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|Title:||PERFORMANCE OF GRAVITY-TYPE SPATIAL INTERACTION MODELS THROUGH DESIGN OF CONSTRAINTS|
|Authors:||Furlonge, R. J.|
|Abstract:||Transport is known to affect and be affected by the urban environment, and spatial interaction models are used to understand and forecast the pattern of travel behaviour in the urban environment. This ability to estimate travel behaviour serves as an aid to the developing and testing of urban planning policy. The technique widely used for this is the gravity model and this model is the subject of inquiry of this research. In spite of the large amount of theoretical and empirical work conducted during the past three decades, the gravity model still does not provide adequate explanations of observed patterns of spatial interaction. It is postulated that the theory which goes into the derivation of the model in terms of specifying the limits of the distribution seems to be weak. This research aims for respecifying the theory for constraints required to derive the model. A related problem concerns the estimation and testing procedures. There is as yet no recommended single goodness-of-fit statistic which satisfies the criteria of high sensitivity and unbiasedness. Twenty-one goodness-of-fit statistics are examined, including those commonly used in urban transportation planning, and then a suggestion is made as to the most sensitive and least biased measure. The data used in this research is for the city of Cardiff, Wales CU. K.}, collected by South Glamorgan Ciii} County Council in 1975 and updated in 1983. The origin - destination CO-DD trip movements for an average weekday, obtained from the home interview survey, were aggregated to a system of sixty-two zones. The shortest path distance and time indices were produced using the network data for both 1975 and 1983. Intrazonal distances and times were not available, so for this research all intrazonal travel linkages are excluded. A detailed analysis is undertaken of previous work done through imposition of various constraints on the distribution. The effects of the trip ends and cost constraints on the performance of the gravity model are investigated. The Cardiff data exhibited two distinct trip residual patterns, apart from the external linkage effects. They were Ci} a pattern associated with the CBD linkage, and CiiD a pattern associated with the neighbourhood zone linkages. None of the models with existing constraint reformulations proved adequate in their performance. A proposed spatial autocorrelation constraint is unable to assist the gravity model in travel description to any major extent. The rnicrodistribution of tripmaking is then redefined, in order to capture the unequal likelihood of individual flows within the linkages. The principle of maximum entropy is used to produce a properly specified model with two deterrent factors, one, a trip frequency function and the other, a trip cost function. Calibration of this model is performed using two criteria. Balancing factors are no longer present. These two criteria are Civ} obtained directly from the principle of maximum entropy. The first criterion is the natural constraint equation: The maximum entropy distribution represents the most unbiased, most random and most objective distribution consistent with the constraints, and there is always a family of most biased probability distributions. The second criterion is the selection of the probability distribution with the minimum entropy, in order to identify the member of the family which gives the best knowledge of the system, under the influence of the information contained in the form of constraints. The principle of maximum entropy thus provided its own calibration criteria and avoided the use of any inherently biased statistic. Since two calibration criteria are used, the possibility of many combinations of multiparameters giving optimum fit, as for a single calibration statistic, is significantly reduced, if not altogether eliminated. A comparison, at forecast, of the new entropy model, the doubly constrained gravity model, and the unconstrained gravity model, revealed the following: Ci} All three models experience difficulty with the CBD linkage and neighbourhood linkage effects. Cii} The new entropy model does not over predict to an appreciable extent. Both of the gravity models produce over- and underestimated residuals to varying degrees. Ciii} The forecast deterrence parameter for the gravity model is from an assumption of the future mean trip length. The new entropy model minimises assumptions, and Cv} there is actually a second stage calibration utilising all available information to give the best Cconservative} forecast. There are indications that any new information concerning CBD linkages or neighbourhood linkages, will consistently improve the new entropy model's forecast capability. A policy should always be devised with its implementation in mind, and the new entropy model grants the planner a great deal of confidence in its use, as it will always lead to non-wasteful implementation. The new entropy model could be very useful in short-term incremental planning. Cvi}|
|Appears in Collections:||DOCTORAL THESES (Civil Engg)|
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