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MODELLING INTERREGIONAL TRANSPORT SYSTEMS*

P. R O B E R T S

Harvard Business School, Cambridge, Mass.

A B S T R A C T

The demand for large-scale interregional transport modelling is growing as the ability to do this type of work increases. There is clearly a promise held out by modelling to answer questions of regional economic growth distribution of benefits and incidence of costs. However, many problems are still to be faced in the design and implementation of these models before these expectations can be fully realized. This paper treats some of these problems with suggestions as to how they can be handled.

Introduction

The development and application of a few successful large-scale multiregional computer simulation models has led to heightened expecta- tions for the use of these models in studies of all types. Although they

appear to hold great promise for a variety of applications in the fnture they are not immediately adaptable to all uses. Their performance for any particular study is likely to be highly variable depending on how well suited they are to answering the policy questions that will be put to them.

It is the purpose of this paper to comment upon the structure of various possible models and to explore some of the limitations that arise in their use for particular policy questions.

A major characteristic of multiregional economic models developed to date in the United States-i .e . the Harvard Model of Columbia (Kresge and Roberts, 1971), the Susquehanna River Basin Model (Hamilton etal. 1969), the Northeast Corridor Transportat ion Study Models (Office of High Speed Ground Transportat ion, 1970), the RAND Model of a Metropolis (Lowry, 1964)- is that they are expensive in terms of both

* An early version of this paper was presented by the author at the Seminar on Mathematical and Statistical Analysis of Transportation and Regional Development Planning held in Honolulu, Hawaii in May, 1969 under the auspices of the U.S.-Japan Cooperative Science Program.

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time and money. They have all required a fairly large team of skilled researchers working over extended time periods of a year or more to develop. Data gathering, model calibration, testing and application have also been time consuming, necessitating a careful balance between empirical and theoretical efforts and wise use of personnel. In every case the size of the computer used tended to impose limitations on the detail incorporated in the models and on the number of possible alternatives investigated. If budgets had been larger and study time less restricted, the models would undoubtedly have been larger and run longer and/or the number of alternatives investigated larger.

The richness of detail that exists in the real world and the tremendous variety of possible choices that can typically be made, suggests to me that we will always be budget constrained in our models. Although archtypical models will undoubtedly emerge, it will always be necessary to restructure models to fit the policy questions at hand. A single model or model type is not likely to dominate for all uses. In order to illustrate this point, let us examine the components making up most models and their specific forms in several model types.

Model Components

All interregional transport models consist of four fairly basic components. Although not all components are found in all models, most are present in some form. These components, shown in Figure 1, are:

REGIONAL STOCKS of industry

Population~ housing~

Changes/ to s t o c k s /

LOCATION MODEL

etc.

evel s of rocks

"~ " ' b e t w e e n ECONOMIC stocks MODEL Spatial real locat ion Regional Economic interactions of stocks potent ials

Transport cost~ Transport/ /Transport grad ien ts \ d e m a n d / / c o s t s

TRANSPORT MODEL Transport interactions between stocks

Fig. 1. Components of interregional transport models.

(1) Regional stocks of industry, population, etc.; (2) a model of economic interactions between stocks; (3) a model of the spatial re-allocation of

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stocks, and ( 4 ) a model of transport interactions between stocks. The interrelations within this overall framework vary from case to case. In some, the model of the economy is replaced by a simple set of demand functions for transport. The computational procedure may also vary from one model to another. In one, the entire set may be solved simultaneously as it is in a linear program. Or, the parts may be assumed to be independent and the model solved recursively.

Regardless of the method of solution all models are forced to deal with time. Less useful models assume a steady state situtation and solve for one time period even where the process is clearly dynamic and where the feedback of certain output is important for determining equilibrium. For most transportation processes however, knowledge of the state of equilibrium at any given time is not as interesting as changes in this equilibrium over time. The more useful models progress through time producing a record of the stocks at each time interval. It is this time dependent record which is most useful for planning purposes. With it, the impact of specific changes can be mapped and evaluated. Without it, the dynamics of change are lost.

Types of Models

Within the broader classification of interregional transport models it is possible to identify a variety of model types. Although any classifi- cation is arbitrary, the breakdown, shown in Figure 2, may be useful in

PU BL IC UR BAN PASSENGER

PRIVATE REGIONAL FREIGHT

Fig. 2. A scheme for classifying interregional transport models.

discussing the characteristics of various models and their uses. The classifi- cations used here involve three areas: public or private policy manipula- tion, urban or regional environment, and passenger or freight domination. The distinctions tend to blur in application, but they will be useful in illustrating the points to be emphasized.

