 2010. The system has a number of uses. It helps the region's planners address issues associated with the allocation of federal and state funds to not only transportation infrastructures but also sewage treatment plants and other capital facilities. The system's projections are also used to inform mandated housing needs studies for each city and county in the region, to inform local government congestion mitigation plans, and to provide inputs to the estimation of stationary and mobile-source air pollutants. The system's documentation provides considerable technical detail and an excellent perspective on the role of integrated land use-transportation planning models within the larger urban/metropolitan planning process. It also educates the reader as to the considerable data requirements and level of effort required to generate such planning forecasts; a process developed over many years in the Bay Area.
Currently missing from the framework is any form of detailed, congestion-sensitive network routing submodel. On a more conceptual note, an unresolved debate within the literature concerns the use of optimization frameworks which seek to jointly solve for both travel activity patterns and urban activity allocations. Much of the issue revolves around whether forcing a jointly optimal solution is a valid target for simulation, given the general instability inherent in, and many additional factors conditioning, urban growth and change. A subissue is the extra computational time and more sophisticated optimization routines it may take to achieve such a jointly optimized solution. The conceptual issue is indeed a complex one and needs to be tied to the specifics of each model's underlying assumptions, computational form, and intended use. There is no doubt that the above mathematical programming developments have helped analysts to shed new light on the meaning of different model structures. They have also provided an effective mechanism for simultaneously introducing a variety of planning constraints into the problem. As to whether, or to which set of planning variables, we need to jointly optimize over may depend on the question being asked. It should certainly depend on the time frame being modeled. Complicating the issue is the tendency to associate a model's objective functions with particular, and in general partial, forms of economic as well as spatial equilibrium; opening up a whole theoretical debate involving the temporal progression in both travel and nontravel prices and their resulting influences on urban form. This issue is developed further in Sect. 2.5 below.
A third line of development draws its inspiration from the intersectoral I-O approach to economic analysis introduced by Leontief (1967). In particular, this approach provides a general framework from which to begin to integrate the manufacturing and other basic industrial activities, which are treated as exogenous inputs to the urban development process by Lowry-based models. The basis of this approach is to extend the classical I-O model to include spatial disaggregations. Notable early developments in this area include the work by Leontief and Strout (1963) and, bringing entropy and therefore logit forms of interaction model into the process, by Wilson (1970, Ch. 3).
We begin with the following definitions. Let Xm = the total output of economic sector m in zone i; Ximn = the output of m from zone i used in sector n in destination zone j; Yim = the final demand for the output of sector m in zone i; and let aimn = a set of spatially explicit technical coefficients which translate a unit of output m into a unit of input n. We then have the following identities:
which in matrix representation implies a spatially disaggregated version of the familiar I-O relation:
where X is a vector of endogenous sector outputs, Y a vector of exogenous demands, A a matrix of technical coefficients, and I an NxN unit, or identity matrix (a matrix composed of 1's in the diagonals and zeros elsewhere). Now (after Wilson et al., 1981, Ch. 10), if we let
we have a set of technical coefficients, aijmn defined as an amalgam of a set of Zjmn destination (receiving) zone specific coefficients, and an attraction-constrained spatial interaction model. This lets us restate Eq. (28) as
which is an intersectoral, destination-constrained spatial interaction model in the popular logit form. With similar forms also possible for origin (production) as well as both production and attraction-constrained coefficients, such developments extend Lowry-like intersectoral modeling, in concept at least, into more comprehensive basic and nonbasic frameworks.
Other variations on such intersectoral/interzonal modeling are discussed in MacGill and Wilson (1979) and Wilson et al. (1981), who also show how such models may be embedded within a variety of entropy-maximizing, utility-maximizing and spatial surplus-based mathematical programming formulations.
A number of operational models make use of such developments in intersectoral I-O modeling, including the MEPLAN, TRANUS, and Kim models listed in Table 2. MEPLAN appears to offer the most experience with, and elaborate extensions of, the approach to date. The following description is based on Hunt and Simmonds (1993) and Hunt (1993, 1994).
