Transportation Systems Planning Methods and Applications 05

Transportation Systems Planning Methods and Applications 05 Transportation engineering and transportation planning are two sides of the same coin aiming at the design of an efficient infrastructure and service to meet the growing needs for accessibility and mobility. Many well-designed transport systems that meet these needs are based on a solid understanding of human behavior. Since transportation systems are the backbone connecting the vital parts of a city, in-depth understanding of human nature is essential to the planning, design, and operational analysis of transportation systems. With contributions by transportation experts from around the world, Transportation Systems Planning: Methods and Applications compiles engineering data and methods for solving problems in the planning, design, construction, and operation of various transportation modes into one source. It is the first methodological transportation planning reference that illustrates analytical simulation methods that depict human behavior in a realistic way, and many of its chapters emphasize newly developed and previously unpublished simulation methods. The handbook demonstrates how urban and regional planning, geography, demography, economics, sociology, ecology, psychology, business, operations management, and engineering come together to help us plan for better futures that are human-centered.

5 Land Use: Transportation

Modeling

CONTENTS

5.1 Introduction5.2 Definitions and Key Concepts5.3 Modeling Spatial Processes5.4 Spatial Interaction ModelingEntropy Maximization • Random Utility Models • Accessibility

• Lowry Models5.5 Modeling Land and Real Estate MarketsBuilding Supply and Land Development • Price Determination5.6 Modeling Urban Economies

5.7 Design and Implementation ConcernsPhysical System Representation • Representation of Active Agents • Representation of Decision Processes • Generic Design Issues • Implementation Issues

5.8 Concluding RemarksReferences

Further Reading

5.1 Introduction

Regional travel demand models typically take as their starting point exogenously determined spatial distributions of population and employment (and any required attributes of these people and jobs) as fixed inputs into the demand modeling system In so doing, they ignore the fact that these population and employment distributions are the outcome of a dynamic process of urban evolution that is partially determined by the nature and performance of the transportation system That is, as illustrated in Figure 5.1, a two-way transportation–land use interaction exists, in which transportation is a derived demand from the urban activity system, but also in which the transportation system influences land development and location choice through the provision of accessibility to land and activities From a policy analysis perspective, the need for a consistent, comprehensive analysis of urban systems is generally well understood, if not always put into practice In particular, note that many transportation problems such as congestion, air pollution, etc., may have their root causes as much in urban form considerations (e.g., excessive urban sprawl) as in transportation system design per se

Integrated land use–transportation models are designed to capture most, if not all, of the processes and interactions shown in Figure 5.1 That is, they attempt to model both urban system evolution and the associated evolution of urban travel demand in a comprehensive and integrated fashion At a Eric J Miller

University of Toronto

minimum, such models are intended to provide the population and employment forecasts required

by traditional travel demand models in a more consistent, systematic, and credible fashion than might

be possible by other methods Specifically, they generate these distributions in a way that is consistent with transportation network configurations, congestion levels, etc Integrated models, however, have the potential to do much more relative to conventional methods, including:

• Providing much more detailed simulation of person and household demographic and nomic attributes, which can be powerful explanatory variables of travel demand

socioeco-• Providing policy analysis capability for a much wider range of land use, transportation, and other policy measures that might influence travel behavior, either directly or indirectly

Despite the potentially important role that integrated land use–transportation models might play in policy analysis, these models are not currently used in a majority of cities A number of technical, historical, and resource-related reasons for this state of affairs exist Integrated models were first built in the early 1960s These early models represented quite exceptional pioneering efforts, but, on the whole, failed to prove overly useful as policy analysis tools, largely because the computational capabilities, modeling methods, and available data of the day simply were inadequate to support the ambitious requirements and expectations of these models The weaknesses of these first-generation models were dramatically documented in Lee’s seminal paper “Requiem for Large-Scale Models” (Lee, 1973), which had a profound influence on planners’ attitudes toward models in general and integrated models in particular for at least the next decade, especially in the United States

Development work on second- and third-generation integrated models, however, continued around the world, slowly gathering momentum as the computer revolution began to provide modelers with computing capabilities adequate to the task of simulating entire cities, as Geographic Information Systems (GIS) provided computerized databases of sufficient breadth and depth to support such ambitious modeling activities, as our theoretical understanding of urban spatial processes increased, and as our modeling methods for capturing these processes in computerized equations and algorithms improved The net result

of these cumulative advances over the nearly three decades since Lee’s requiem is that a considerable variety

of integrated models are in operational use around the world, with this number growing steadily

FIGURE 5.1 The urban transportation–land use interaction (Adapted from Meyer, M.D and Miller, E.J.,þUrban

Transportation Planning: A Decision-Oriented Approach, 2nd ed., McGraw-Hill, New York, 2001.)