Perhaps the most important distinction is that between public and private ownership. If the model is to be used primarily for exploration of public transport policy, it will typically be structured quite differently than it would be if it were used to explore the choice of action of a private profit-maximizing firm. The differences are due primarily to two things: the goal measures and the treatment of the transport network. There is also less necessity in a model of a private firm to feed back to the

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balance of the economy. Though, increasingly, it is useful to consider the firm within its industry setting.

Distinguishing between urban and regional transport models is primarily a matter of scale. When each geographical point in the model is an intersection of two roads or streets, the important characteristics are quite different than when a point represents an entire urban area. In the former, the timing of the traffic signals may be significant, while in the latter, delay functions are more aggregated. A subtle but perhaps more important difference is the nature of the location routines. In the case of regional models, migration and relocation are more easily explained at the present time using familiar economic criteria than they are within the more complex and apparently more subjective urban area. For these reasons, I feel that these urban or regional subclassifications are useful, at least at this point in time. As increased urban modelling sheds more light on urban location processes these differences may disappear.

The justification for separating freight models from passenger models in this scheme, is the difference in character of the demand for passenger transport from that for freight. Passenger demand is highly subjective. That is merely another way of saying that there are an extremely large number of factors that influence the decision to travel, the choice of mode and route and the determination of the destination. Freight, by contrast, is subject to far fewer considerations and they are more easily quantified. Moreover, freight transport is frequently performed separately from passenger transport in the real world. It uses different equipment, and travels on an individual time schedule. There are, however, notable exceptions such as the belly freight of airlines, and the mixed traffic on public highways. Nevertheless, the models can easily make an assumption of independence and probably should in most cases, be constructed as completely separate models.

Thus, the classification scheme defined above, leads us to distinguish urban freight models used for private decisions from intercity freight models used in public decision making. These two situations would be so different in practice that to expect the same model to do both is folly. There is now, and I believe there always will be, a need for a variety of models to help in the analysis of transport projects.

Other Features of Models

The classification scheme described above tends to point out the more important features of a model system. There are a number of other features of design that deserve mention, because of the special attention

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that they must be given during the design of a model system for a particu!ar situation. These are the role of choice variables, model view- point, political actors, simulation versus optimization and full, versus partial, equilibrium.

Choice variables are those variables embodied within the model system than can be varied to change the design under consideration. The settings of the choice variables within the model will correspond closely to the outcome of particular real-world decisions. Thus, the selection or rejection of a particular link for inclusion within the highway system may be paralleled within the model by the setting of a choice variable to one or zero. Choice variables almost always "belong to" a particular actor in the real world, at least from a legal point of view. The decision to select or reject a highway project belongs typically to government. Rarely does this authority lie with more than one actor except in a hierarchical sense. For example, the decision to build or not to build a freeway link is generally considered to be a government decision generally, but more specifically it is the decision of the highway commissioner.

If a simulation model is to be useful it must deal with this "owner- ship" of choice variables. The way this is typically done within the model is to adopt the viewpoint of a particular actor. The choice variables of the actor whose viewpoint is being taken are explicitly isolated and dealt with inside the model in a coordinated way as input to "the plan." Typically, these choice variables are treated as exogenous to the operation of the simulation model.

Other actors cannot be ignored. It is important to isolate them also and to incorporate them explicitly within the model. These actors may be political interest groups or may be characterized by some other simpli- fying label, such as shipper, carrier, etc. These actors are also faced with their own choice variables. The extent to which these choices are correctly presented to the actors and they in turn are allowed to respond as they would in the real world determines the behavioral content of the model. To do this requires that the model incorporate within it some knowledge of the goals of the actor (cost minimization, profit maximization) or empirical evidence from the real world (regression coefficients).

The selection of choice variables can be accomplished in one of two ways. Either the choice variables are selected exogenously as a part of a trial plan or they are determined by the use of some optimization scheme. Each has its advantages. Use of optimization usually implies excessive simplification. Use of simulation may involve the selection of so many choice variables that it is impractical to at tempt to find the best. In fact, one may be completely lost in so many variables. One compromise is to use optimization routines to select appropriate choice variables for those

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actors who are not the principal focus and to use simulation to try the various possible plans of the actor whose planning viewpoint the model reflects. This approach has the virtue of being able to handle a fair amount of detail without the necessity for deciding the choice actions of each of the subactors.