Land and transport are treated in MEPLAN as two parallel and interacting markets. Behavior in each system is modeled as a response to price or price-like signals (including travel disutility). As with other operational approaches a key relationship is the effect on locational accessibility of travel cost and time changes, which find their way back, in a temporally lagged manner, into a set of activity-location models. This once again occurs in a Lowry-like context, but within a much extended set of sectoral selection options, subject, given suitable data, to explicit market pricing variables. Within MEPLAN, the demands for transport are calculated directly from the interactions predicted by the spatial economic system defined within the land use model. The need for a trip distribution modeling step is obviated by the direct translation of what are termed trade flows, or "trades" from the land use model into suitable modal volumes. An elaborate interface between the land use and transportation models translates these trade flows (labor, materials, services) into mode specific trip matrices. Trips are assigned to modes by logit models and, subsequently, onto the highway network using a version of Dial's (1971) probabilistic, multipath assignment routine that takes into account costs and congested travel times. In terms of the simulated dynamic, land use is influenced by the pattern of use in the prior period and by previous period transport accessibilities. Transport is influenced by previous infrastructure and present activity patterns arising from land use.
The land use model here requires further elaboration. Within this model, goods, services, and labor (households) are grouped into various categories, or "factors." Some factors are consumed in the production of other factors within a modified I-O framework. Total consumption of any factor n, TCjn, in land use zone j is computed on a zone by zone basis using equations of the form:
with
where m and n again refer to different factors of production, ajmn = a "demand coefficient" equal to the volume of factor n consumed in production of factor m in zone j, DCjn and QCjn refer respectively to the endogenous and exogenous components of the total volume of factor n consumed in zone j, and Tgjm refers to the total volume of factor m produced in zone j. Such a factor may be employment within the retail sector, for example, leading to a set of "trade flows" which are subsequently also converted into vehicular trips.
Flexibility is added to this modeling system by allowing the demand coefficients, ajmn, to be treated as either fixed, factor price sensitive, or factor price and income sensitive. Price elastic consumption is modeled using the following equation:
where aj*mn = fixed consumption, Tpjn
=
the price of consuming a unit of factor n in zone j, = a price sensitivity
parameter, and b = a constant. Alternatively, a Stone-Geary consumption
function (Theil, 1980) can be invoked, which represents households as
utility maximizers in the consumption of housing space and various goods
and services (see Hunt, 1993, for mathematical details of what is an
embedded optimization problem).
The transfer of factors between land use zones is introduced by allowing demand arising in a given zone to be satisfied by production brought from other zones using the following logit model:
where Hunt (1993) defines Vin to be:
and where tijn = the volume of factor n produced
in zone i and consumed in zone j; n
= a dispersion parameter associated with the distribution of production of
factor n; and where the four terms on the right hand side of
Eq. (39) refer respectively to the cost of producing a
unit of n in i (Tbin), the disutility of travel
between zones i and j, (dijn), a size term which
accounts for the a priori likelihood that a unit of factor n is
produced in zone i (sin), and a zone-specific
disutility associated with producing factor n in zone i (Qin).
The price associated with consuming a unit of factor n, given as Tpjn in Eq. (34) above is endogenously determined within MEPLAN in one of two ways (Hunt, 1993). One way is to compute it as the weighted average of the cost of producing and shipping the factor in each zone i plus the cost of getting it to zone j, as follows:
where ijn
= the monetary cost of transporting a unit of n from i to j, and Qpjn
= an exogenous component of the price in zone j (to help calibrate the
model, or to introduce taxes into the framework). Alternatively, an
iterative process can be used to establish it as the market price which
results from equilibration between supply and demand for factor n in a
zone:
where Tpjn' = the unit consumption price for factor n in the previous model iteration, and Sjn = the total availability of factor n in zone j.
Equation (41) is typically used to represent the market process that establishes the price for floor space or land, with the demand for land being elastic with respect to price, thereby allowing total demand to respond to zonal space constraints. The resulting prices, as established by Eq. (34), then determine the costs of production within zones, i.e.,
where Tbjm = the cost of producing a unit of factor m in zone j, and Qbjm is another exogenous component of the cost of producing, in this case, a unit of factor m.