Housing Commercial

Floorspace Land Development

Residential Location Firm Location

Location Processes

Labor Market

Exchange of Goods & Services

Activity Interactions

Personal Activity

Patterns

Road Transportation Services

Transit Motorized

Non-Goods &

Services

Travel Demand

Personal Travel Auto Ownership

Road

Transport Network Flows

Transit Motorized

Non-The purpose of this chapter is to provide an introductory overview of integrated land tation modeling A single, relatively short chapter such as this one cannot possibly cover the entire contents of such a complex subject Rather, it has the more modest objectives of sketching the general structure of such models, presenting some of the key modeling principles and methods typically used in current models, and discussing some of the critical design and implementation issues that a planning agency should consider in the development and use of such a model.

use–transpor-5.2 Definitions and Key Concepts

In speaking of land use, travel demand modelers often are simply using this term as a shorthand expression for the zonal population and employment distributions that they require as inputs to their models More formally, land use refers to the way in which land is used, in terms of the buildings built upon the land (houses, stores, schools, factories, etc.) and the activities housed within these buildings (in-home activ-ities, shopping, education, work, production of goods and services, etc.) As such, land use is essentially synonymous with urban form, which is a term often used by geographers and regional scientists Given that it is the participation in out-of-home activities that gives rise to the need for travel, transportation system analysts often speak of the urban activity system, which consists of both the physical built form and the spatial–temporal distribution of activities that occur within this built form In this chapter, as a

matter of convenience, we will use the terms land use, urban form, and urban activity system more or less

interchangeably, while recognizing the nuances that actually exist among these terms

From a modeling point of view, the key point to recognize is that, as shown in Figure 5.1, four interrelated but distinct processes define the evolution of the urban activity system over time:

1 Land development, in which the built form changes over time as land is developed and as existing buildings are modified or redeveloped over time This is the process by which land use, per se, evolves

2 Location choice, in which households and firms decide where to locate, given the location natives (vacant dwelling units or commercial floor space) available at the time the location choice

alter-is being made

3 Activity scheduling and participation, in which households plan their daily lives and then execute these plans in terms of actual participation in activities and the travel associated with this activity engagement

4 Commercial exchange of goods and services, which includes the full gamut of physical interchanges

of persons, goods, and services generated by the urban region’s economy, including firm–firm interactions (goods and services exchanges of inputs and outputs), firm–worker labor exchanges (work trips), and firm–household interchanges (shopping, personal business, etc.)

Note that both of the latter two processes occur within a short-run decision-making time frame within which the distribution of residential locations, firm locations, etc., is (temporarily) fixed Thus, implicit

in Figure 5.1 is a temporal dimension in which all four processes are constantly “running,” but in which each process tends to operate within a different decision-making time frame and within a different set

of constraints Land development decisions are generally very long run in nature, which for large projects can often play out over literally decades from project conception to final construction Location choices are also long run in nature, but generally display greater fluidity than land development processes, and certainly are constrained at any given point in time by the supply of available options, as determined by the higher-level land development process Household activity and travel and commercial economic exchanges are obviously much shorter run in nature, playing out on a daily basis.1

1 This is not to say that some of these processes cannot exhibit considerable stability over time For example, it is not likely that most workers actively re-evaluate their choice of mode to work each and every workday But they do execute

a daily activity schedule that includes the journey to work, and this activity schedule certainly can and does change within shorter time frames than longer-term choices such as residential location

In parallel to the urban activity system is the transportation system, which similarly evolves over time through a combination of longer-run supply decisions concerning the provision of physical infrastructure and the services operated within this infrastructure, through to the short-run, day-to-day personal travel and goods movements that occur within the system and determine its operating performance levels.Household auto ownership decision making (e.g., how many vehicles of what types to own or lease) has been included as an explicit box within the transportation system to highlight the important role that it plays in the overall transportation–land use interaction Auto ownership obviously has a profound influence on travel behavior in terms of mode choice, destination choice, and even trip generation rates

