Trip Distribution Model Research Articles

Proof of global convergence of an efficient algorithm for predicting trip generation, trip distribution, modal split and traffic assignment simultaneously on large-scale networks

Safwat and Magnanti have developed a combined trip generation, trip distribution, modal split and traffic assignment model that can predict demand and performance levels on large-scale transportation networks simultaneously. An efficient algorithm for predicting equilibrium on the model was suggested by the authors and applied to large-scale systems. The algorithm was found to consistently converge very rapidly in all cases. A formal proof of convergence was not available at the time of those applications. This paper provides a formal proof of global convergence of this efficient algorithm under no additional assumptions on the model. This proof should strengthen the methodology and further encourage its widespread implementation for transportation planning studies, particularly those of a large-scale nature.

Generalized power model for trip distribution

In this paper a trip distribution model is proposed, based on the concepts of conventional trip distribution, linear regression analysis and power transformation on the independent variable. The proposed model takes into consideration the relationship between trips from an origin to a destination (dependent variable) and attraction of the destination (independent variable). Regression analysis is used to determine the parameters of the relationship which is optimized by varying the power parameter. Regression parameters and the optimum power parameter are used in formulating the trip distribution model. The functional form of the proposed model has a generalized application. Distinctive models can be derived from the generalized model by using appropriate independent variables to suit the given data. Therefore, this model is termed as Generalized Power model for trip distribution. In this paper two typical applications of the model are given as examples. Both models have been developed using cordon origin-destination (O-D) survey data of Red Deer in Alberta. The paper includes discussion of results and conclusions.

Explanatory and forecasting capabilities of trip distribution models

Trip distribution models attempt to capture two effects and these are changes in the overall scale of travel between some base year and forecast year as well as fundamental changes in commuting structure. The paper begins with a very brief discussion of observed commuting changes in the Toronto region between 1971 and 1981 using the census journey-to-work data. The abilities of a doubly constrained gravity model to emulate interzonal commuting flows in 1971 and 1981 are examined as well as its ability to forecast 1981 flows. These explanatory and forecasting capabilities are compared with those of a Fratar-type trip distribution model. The trip interchange residuals for both model types are isolated and interpreted in terms of the changes in spatial structure that have occurred in the Toronto region over the analysis period. It is concluded that the forecasts provided by the Fratar model are much superior to those of the aggregate doubly constrained gravity model. Both model types have difficulties in emulating shifts in commuting structure that are due to fundamental changes in living and working patterns by the various socioeconomic groups.

Intraprovincial trip distribution model

A town (or city) in a province generates external trips to other towns and cities for various purposes. A cordon origin–destination (O – D) survey shows the origin and destinations of the external trips of a town. An individual external trip distribution model is developed for a town using the cordon O – D survey data. The external trips are recognized as intra provincial trips and therefore the model is called intraprovincial trip distribution model. The data used in this study is taken from cordon O – D surveys done in Alberta.In the formulation of the model, a functional form that uses a linear relationship between the dependent and the independent variables and power transformations on the independent variable is considered. The parameters in the model are obtained by regression analysis. The models are validated by statistical measures and tests. In this paper, an individual model is developed for each of the seven cities and towns chosen for this study. The formulation and development of the model, regression analysis, and validity tests are described in detail. Key words: cordon survey, intraprovincial trips, model, power transformations, regression analysis, trip distribution.

TRIP DISTRIBUTION MODEL USING TRIP LENGTH DISTRIBUTION

New trip distribution model is proposed. The model is intended to estimate the trip length distribution for each zone using trip length distribution sub-model first, and then to estimate the trip distribution based on the estimated trip length. The model enables us to estimate trip distribution with similar accuracy as the gravity model when the person trip survey is available, and with relatively good accuracy only using data on number of generated trips, number of attracted trips and distance between zones even when the person trip survey is not available. The model is applied to several person trip survey data and show good performance.