Running the MEPLAN model involves solving simultaneously for the above equations, in practice via a sequence of nested iterations. Hunt (1993) describes the above process as a series of "chains" in prices and costs that run opposite to the "chains" in demand (the I-O structure), beginning whenever a market price is determined by a constraint on supply (typically supply of space) and resulting in the prices for factors being exported. In terms of the overall simulated dynamic, land use is influenced by the pattern of such use in the prior period and by previous period transport accessibilities. Transport is influenced by previous infrastructure and present activity patterns arising from land use. Once the system of land prices and trades has settled down to provide a single point in time representation, recursion then moves the system from one equilibrated point to another--a cross-section static-recursive system supplemented by judicious use of lagged effects between some variables.
Within this general framework, a range of different travel modes, household groups, and industrial sectors have been tailored to specific studies (see Hunt and Simmonds, 1993, for examples). This can include walk and mixed modal trips; assignment of combined freight and passenger flows to networks; the modeling of work, education, shopping, and other nonwork trips, and home delivery of goods. A further MEPLAN module uses the results from these models to carry out a detailed cost-benefit analysis, including social and environmental indicators. While data requirements for a fully implemented model are potentially rather daunting, Hunt and Simmonds (1993) claim that the generality of this highly synthetic modeling framework allows it to be tailored to handle relatively modest data inputs--no more than less comprehensive systems which do not contain any land rent, production costs, or other pricing variables. This is a testimony to many years of software and model refinement. They do, however, point out the difficulties often involved in selecting the model's many parameters, typically involving extensive iterations and retrials, not always in a purely automated fashion (see Hunt, 1994, for a discussion of this process).
The concept of treating both land and transportation systems as market processes with endogenously determined costs, as exemplified by MEPLAN, grew out of the urban economics literature. Beginning with the work of Wingo (1961) and Alonso (1964), this involves the application of neoclassical economic theory to urban land use patterns, notably residential land use, which is allocated across space on the basis of a land market clearing process. Mills and Mills and Hamilton (1989) and Bertuglia et al. (1987) provide reviews. Under this general approach, individuals are assumed to maximize utility by selecting an optimum residential location, which in turn depends on a trade-off between housing price (which in the early models simply decreased with distance from the CBD) and transport costs (which increased with distance from the CBD). This trade-off is represented in the form of a "bid-rent function," which describes how much each household is willing to pay to live at each location. On the supply side, each location is simply assumed to be rented to the highest bidder. Such bid-rent functions are now incorporated in a number of operational models.
The work of Mills (1967, 1972), using linear programming formulations, further advanced the notion of a spatial market equilibration process in which stability occurs when all households of a given type (typically reflecting income group) are located so as to be equally well off. Subsequently, these same notions have been extended by Anas (1984) and Kim (1989) into more comprehensive, nonlinear, entropy/utility-maximizing and network-based programming forms. This includes empirical work to implement their ideas, both using Chicago area data. This work also has important overlaps with the combined modeling of Boyce and colleagues (see Boyce et al., 1983, 1992, 1993) discussed in Sect. 2.4.2 above, where the ideas of systemwide optimization across a number of choice dimensions (mode, location, etc.) find a basis in the search for a suitable, systemwide equilibration of various travel and land use supplies and demands. An excellent text by Oppenheim (1995) now also offers a comprehensive mathematical treatment of the connection between individual choice behavior based on an economic (utility maximizing) rationale and an urban system's behavior in searching for an equilibration between transportation supplies and travel demands.