It also, however, affects residential and employment location choices, and in turn is influenced by these location choices (if I don’t own a car, my choice of work locations may be limited; households living in suburban locations, on average, own more cars than ones living in central cities; etc.) Although not usually discussed in these terms, household auto ownership is a supply process in which households are able to supply themselves with transportation services that occasionally complement (e.g., commuter rail park and ride) but more usually compete with publicly supplied transit services

The transportation and urban activity systems interact in three primary ways First, the activity system drives the transportation system on a daily basis in terms of determining the need for travel Second, transportation system performance influences this daily activity scheduling process in terms of defining the times, costs, reliability, etc., involved in traveling from one point to another by different modes of travel, thereby influencing the choice of activity location (e.g., shopping at a mall with convenient, free parking

vs downtown, where parking may be expensive and in short supply), activity timing (e.g., shop during peak hours to avoid traffic congestion), etc And third, in the longer run, the accessibility that the trans-portation system provides to land and activities influences over time both land development and location choice processes This accessibility is supplied both publicly, through the provision of physical infrastructure and public transit services, and privately, through ownership of personal-use automobiles

off-Most of this handbook is devoted to modeling travel demand and to understanding the activity–travel interaction Therefore, this chapter takes this understanding and associated modeling methods as given and focuses on the longer-run processes of land development and location choice processes, as well as the role that transportation plays in these processes through the provision of accessibility

Land development, residential and commercial real estate activity, and economic interchanges ously all occur within the framework of markets, in which demand (consumption) and supply (produc-tion) processes interact and determine the exchange of land, floor space, goods and services, etc., as well

obvi-as the prices at which these commodities are exchanged Thus, any model of the spatial evolution of the urban activity system should account for both demand- and supply-side processes and should generate the prices (which are both outcomes of and primary inputs into these processes) as endogenous com-ponents of the model

A primary output from an integrated model should be the environmental impacts of the urban activity and transportation systems, including greenhouse gas emissions, mandated air quality emissions, agri-cultural land consumption, and other environmental indicators of policy importance Indeed, one of the primary motivations for developing an integrated modeling framework is to better address the short- and long-run environmental implications of transportation and land use policies Many modelers speak

of integrated land use–transportation–environment models (Wegener, 1995) to emphasize this point The environmental component of such models, however, is in itself a complex modeling problem; this will not be discussed in detail in this chapter

At least three classes of models exist that deal in a systematic, computerized way with the estimation

of future land use distributions Land accounting and allocation models typically are GIS-based, based systems for estimating future land development on a zone-by-zone basis based on empirically observed past development patterns Examples of this approach can be found in Landis (1994) and Yen and Fricker (1997) While relatively simply to apply, these models are not discussed further in this chapter since they generally are not sensitive to either the transportation system (and so are not useful in the analysis of transportation policies) or the intraregional economic and market processes that are presum-ably major determinants of both the location and timing of land development

rule-Optimization and normative models attempt to generate optimal urban forms, given an assumed objective function that is optimized, subject to a set of system constraints Examples of optimization-based models can be found in Brotchie et al (1980), Caindec and Prastacos (1995), and Kim (1989) While useful for exploring what optimal urban forms might look like, as well as how different policies might alter this optimal outcome, such models generally provide little insight into the likelihood that such outcomes will actually occur, or of how the urban area might actually evolve from its current nonoptimal state to the desired optimal future state (given that the actual behavioral processes driving urban evolution are rarely, if ever, inherently system optimizing in nature).