Another point worthy of mention is the treatment of equilibrium. For some models, principally interregional freight models or urban passen- ger models, the equilibrium level of all state variables over time is what is being sought. Finding equilibrium in the process is therefore a primary reason for using the model in the first place. For other models, such as interregional passenger models, it does not appear to serve any particular purpose to have the output of the process feed back into the overall economic equilibrium mechanism. This is also true of special purpose submodels such as those for housing stock or vehicle purchase or mainte- nance. Their impact on the economy as a whole is relatively minimal.

For models in which equilibrium is crucial, it is necessary to either solve simultaneously, solve recursively or iterate. For iterative solutions, it will be important to guard against oscillation and to guarantee con- vergence. For those processes where overal equilibrium is not important, it is possible to progress through time by exogenous specification of the driving variables or alternatively the harnessing of the dependent model to an independent model of the driving force such as the economy or the population growth.

Not all questions are appropriately answered with models of the entire transportation system of the nation, yet they may still involve what are clearly equilibrium processes. For example, the makeup of the vehicle fleet of a country is determined by the present stocks of vehicles, the interest rate, the availability of foreign exchange, the import tax on vehicles and spare parts and the cost of a mechanic's labor. Equilibrium is achieved by balancing the discounted present value of repairing the vehicle and incurring a stream of expected maintenance costs and the cost of acquiring a new vehicle.

Building the detail into an overall system model to be able to address this problem directly appears to overcomplicate the basic system model, yet, the solution to this problem depends significantly on system-wide variables such as total ton-miles to be moved by the highway, the mode, and the number of vehicle hours required to move it. Two methods for handling this appear to be possible. First, a separate model for the repair or scrap and rebuy decision could be developed with exogenous input of vehicle requirements and pricing policy at each time period. Or, alternatively, this submodel might be attached to the larger system model without feedback and run in conjunction with the larger

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model. In this case we would have an example of the system model being used to furnish the driving force for a separate but dependent model.

Public Models

Models of transportation processes designed for use in planning public policy are typically complex. The challenge is to make them useful without excessive complexity. If this is to be done, it is crucial that some notion of the type of policy decisions that are going to be put to the model be known in advance. If the model is to be used in the evaluation of user tax policy it may be constructed somewhat differently than one used exclusively for determining project feasibility.

The difficult trade-off in constructing public policy models is the need for comprehensiveness on the one hand and responsiveness to typical choice variables on the other. Nowhere is this more evident than in the determination of the extensiveness of the network to be used to answer certain policy questions. Must a single link in the network representation of the overall system represent a single roadway or railroad, or can it be allowed to represent the transport facilities in an entire corridor? When there is a one-for-one correspondence between the network representation and the actual facility it is possible to consider policy questions dealing with the features of its design such as length, design speed, and the resulting consequences, travel time, fuel consumption and degree of congestion.

For links which are representative of an entire corridor this becomes more difficult. The traffic carrying capacity of a corridor of links is difficult to assess, as are the performance characteristics. One approach that has been proposed is the modelling of the more important links on a one-to-one basis and the remainder of the system using a "spider" network which connects nearest neighbor roads. In general, the use of simplified networks as representations of more articulated real-world networks is not well understood. We have almost no experience in using them.

A wide variety of public policy decisions are typically of interest to the government agency responsible for constructing and using these models. In the United States Department of Transportation, for example, the range of public policy issues includes evaluation of present trends in technology, identification of new transport technologies, formulation of programs for encouraging growth in underdeveloped regions, redistribu- tion of income to socially deprived groups, and finally the determination of demographic and geographical effects of major new programs. A list of

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potent ia l pol icy quest ions which might be directed toward interegional

t ranspor t models is given in Table I.