By combining Mills's ideas of a general urban system equilibrium with Wilson's approach to probabilistic spatial interaction, Boyce et al.'s notions of combined transportation-facility location models, and Beckman et al.'s concept of equilibrated demand and supply over networks, Kim's Integrated Urban Systems Model for Chicago (1989) offers a complex if computationally tractable model with strong ties back to urban economic principles. The model offers a general equilibrium solution between the demand for and supply of transportation and activity locations in the strict economic sense. Like the MEPLAN model discussed above it also determines prices endogenously, if in a different way. It is selected for presentation here because it shows quite clearly its strong linkages to the type of inter-regional input-output modeling described above, while also being formulated (and therefore succinctly presentable) within a single mathematical programming framework. Specifically, Kim's combined model of "land use and density, shipment route and mode choice with network congestion" has the form (Kim, 1989, p. 88):
subject to:
where the following are exogenously supplied model variables:
ijprk
= the incident matrix; = 1, if route p from zone i
to j by mode k includes link a for shipping r;
= 0, otherwiseand the following variables are solved for within (endogenous to) the model:
represents the total amount of commodity r shipped to zone
i from all other origins and 
represents the total amount of commodity r shipped from i
to all other destinations.Substitution between land and other inputs is represented by the aqrs coefficients, in which s represents a production technology which equates with various intensities of land use. Within the model, goods and services can therefore be produced in tall buildings by using smaller land-output ratios and higher capital-land ratios, as typically observed in the service sector in many urban areas.
The objective function (43-44) is a joint minimization of the solution to a Wardrop equilibrium assignment of flows to network links [recall Eq.(6)-( 9) above]; the total costs of exporting commodities out of the urban system; and the total land plus rental costs summed over all zones, commodities, and production techniques used in the urban system. Equation (45) ensures that the model-assigned link traffic volumes equal the volumes assigned to all origin-to-destination specific paths using that link, and Eq. (46) constrains zonal exports of each commodity r to match given totals. Equation (47) ensures that the total amount of commodity r produced in zone i plus any brought into it from other zones is at least equal to the amount of r sent to other zones, used in other sectors, and exported from the zone. Equation (48) ensures that all commodity r production summed over all s-intensity land uses equals the total production of r and that flows of r from i to j are correctly summed over all modes and network paths used in the traffic assignment model. Equation (49) ensures that a suitable level of entropy (spatial dispersion) in destination and mode choices takes place (these can be solved as nested logits), and Eq. (50) ensures that the amount of land used to produce commodity r in zone i at various intensities of use s does not exceed the amount of land available for the purpose. Finally, Eq. (51) sets nonnegativity constraints on all flows, zonal product totals, and exports.
Solution of the program yields a combined network demand-supply balance supported by an allocation of activity levels to zones which ensures that the marginal cost of producing r at location i plus the equilibrium unit shipment cost from i to j by mode k should equal the marginal cost of producing r at location j. Also at equilibrium, commodity r in zone i will be produced at intensity level s as long as the net benefit associated with doing so is at least equal to the capital (R) plus land (L) costs of producing a unit of r in i at that intensity level.
Kim (1989) has managed to calibrate a version of this model, at a rather aggregate spatial (zonal) level, using various and extensive data sources collected for the Chicago region. To date this model does not appear to have been applied in a policy study to which its output was a required contribution. Nevertheless, the various calibration routines exist, and in this sense the model is an operational one. The approach demonstrates the possibility of bringing important aspects of urban economic theory into intersectoral, spatial-interaction-based discrete choice models in order to move towards more comprehensive urban modeling frameworks. As described, the model does not contain a procedure for translating its activity allocations into actual land use arrangements within zones. However, it does operate directly upon detailed representations of modal (highway and rail transit) transportation networks. In the above form it appears best suited to a decidedly strategic, multiyear analysis of alternative urban development options.
Microanalytic simulation, or "microsimulation" for short, refers to the method of generating random numbers from within prespecified probability distributions, which numbers are then assigned to a specific response or response value. For our purposes such a response may be associated with a particular traveler attribute or with a specific travel choice. The idea is to generate a series of traveler attributes and/or travel choices in this manner, to build up a detailed representation of specific trips or multitrip travel activity patterns. Summing over all of these individually simulated travel patterns provides aggregate values for planning studies. With the advent of low-cost, high-powered computers, this procedure has become an increasingly popular analysis tool.
In recent years, the technique has been applied within a range of multistage decision-making models. These include the use of the Recker et al. (1986) STARCHILD model to represent a complex series of individual traveler-within-household decision-making processes and of the Harvard Urban Development Simulation (HUDS) (Kain and Apgar, 1985) and California Urban Futures Model (CUFM) (Landis, 1994), both large-area housing simulation models, the latter with a potential for analyzing transportation improvements. Most recently, Barrett (1994) describes an ongoing set of developments in which Monte Carlo simulation once again plays a key role. This is the TRANSIMS modeling effort funded by the Federal Highway Administration as an experiment in simulating a complete areawide set of individual traveler-based urban activity patterns. Microsimulation is also the technique around which the MASTER land use-transportation model described below is constructed (Mackett, 1990b).