The focus of this chapter is on descriptive and behavioral models that attempt to simulate the evolution

of the urban activity system explicitly over time from a known base state to a (most likely or expected) future state Such models typically move forward in fixed time steps ranging from 1 to 10 years in length,

in which the system state at the end of each time step is predicted as a function of the system state at the beginning of the time step, exogenous inputs that are expected to occur during the time step, and the endogenous processes being explicitly simulated within the model A wide variety of models have been developed to operationalize Figure 5.1; they vary in terms of the comprehensiveness of processes included in the model, treatment of time and space, choice of modeling methods, etc

For example, Figure 5.2 presents the flowchart for UrbanSim, which is very representative of current practice in operational integrated models As shown in the flowchart, population and employment distributions in a future year are the outcome of a land development process and move or location choice decisions of households and businesses in the real estate market These land use distributions drive a conventional travel demand model, which in turn feeds back measures of accessibility to the land use model Other important components of the modeling system are models that predict how the households and businesses evolve over time, which in turn depend on exogenously forecasted regional control totals (total population growth, total employment growth by sector, etc.)

Miller etþal (1998), Southworth (1995), and Wegner (1994, 1995) all provide detailed reviews of UrbanSim and other operational integrated models In this chapter, rather than describing in detail these models (all of which differ in many detailed ways from one another), we focus first on discussing some

of the key modeling methods that are generally employed in these models, and then on important design and implementation issues involved in the development and application of an integrated land use–trans-portation modeling system in an operational setting

5.3 Modeling Spatial Processes

As has been discussed above, the fundamental rationale of integrated land use–transportation models is

to model the spatial decision processes that shape the physical form of an urban area over time and determine the physical flows of people, goods, and services within this area These spatial decision processes include:

• Decisions to develop or redevelop land for various purposes

• Location and relocation decisions of firms

• Residential location and relocation decisions of households

• Labor market decisions of workers (what job to take, where) and employers (what worker to hire)

• Activity–travel decisions of persons and households

• Economic interactions among firms that result in the flow of goods and services among them

In order to deal with this diverse and complex set of processes, a variety of modeling methods and theoretical constructs are required These include:

• Models of spatial interaction and accessibility

• Models of land and real estate markets

• Models of intraregional economic interaction

Each of these is discussed in some detail in the following sections.

5.4 Spatial Interaction Modeling

The decision of what store to travel to from home to purchase a certain good, the decision of what neighborhood to live in given where one works (or where to work given where one lives), or similar decisions involve the flow or interaction between two points in space (home and store, workplace and residence, etc.), as the outcome of the selection of the destination of the spatial interaction (the store, the residence, etc.), generally given the known location of the interaction origin (the home, the workplace, etc.) Such spatial interactions literally define the transportation–land use interaction, and so it is not surprising that models of spatial interaction play a central role in virtually all integrated models.Two theoretical approaches dominate the modeling of spatial interactions: entropy maximization (also known as information minimization) and random utility theory A unique feature of these two approaches

is that in the most commonly applied case they result in exactly the same mathematical model Despite this convergence of the two approaches, it is useful to consider both briefly, since each approach provides its own insights into the fundamental assumptions underlying the operational model In order to make comparisons between the two approaches more concrete, let us consider as an example the choice of a residential location zone for a one-worker household, given that the place of employment for the worker is known

FIGURE 5.2 Urbanism flowchart (Adapted from Waddell, P., An Urban Simulation Model for Integrated Policy

Analysis and Planning: Residential Location and Housing Market Components of UrbanSim, paper presented at the 8th World Conference on Transport Research, Antwerp, Belgium, July 1998.)

Forecast

Base Year Land Use

Demographic Transitions

Household Move/Locate

Economic Transitions

Business Move/Locate Real Estate

Market Clearing

Population &

Employment

Travel Demand Model

Public Policy/

User Interface

URBANSIM

EXOGENOUS INPUTS

5.4.1 Entropy Maximization

The concept of entropy maximization for modeling spatial processes was first developed by Alan Wilson

in a seminal paper in the 1960s (Wilson, 1967) as a means of providing a theoretical foundation for gravity-type models of trip distribution It was later shown that Wilson’s model could also be derived from fundamental concepts of information theory (Webber, 1977), which was first developed for appli-cations in communications The basic notion of entropy maximization is to develop a model that generates the most likely estimates of the spatial interactions of a set of actors (in this case, households looking for a place of residence), given limited information about the actors and the outcomes of their decisions In particular, it is assumed that this information can be expressed in terms of constraints on feasible outcomes of the actors’ decisions For example, define the following terms:

Hi|j= the number of households whose worker is employed in zone j and lives in zone i

Hj = the number of households whose worker is employed in zone j

tij = the travel time by auto from zone i to zone j during the morning peak period