TABLE I

Possible Public Policy Issues which could be Directed toward Interregional Transport Models

Evaluation o f future result of present trends

Extent of coming urban growth Future of the railroad Introduction of new aircraft presently under construction

Effects of growth in air freight Solids pipelines Possibilities for the land bridge concept Future of recreation travel and vacation homes

Identification of promising new technologies

VSTOL aircraft High speed ground transportation Tube trains Personal helicopters Truck trains Advanced eontainerships

Encouraging growth of underdeveloped regions

Elimination of regional transportation disadvantages Industry promotion schemes Recreation as a development tool Coordinated policy manipulation to encourage development Tax incentives to industry location

Encouraging redistribution to socially deprived groups

Undesirable patterns of migration Elimination of ghetto conditions Free transit service Use of toll facilities

Economic and demographic effects of ma/or new programs

Evaluation of major new additions to present interstate program Urban freeway program Urban mass transit program Government promotion of new towns Impact of future defense programs Impact of major changes in regulatory policy Financing issues for major transport programs

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It is clear that the entire range of issues cannot be addressed with a single model. It is conceivable that a dozen or so closely related topics might be addressed by a properly designed model and that specially adapted models might be constructed to handle still others. The key to developing useful models appears to lie in developing modular models. It would then be possible to pull out one portion of a model and put in another with more detail. However, this is easier said than done.

One distinction between urban and interregional models deserves special comment. In urban situations the character of the area is deter- mined by the spatial relationships between industry, commercial businesses and the residences of the population. The location routines must locate new residences so that they are accessible to existing develop- ment. Therefore, one principal determinant of equilibrium has to do with passenger transportation. In interregional models, by contrast, the location portion of the model deals principally with industry location relative to the supplies of raw materials and markets and their effects on industry profitability. Population migration, though important, does not enter into the equilibrium determination in a fundamental way.

If, in the future, the development of interregional passenger trans- port advances to the point that it is economically and personally attractive to live in one city and work in another quite distant on a wide-spread basis, the nature of the location routines within the models will change and equilibrium will have to be sought more in the nature of the urban models. At the present time, however, the development of operational urban models lags somewhat behind interregional modelling efforts.

Another problem which faces the designer of interregional models in highly developed and complex economies, such as the United States, is the isolation of the system of primary interest from the national economic system as a whole. The interregional interdependencies of production and consumption in such a system make separation and independent treat- ment of a single region difficult if not impossible in many cases.

A number of possible methods of treatment appears to be possible. Some of the possibilities are shown in Figure 3. In Figure 3A, the typical t reatment of a national model is shown with foreign trade handled exogenously. One approach to improved regional t reatment is to use the remainder of the nation as the outside world as shown in Figure 3B. This has the disadvantage of being almost completely unable to handle the interdependencies that arise in a highly developed economy. In Figure 3C, a method for overcoming this objection requiring a two-level model is illustrated. One level is the national model. The second level is the regional model. The disadvantage of this approach is the complexity introduced into the whole modelling structure by the two-level system. A more

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A national model with regional treatment

A r e g l o n a [ model w i th in a n a t i o n a l s y s t e m

A r e g i o n a l model within A na t iona l mode l w}th a n a t i o n a l s y s t e m wi th r e g i o n a l t r e a t m e n t of subregional breakdowns subregions

Fig. 3. Treatment of regional submodels. (A) A National model with regional treat- ment. (B) A regional model within a national system. (C) A regional model within a national system with subregional breakdowns. (D) A national model with regional treatment of subregions.

simplified approach is the t r e a tmen t o f the ent i re na t ion as a single system. This is shown in Figure 3D. Here, the region o f special interest is disaggregated to a greater degree than the remainder o f the na t ion but the s t ructure remains the same for all regions. Much work remains to be done in the exp lo ra t ion o f the appropr ia teness o f each approach for d i f ferent problems.

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Private Models

There are two basic differences between public and private models. The first involves the viewpoint to be used. Whereas with public models the viewpoint taken is that of the government, with a private model the difference in viewpoint results in a completely different set of control or choice variables. If the planning entity is a manufacturing firm the network can be treated in an entirely different fashion since the firm has little or no interest in manipulating the design features of particular transport facilities. Secondly, the objectives of a private firm are somewhat easier to state quantitatively than are those of a public body. Whereas a public body may be interested in several objective measures and the impact on various interest groups traced out as a method of getting at the political implications of a plan the private firm's objectives may at times be stated succintly as profit maximization.

A problem in the modelling of private systems is their relation to the larger economy and its distribution over space. The physical distribution system of a firm will depend significantly on the available market at different points in space and that firm's ability to compete effectively to capture the market or a port ion of it. Thus, an industry may.conta in several firms competing with each other over the entire system. Adequate representation of the competitive interactions may be difficult to model. The location of individual components of a firm's production and distribution systems is determined therefore with the individual profit- ability of each firm in mind, not with overall economic efficiency as the criterion. Use of an overall macroeconomic model as the driving force for the economy and its markets may have utility here.