The principal utility of the microsimulation approach is that it lets us incorporate a number of dimensions of both individuals and their choice processes which would otherwise require an excessive amount of disaggregation in model-based accounts. Within the Dortmund model listed in Table 2, for example, Monte Carlo based microsimulation is used to simulate the intraregional migration of households as a search process on the regional housing market (Wegener, 1982b). Here the technique was used to overcome an otherwise impractical disaggregation of this submodel into 30 household types, 30 housing types, and 30 traffic zones, yielding 24.3 million possible kinds of moves to be analyzed.
A second appealing feature of the method is that it is relatively easy to understand and to implement. To create a piece of software to simulate a particular process using Monte Carlo simulation, all that is required is a suitable random number generating routine, a suitable probability distribution (or the raw data itself, perhaps in histogram form), a routine for allocating values between 0.0 and 1.0 to randomly selected choices on the basis of this distribution (data), and a routine for collecting the results of the sampling exercise. All are readily available today on personal computers. A more significant challenge involves the acquisition of suitable data, the determination of a suitably representative sample size for analysis purposes (for which well established methods exist in most cases), and the ability to place such sampled responses within an appropriate modeling framework. Procedures must also be developed to capture the cumulative effects of common activities such as traffic congestion and spatial agglomeration of commercial or industrial activity. This raises some interesting and challenging questions for model design, issues not yet clearly elaborated within the literature.
A third useful feature of the method is that it allows not only the explicit tracking of simulated individuals' (travelers, households, companies) status over time, but also a detailed tracking of the simulated changes in the use of individual land lots. Where suitable time series data exists, even at a quite aggregate level of resolution, this provides a useful means of checking the reasonableness of the model processes underlying the simulated outcomes. Scrutiny of such microsimulated temporal paths has also been found by the present author to provide useful insight into the implications of using alternative model forms as well as alternative parameter values to replicate a particular multistage process (Dale et al., 1993). Certainly, microsimulation offers a good deal of flexibility in experimenting with different event sequencing, which is not present in traditional land use or transportation planning models. Its application to the nature and timing of landowner and land developer decision-making processes offers an interesting possibility here.
The MASTER model (Micro-Analytical Simulation of Transport, Employment and Residence), developed in the United Kingdom by Mackett (1990a,b), is an integrated land use-transportation model based on microsimulation, using Monte Carlo methods to simulate the decision processes that a set of individuals and their households go through over time. The following description is based on Mackett (1990b), where additional details are to be found.
Households are considered one at a time, but are grouped together at certain points in the simulation to allow use of aggregate values. The first processes considered are demographic ones, including aging, giving birth, dying, divorce, and marriage. Population change is modeled explicitly within the model. Marriage and divorce lead to the creation of new households. With divorce, what were once joint possessions, including children and automobiles, are divided up. Divorcees become one class of "forced movers." Voluntary movers include newly married couples, singles leaving the parental home, and wholly-moving households influenced by changes in a family's life cycle. Both public and private housing markets are recognized, and dwelling occupancies are tracked from one period to the next. Choice of residence zone is based on a weighted function of generalized travel to work costs for the head of household. Both the supply of jobs and dwellings are exogenous, zone-specific inputs to the model. Zone size appears to be at the discretion of the modeler, recognizing of course the geographic detail contained in the available data. Choice of dwelling type is based on household size and composition. Other household members' job selections are also considered, and changes in economic status for simulated individuals may include redundancy and retirement. The availability of vacant dwellings is tracked for each residence zone in the system. Changes in economic activity are considered after a household moves residence. Young people become economically active as a function of their education level, sex, and parents' social group. They become employed, unemployed, or, eventually, retired. Retirements and job changes create job vacancies. Jobs are associated with specific salary ranges.