Ni = the number of housing units in zone i

H = total number of households

The task for the spatial interaction model is to predict Hi|j, given known values of Hj, tij, and Ni Many possible estimates of Hi|j might be generated through a variety of models To be internally consistent, however, all such estimates should satisfy logical constraints defined by the known information Even in this simple example, many possible constraints might be imposed In this particular application, the most common set of constraints used are

(5.2)

(5.3)

Equation (5.1) simply imposes the logical constraint that the total number of households assigned to all possible residential locations for a given employment zone must equal the number of households associated with this employment zone In Equation (5.2), tavg is the observed average travel time from home to work (assuming that all work trips occur during the morning peak period by the auto mode), and this constraint imposes the condition that the predicted distribution of worker residential locations should be such that the predicted average travel time to work (i.e., the left-hand side of Equation (5.2)) reproduces the observed average travel time for the system being modeled

Equation (5.3) imposes a similar sort of constraint, where the left-hand side of the equation is the predicted average value of ln(Ni), weighted by the number of households choosing zone i for their place

of residence, while the right-hand side (Navg) is the observed average value of this term The rationale for the specification of Equation (5.3) in this particular form is not particularly intuitively obvious It is chosen primarily because it generates an attractive final model functional form for Hi|j, as is seen below.Wilson and others have shown that the most likely equilibrium estimates of Hi|j are obtained by maximizing the so-called entropy function:

is desired, then a different form of the constraint could be written, chosen so that when the new version of Equation (5.5) implied by the new constraint is maximized, the desired term emerges in Equation (5.6) A similar comment holds for the travel impedance term, exp(βtij), or any other term that is included in the model.Given that entropy maximization seems to merely regenerate a standard gravity model, it is important

to note this method makes at least two major contributions to spatial interaction modeling The first is that entropy maximization provides a formal mathematical and theoretical foundation for gravity models that, prior to Wilson’s seminal work, were often criticized for being without any sound theoretical basis Indeed, information theory shows that, given the problem definition (i.e., the need to predict system behavior given limited information about feasible combinations of that behavior), gravity–entropy mod-els generate the most likely (also sometimes referred to as the least biased) estimates of system behavior achievable given the available information

Second, entropy maximization provides a formal method for generating model functional forms and estimating model parameters The functional form of Equation (5.6) can not be arbitrarily chosen; it must be mathematically derivable from a set of logical constraints Admittedly, freedom exists in the choice of con-straints, as illustrated in the example above, but this is no different than the freedom available to modelers in the selection of variables (and their functional form) to include in the systematic utility function of a random utility maximization model The method to be used in model parameter estimation is also not arbitrary αand β in Equation (5.6) must be chosen so that the constraints in Equations (5.2) and (5.3) hold for the base calibration data set These equations can be efficiently solved using the Newton–Raphson root-finding method

5.4.2 Random Utility Models

If we define Pi|j as the probability that a household whose worker is employed in zone j resides in zone i,

(5.7)and if we note that xa = ealn(x), then Equation (5.6) can be rewritten as

ββ

in functional form and estimated parameter values This is a powerful and perhaps surprising result (given the seemingly quite different theoretical starting points of the two approaches), which seems to

be often overlooked by modelers within both the entropy and random utility modeling camps In particular, the convergence of the two approaches allows modelers to better understand the strengths and weaknesses of spatial interaction models in general

Starting with Lerman’s (1976) seminal application of multinomial logit modeling to the residential location choice problem, random utility models of both the multinomial and nested logit form have been applied to

a wide variety of spatial choice processes and, indeed, are the standard tool for modeling these processes in virtually all currently operational integrated models In general, random utility models have been found to

be very flexible and powerful tools for modeling spatial processes for a variety of reasons, including:

1 The explicit tie to microeconomic theory is a powerful one that aids considerably in model specification, validation, and interpretation

2 Random utility theory is very general and permits a variety of specific models to be developed and applied (multinomial logit, nested logit, probit, generalized extreme value models of various types, etc.) In particular, to the extent that we know (or at least have strong enough insight to hypothesize) that correlations among outcomes exist that cannot be handled within the entropy–multinomial logit framework, we can extend our random utility framework in appropri-ate ways to accommodate these correlations.3