Industry location is related to space in two separate ways. One, there are attributes of a particular point in space which are related to space only in that a particular point has a particular list of attributes. This has no relationship to transportation and transportation models are not needed to make the locational decision. Secondly, there are attributes of spatial location at a point that arise specifically out of the transformation that is performed by transportation. For example, there is the increase in the unit cost which typically arises as the result of placing a commodi ty on sale at a point further from the factory. For these situations realistic representation of the transportation system is needed. Specifically, what is needed are models of the firm which include markets, inventory systems, transportation and production processes. In the transport system the handling of economies of scale in transporting larger size shipments and its effect in both inventory and production should be sought in our modelling efforts. The existence of models for industry location for use

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by industries will undoubtedly lead to better industry location models within public decision models.

Problems in Modelling

Although there are many problems in modelling, a number of which have already been discussed, there is one problem which deserves further comment. That is the problem posed by the interaction of various disciplines in the model building and application phases of a project involving interregional transportation models. Perhaps, the most serious constraint in the entire process involved in a simulation approach including data collection, computer constraints, etc., is posed by the attention to the detail of the model, the data and finally, in the exogenous specification of inputs which must be performed by the " run" team. For ease of communication and understanding of the way in which the model is working (or not working) the team should be small and its members should be generalists with an understanding of more than one discipline if possible and a complete knowledge of one section of the model. This tends to limit the size of the effort, however, since there is an upper limit on the amount of detail that can be comprehended and dealt with by a single individual.

As we gain more knowledge about how to build models of inter- regional transportation some parts of the proces may become more standardized and universal. This will allow us to extend out interests to special problem areas. It appears, however, that where there is a great deal of interaction between the components of the system there will always be problems with placing the model on a computer, debugging it and using it for development of real world policy caused by the ability of the individuals to perceive the system and to deal with it. We are therefore challenged by the need to bring more disciplines to bear on the construc- tion and operation of these models.

Finally, it is clear that the final use of the models constructed must be kept in mind during all phases of model development and use. The total cost of the planning process, including cost of model formulation, model development, data collection, calibration, alternative plan formula- tion and testing of plans is obviously relevant and must be considered. It may become necessary in particular cases to employ models that are not as well developed as we would like or data that is not as rich as it could be because of the lack of funds.

The incidence of interregional transport modelling as the method of

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establishing the rationale for particular policy actions is obviously in its early stages. There will undoubtedly be requests to model the transport system of the entire country in order to answer certain policy questions. Certainly, there is not now, nor will there ever be a large, general purpose interregional model of the transport system of this country which is capable of handling all policy questions which could be addressed to it. Within limits on both the detail and size of the model, and the complexity of the policy question being addressed modelling the transport system of the country may be an entirely reasonable course of action. It could also be a naive and extremely ill-conceived course of action for others. However, as our arsenal of techniques enlarges and our ability to use them effectively grows, we should be in an increasingly better position to answer properly well-stated policy questions.

Perhaps the most important contribution that can be made by a model is the insight which accompanies knowledge of its structure and operation. In many ways manipulating a well-conceived and calibrated model is much like gaining experience with the real world. Clearly, understanding gained through model building or model manipulation is as useful as that gained from long association with the system in the real world. By modelling and by communicating the results of this modelling we can, as well, build on the understanding of others. However, in concluding perhaps it is worthwhile to remember that a model is only a simplified abstraction of the real world. It is essential therefore that we keep in mind the important ways in which the model deviates from the real world and take these into account in deciding the actual course of action to be recommended.

References

Hamilton, H. R. et al. (1969). Systems Stimulation for Regional Analysis. An Applica- tion to River Basin Planning. Cambridge, Mass. : M.I.T. Press.

Kresge, D. T. and Roberts, P. O. (1971). Techniques of Transport Planning, Vol. 11, Systems Analysis and Simulation Models. Washington, D.C.: The Brookings Institu tion.

Lowry, I. (1964). A Model of Metropolis. Santa Monica, Calif.: The RAND Corpo- ration.

Office of High Speed Ground Transportation (1970). Northeast Corridor Transporta- tion Project Report. Washington, D. C.: U.S. Department of Transportation.

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