The transportation processes modeled are becoming an auto license holder, car ownership, car availability, and choice of mode to work: each variously functions of age, sex, household income, household composition, and mode-specific costs of travel. To change mode of travel to work, either a change in job or home location or a change in vehicle ownership or availability must occur or a significant change in travel costs must be introduced. Logit forms are used to select the mode of travel. If family members work along the same travel corridor, carpooling is also possible. Only the work trip is discussed, shopping and other trip purposes are not included in the process described. Assignment of traffic to specific routes is also not included in the model, therefore, congestion is not modeled explicitly. Mackett suggests that including such a routine would be relatively straightforward. However, it would require an expansion of the results from the 1% sample of households he suggests is sufficient to calibrate the model, up to a 100% sample for the purposes of placing the aggregate travel demands for roadspace to network capacities. It's not clear how this would be accomplished.
Mackett (1990b) compared the application of the MASTER model with the Leeds Integrated Land use Transportation (LILT) model, a more traditional, if extensively modified, Lowry-type of zonally aggregated simulation model. In his analysis, he compared the sensitivity of the two models to large increases in bus fares and automobile operating costs. He computed two sets of model-specific linear elasticities for automobile ownership; mode choice to work; and work-trip length, time, and costs changes. He also compared linear elasticities associated with employment and population redistribution over the 20-year time frame. His general finding was that the MASTER model produced sensible results, and that differences in elasticities between the two models were readily interpretable.
While such findings are reasonably encouraging, Bonsall (1982) points out that microsimulation is not panacea for data-hungry simulation models. He concludes that using the technique in conjunction with suitable travel activity scheduling models (see Sect. 3.3 below) and sample enumeration techniques offers some attractive possibilities. However, he emphasizes the need to establish carefully the accuracy of the mechanisms being simulated and, in particular, the applicability of generic procedures to different traveler groups.
Figure 6 presents a general representation of the sort of discrete multiperiod dynamic employed by currently operational systems in their attempts to simulate the evolution of the urban system. The usual means of forecasting the effects of different transportation system improvements into the future is to "fit" both the transportation and land use models to a base year, denoted as time period t, and then try to project these same relationships forward into time period t + 1. The time interval between time t and t + 1 in Fig. 6 varies by modeling system, from as little as 1 year to as many as 30. In the simplest case, a single 20-or 30-year time interval may be used to project both transportation and land use forward in time under various investment and growth scenarios (the Puget Sound Council of Government model used such an approach). A better approach is to iterate through successive shorter-term(1-, 2-, or 5-year) forecasts, using the results from the latest forecast as a baseline for each subsequent projection. Some model structures can allow both options. Anas (1994) indicates that the METROSIM model can be used either to obtain a one-shot, long run equilibrium forecast for transportation and land use in a metropolitan area, or to create a sequence of annual changes in both land use and transportation which can be run until convergence to a steady state is achieved.
Difficult to predict changes, such as changes in the location of new basic employment, are usually handled, even within the more advanced models, in an incremental fashion and often treated as exogenous inputs. Residential, service, retail, and, in some cases, selected manufacturing employment activities are then advanced and redistributed on the basis of travel cost-adjusted locational accessibilities. How this occurs in practice varies by modeling system. Both residential and employment activity Multi-Period, Recursive Simulation of Urban System Dynamics locations may be stabilized within a single time period, or one may be related to another in a subsequent time period using lagged equations (recall the ITLUP model description above). The accessibility-based travel patterns which result from such redistributions are often simulated to reach a stable demand-supply equilibrium during the current time period. Alternatively, the process may become a more open-ended one, in which constant readjustments in both land/floorspace allocations and transportation infrastructure and services are taking place within lagged equation forms (see Wegener, 1994, for a discussion). For example, Hunt and Simmonds (1993) conceptualize the urban dynamic simulated in MEPLAN as follows (pp. 223-224): "In each market there is at any time an adjustment towards equilibrium. However, this adjustment is limited. It is limited by the impossibility of instantaneous changes in either building stock or transportation infrastructure and by the imperfection of the information exchanges in the system. This leads to delays and lags in the adjustment of the system to its own price and congestion signals. The result is that the urban structure continually moves toward but probably never reaches an equilibrium."