3 The nested logit model structure, in particular, is an extremely attractive and practical method for developing a complex modeling system such as an integrated model, in which many submodels (residential location choice, auto ownership choice, activity–travel decisions, etc.) must coexist and interact in a logical, consistent fashion The ability to feed back inclusive value terms describing the expected utilities derived from lower-level choices (e.g., travel) into more upper-level decisions (e.g., residential location choice) is an exceptionally efficient and theoretically well-defined method for submodel interfacing This point is discussed in further detail below in the special and impor-tant case of the use of accessibility terms in spatial choice models

4 The availability of standardized parameter estimation software greatly facilitates the development

of operational models

5.4.3 Accessibility

Closely tied to spatial interaction is the concept of accessibility Put very simply, accessibility is the raison d’etre of the transportation system: to provide the ability for people and goods to be able to move efficiently and effectively from point to point in space in as unconstrained a fashion as possible Given this, accessibility obviously must play a central role in the transportation–land use interaction, and measures of accessibility surely must be important explanatory variables in models of spatial decision processes That is, all else being equal, households presumably will prefer to choose residential locations that provide high access to jobs, stores, good schools for their children, recreational facilities, etc., while businesses will similarly desire locations that provide good access to both their customers and their suppliers

Before constructing operational measures of accessibility, it is useful to identify the attributes of such

a measure implicit in the loose description of the term provided above These include the following:

1 Accessibility is a point measure, in that each point in space has its own level of accessibility For example, a point in the downtown of a city will likely have a different level of accessibility to theatres and other cultural facilities than a point on the suburban fringe

2 Equations (5.2) and (5.3), which must be solved within the entropy formalism to determine the estimates of α and β for a given base set of data, are also the maximum likelihood parameter estimation equations that must be solved within the random utility formalism.

3 Note that entropy-based models assume that all outcomes are equally likely, except as constrained by the imposed constraints As a result, the entropy formalism does not readily generalize to allow for the sort of correlations among outcomes accomodated by generalized extreme value, probit, and other random utility models.

2 Accessibility is activity specific The same point in the downtown will have different accessibility levels

to cultural facilities, schools, and big-box building supply centers, to name just a few activity–land use types of possible interest to households considering the downtown as a possible place of residence

3 Accessibility depends on the ease of travel to potential activity sites The more activity sites within

a convenient travel distance and time, presumably the higher the level of accessibility Given this, accessibility varies by mode (e.g., the points accessible within a given travel time will be different

by car, transit, walk, etc.) and time of day (e.g., peak vs off-peak)

4 Accessibility depends on the attractiveness of the activity sites available If there are many rants within walking distance of my workplace, but if they are all expensive, serve poor quality food, and provide substandard service, then my accessibility to lunchtime eating establishments

restau-is low regardless of the number of sites nominally available

5 Accessibility is an integrative measure of the potential for spatial interaction If there are a large number of inexpensive, cheerful, high-quality restaurants close to my workplace, my accessibility

to lunchtime eating establishments is high, regardless of whether I actually make a trip to one of those places on a given day or not

Given these attributes, many measures of accessibility have been developed for a variety of applications, including their use as explanatory variables in integrated models Probably the simplest such measure involves defining a maximum travel time threshold (e.g., 15 or 30 min) and then adding up all the opportunities for a given type of activity (employment, shopping, etc.) that lie within this travel time threshold for an assumed mode of travel for a given point For example, in the residential location choice problem discussed above, the accessibility of a given employment zone j to residential housing oppor-tunities within a 30-min drive of zone j during the morning peak period would be

(5.9)where δ(tij) equals 1 if tij = 30 min and 0 otherwise

Equation (5.9) meets all of the criteria developed above for an accessibility measure It is defined for a point in space (zone j); it is specified for a particular activity (residential location); it depends on the attractiveness of the activity sites available (in this case, simply measured by the size of the activity site —

a very common approach in operational models); it depends on the travel mode (auto) and time of day (morning peak period); and it integrates over the region around the reference point to yield an overall measure of residential location potential for this point It is also an attractive measure in that it is very easy

to compute, especially given modern Geographic Information Systems that readily compute such measures.The major limitation of Equation (5.9) is that it does not capture the interaction between site attractiveness and location For example, consider two zones that both have 1000 housing units within a 30-min drive In the case of zone 1, all 1000 units are actually a 10-min drive away, while for zone 2, the 1000 units are all located 25 min away Equation (5.9) will return exactly the same level of accessibility for the two zones (i.e., 1000), whereas it is more likely that we would consider zone 1 to have the higher accessibility in this case