The implication is that transportation system changes, notably major infrastructure investments in new highways or rail transit lines, will need time to affect urban land use patterns. Once introduced, such land use patterns may then also, but within shorter time frames, induce further changes in urban travel demand. Just how this is accomplished in terms of intraperiod versus interperiod increments often depends upon the time interval chosen between model iterations, which in turn usually depends upon the original purpose behind a model's development.
Greater subtlety as well as realism is introduced into the more elaborate modeling approaches by allowing different rates of change in housing and transportation stock adjustments versus residential and employment activity reallocations, or versus short range travel (mobility) adjustments. Wegener's (1986) model for Dortmund provides one of the most conceptually satisfying implementation of such ideas in practice. His approach is presented briefly below.
As we learn, and perhaps in order to learn, more about the true nature of urban system dynamics, it appears that increasingly comprehensive urban simulation models are required. The Dortmund modeling system, along with MEPLAN, METROSIM, and the 'Bay Area system of models containing POLIS, all strongly reflect this trend. Wegener's Dortmund model is selected for review below. It not only offers one of the most advanced implementations of a multistaged urban land use-transportation systems dynamic to date, but also makes innovative use of spatial interaction models as well as microsimulation methods within its framework.
The Dortmund modeling system was developed for the city of that name in Germany by Wegener and colleagues (Wegener, 1982a,b; Wegener, 1986; Wegener et al., 1991). Dortmund, as discussed below, refers to the intermediate level model in a three model hierarchy. Within this hierarchy, a macroanalytic model of economic and demographic change simulates employment by industrial sector and population by age, sex, and nationality within each of 34 labor market regions, as well as interregional migration rates within the State of Nordrhein-Westphalen. Dortmund is a mesoscopic spatial model which uses this regional context to simulate the intraregional location decisions of industry, residential developers and households, and associated public policy impacts in the fields of housing and infrastructure. The model was developed primarily to study the impacts of long-range economic and technological change. The model was also used recently by Wegener (1995a) to examine the effects of urban activity reorganization on the reduction of carbon dioxide emissions.
The Dortmund model is applied to a 30-zone region centered on the city of Dortmund, a region with a population of some 2.4 million residents. At the third level in the complete model hierarchy is a microanalytic model of land use development within any subset of 171 statistical tracts in the Dortmund urban region. Tracts vary greatly in size, but the majority contain between 2000 and 5000 residents (Wegener, 1982a). The purpose of this more spatially detailed model is to allocate construction generated by the mesoscopic or zonal Dortmund model to tracts within a zone.
The following description is focused on the mesoscopic model only and is based largely on the version described in Wegener (1986). A simulation run involves seven interlinked submodels dealing respectively with (1) car ownership and transport; (2) aging of people, households, dwellings, and workplaces; (3) relocation of firms, redundancies, and new jobs; (4) nonresidential construction and demolition; (5) residential construction, rehabilitation, and demolition; (6) labor mobility (change of job); and (7) household mobility (change of residence).
A good deal of thought has been put into the issue of simulating urban dynamics. Wegener (1986; see also Wegener, Gnad, and Vannhahme, 1986) classifies urban and regional changes as falling within either fast-, medium-or slow-response processes. While relatively rapid changes in mobility can be brought about by trip mode or route choice and, possibly a little more slowly, by home, job, or firm relocations, much slower processes are involved in changing the more expensive physical structures of the city (its housing, factories, office and shopping centers, and transportation routes). Also at work are medium-speed changes, involving either socioeconomic or technological developments forced on the area by broader regional or national influences: such as economic cycles, biological changes such as population aging, or the advent of new technologies which are again not area controlled but over time are area affecting.