To overcome this difficulty, a common second measure of accessibility that has been used is the denominator of a spatial interaction entropy–gravity model In the example being considered here, this means using the denominator of either Equation (5.8) or (5.9), that is:

(5.10)Equation (5.10) obviously also meets all the criteria listed above, with the added advantage that it weights the contribution of the site attractiveness to the overall level of accessibility by the level of difficulty involved in getting there In the simple numerical example introduced above, if α = 1 and β = –2, then the accessibility of zone 1 would be 10, while zone 2’s accessibility would only be 1.6 — reflecting the fact that zone 2 is located more remotely from the housing units than zone 1 Equation (5.10) has another advantage: it directly relates the concept of accessibility (which, recall, describes the potential to interact

over space) to actual spatial behavior, through the use of a term taken from a model of spatial choice Given these advantages, terms such as those in Equation (5.10) have been used as explanatory variables

in many land use–transportation models over the years

Despite the plausible nature of Equation (5.10) as a definition of accessibility, its selection is ad hoc

in that it was simply pulled out the air as a reasonable measure As noted above, Equation (5.9) is a standard logit model, derivable from random utility theory Given this, the expected maximum utility

to be derived by a worker employed in zone j from the choice of a residential location is a known value

It is the so-called inclusive value or log-sum term:

(5.11)

Ben-Akiva and Lerman (1985) convincingly argue that Equation (5.11) is the appropriate definition

of accessibility within a random utility framework, since it defines the potential benefit (i.e., expected utility) to be derived at point j from participating in the given spatial process Equation (5.11) is merely the logarithmic transformation of Equation (5.10), so both measures will generate the same ordinal ranking of accessibilities for a set of zones (given the same model and data), but it is argued that Equation (5.11) is the preferred functional form to be used, since it completes the task of linking the definition of accessibility to the spatial choice processes that underlie and provide meaning to the concept of utility

In most practical applications, what this means is that a nested logit structure can be used to link travel decisions and location decisions within the integrated model Figure 5.3 provides a simple extension

of the residential location choice case that we have been considering, in which the problem is now defined

as one involving the choice of both residential location and mode to work, given a known workplace and a one-worker household As shown in Figure 5.3, this can be modeled as a nested logit model, in which the longer-run place of residence choice is the upper level and the shorter-run work trip mode choice is the lower level A simple (but representative) set of equations for this system might take the following form:

φφ

Place of Residence

Mode to Work

i to j; Xi|j is the column vector of explanatory variables influencing the choice of residential zone i for workers employed in j; φ is the scale parameter (0 ð φ ð 1); and γ is the column vector of parameters.

Ii is an accessibility term defining the access to workplace j from i provided by the transportation system As this accessibility increases (due, for example, to an improvement in any mode of travel between

i and j), the likelihood of the household locating in zone i increases Note that this decision is based on travel potential, not on actual travel choice The latter is only made in the lower level of the model, within the day-to-day activity–travel decision making of the household’s worker

5.4.4 Lowry Models

Spatial interaction models define the primary organizing principle of a class of integrated models known

as Lowry models, named after the seminal work of Lowry (1964) Figure 5.4 provides a simplified overview of the Lowry modeling framework Key elements of the Lowry model are the following:

1 Basic vs retail employment Lowry divided employment into two fundamental types: basic and retail Basic employment involves economic activities whose magnitude and location are not a function of a local market, but rather are determined by more macro, extraregional factors Examples include export-oriented industries, national and international corporate headquarters, major universities, etc The determination of how much and where such employment activities

FIGURE 5.4 Lowry model flowchart (Adapted from Meyer, M.D and Miller, E.J.,þUrban Transportation Planning:

A Decision-Oriented Approach, 2nd ed., McGraw-Hill, New York, 2001.)

Basic employment by zone (exogenous input)

Generate total households

= f(total workers)

Allocate households to zones (logit spatial interaction model)

Violate density constraints?

No Change in employment negligible?

Stop