This conceptual framework is translated into practice in a number of ways. Rather than simultaneously determining locations as trip ends in a unified transport-and-location equilibrium, an explicit separation of the transportation and land use subsystems is maintained. The transportation model iteratively solves for a user-optimal set of flows where car-ownership rates, trip rates, trip destinations, and mode and route choices are in capacity (congestion) constrained equilibrium; accomplished by using an extended version of Evans' (1976) algorithm. At the trip distribution stage this involves calculating sixteen interrelated spatial interaction models for work, shopping, services or social, and education trips for four socioeconomic groups and three travel modes: car, public transport, and walking. First, however, household car ownership and trip generation rates are computed within an iterative process which makes such choices nominally subject to a household budget constraint on travel and car ownership costs. Within this framework, mode choice is nested within destination choice and recognizes car availability as well as generalized travel costs (recall the discussion in Sect. 2.3 above).
The framework distinguishes in a reasonably traditional way between nondiscretionary forms of travel (work and school trips) and discretionary travel, such as shopping and social trips. It does this by using doubly-constrained spatial interaction models for the former and production-constrained forms (logits) for the latter. However, the work trip model is solved only once, for the base year. Subsequent and matrix element specific adjustments to this home-work trip matrix then rely on direct inputs from the submodels dealing with change in residence and change in job respectively. This is done to get around the problem (also noted by Mackett, and by Wilson) of inappropriately using doubly constrained spatial interaction models in a dynamic context. That is, such a model may require that workers who have changed neither home nor workplace over the current time period be assigned to another cell in the work trip matrix in order to satisfy a revised set of zonally aggregated trip generations (workers) and attractions (jobs). This leads to an overestimation of the effects of changes in transport costs on the resulting pattern of urban commuting. By limiting the ability of such interaction models to reallocate work trips, the impacts of transportation costs on the subsequent location of these home and workplace activities becomes less direct, more lagged and more aggregate in its effects than would be the case if spatial interaction models were used less discriminately. The reader is referred to Wegener (1986) for an elaboration of this matrix-adjustment process.
Within Dortmund transportation cost and related accessibility changes are anyway not the only determinants of locational change. They are traded off against other non-transportation variables which appear to be at least as important in the evolution of urban form, a point made frequently in the recent empirical literature (Giuliano, 1989). The simulation takes place in 2-year cycles (up to a 30-year planning horizon), allowing a "perception delay" of 1 year, on average, to take effect. The transport model is processed at both the beginning and end of each 2-year simulation period. Through the implicit lag structure of this recursive system, changes in land use variables only become visible to the transportation model at the beginning of the next (2-year) time period. Longer delays are accounted for in some submodels. New housing only finds its way onto the market three or more simulation periods (6 years) after a simulated change in the transportation system has occurred. As a practical matter, the spatial distribution of urban activities is allowed to change within the modeling process in two ways. One way is through "aging," which in the model depends only on time and not endogenously modeled choices. The mechanics of this aging process involve the use of a probabilistic Markov process, which is applied once each model iteration within an aging submodel. An additional practical facet of the approach is the recognition that the opening or closing of large industrial plants may not be predictable by any modeling system, hence their treatment as exogenously entered "historical events." All other changes depend on accessibility based spatial choices generated explicitly within the model. For this purpose the model uses nested logits and a variant on the inclusive value method described by Fisk and Boyce (1984) as its basic building blocks.
2. Coordinated through the British Transport and Road Research Laboratory, the ISGLUTI effort carried out comparisons of nine different land use-transportation models using data from cities in seven different developed countries (Annerstookt in the Netherlands; Tokyo and Osaka in Japan; Dortmund in Germany; Leeds in the England; Bilbao in Spain; Uppsala in Sweden; and Melbourne in Australia). Subsequent work has extended these model comparisons to (a) the application of more than one model to the same city (see Wegener, Mackett and Simmonds, 1991) and (b) the application of the same model to more than one city (Mackett, 1991b). This sort of coordination is now being continued through the SIG1 working group within the World Conference on Transportation Research.
3. A summary of the transportation programs and provisions of the CAAA has been written by the Federal Highway Administration (FHWA, 1992a). Summaries both of the complete ISTEA, and of its air quality programs and provisions are also provided by the Federal Highway Administration (FHWA, 1992b,c).
4. Doubly constrained spatial interaction models have been popular as journey-to-work models where a planning agency has census data or other means of producing what it considers reasonably accurate estimates of zonally based trip productions and attractions.
5. A probit model was calibrated against 1990 Census data to project household income distributions within each census tract.
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