COMPARATIVE STUDY OF SOME TRAFFIC ESTIMATION MODELS BY OBSERVED LINK FLOWS REGARDING GENERATION TRIPS AS UNKNOWNS

In this paper, we presents some kinds of traffic demand estimation model by observed link flows regarding generation trips only as unknowns, which are formulated by minimizing the sum of square errors between observed and estimated link flows, and investigate the differences in these model properties concerning prediction errors caused by noises in the given and the observed data. This comparative study is done by computer simulations using artificial data. The main results are as follows:(1) The trip distribution model, which gives a best goodness of fit on an existing or earlier OD pattern, must be choosed in order to estimate the OD matrix.(2) If the OD matrix change by the number of generation and attraction trips, we must use the gravity model satisfying two trip end constraints.

A study of the spatial distribution of transportation‐an alternative approach and evaluation

Abstract This study intends to investigate a calibration procedure for a proposed combined trip generation and distribution model which is based on the concept of accessibility. Apart from the proofs of the existence and uniqueness of the solution, the computation efficiency is evaluated by using Cesario's data (1). The calibration procedure is further tested with empirical data which is obtained from an actual transportation survey carried out in Kaohsiung City of Taiwan, the Republic of China.

Analytical derivation and behavioral interpretation of a model combining trip generation and distribution

The disjointedness of the planning sequence of trip generation and trip distribution is the main subject of this paper. We approach this disjointedness problem by analyzing the central properties of the independently discovered balancing methods of trip-distribution models in relation to two critical issues. First, in the current planning sequence, it is usual to start by forecasting how many trips will begin (production) and end (attraction) in each zone. This forecasting is done by estimating the production of trips independently from the attraction of trips and vice versa, and then forcing some mechanical balance of total trips being generated in the urban system. Second, in the same planning sequence, the output of this trip-generation process is the input to the next one (trip-distribution process): forecasting the matrix that describes the number of trips between each pair of zones. This forecasting is done in general by updating an equivalent obsolete matrix that was obtained from an origin-and-destination survey. The updating is generally accomplished by adjusting the outdated matrix with the so-called balancing factors. It is the purpose of this paper to support the balancing-factors approach in forecasting trip-distribution matrices with a methodological interpretation and to explain behaviorally the balancing factors; and in the process, to show the spatial interaction between trip production and attraction and the emerging need for simultaneous specification and estimation of the whole trip-generation process.

External Zones in Trip Distribution Models: Characterization and Solvability

The problem of incorporating zones outside the study area in a spacial interaction or trip distribution model is analyzed in this paper. The framework for the analysis is based on the maximum likelihood formulation of the problem, whose equivalence to the entropy maximization model was established in general by Wong (Wong, D. S. 1981. Maximum likelihood, entropy maximization, and the geometric programming approaches to the calibration of trip distribution models. Trans. Res. 15B 329–343.). We shall deal with two cases—when the number of incoming (or outgoing) trips to the study area is restricted, and when it is unrestricted. Based on this approach, we present a unified numerical solution methodology for these classes of problems. The sensitivity of the model with respect to changes in certain restrictive parameters will be examined. As a result, we characterize the solution space for certain values of the parameters under consideration. A numerical example is used to illustrate our presentation.

DISAGGREGATE TRIP DISTRIBUTION MODELS

The principal method used in transportation studies to forecast matrices of person trips between origins and destinations is usually an aggregate gravity model. This paper presents the theory and methods for the application of disaggregate estimation of probabilistic choice models to trip distribution. The most important practical differences between the aggregate and the disaggregate models are in the model estimation stage. Disaggregate models can be estimated with smaller traveller surveys and place an emphasis on the specification of utility functions with a larger set of explanatory variables. The paper deals with the issue of aggregation of actual destinations into traffic zones, also addressed by aggregate trip distribution models. However, it presents an aggregation of alternatives theory that was developed for disaggregate logit models based on the concept of random utility. Destination choice models are presented that were estimated in two recent studies in Paris, France, and in Maceio, Brazil, using the methods described.

Traffic assignment by trip type using volume restraint and link restraint for application in small urban areas

AbstractThis research involved the development of a new traffic assignment model consisting of a set of procedures for an urbanized area with a population of 172,000. Historical, social, and economic data were used as input to conventional trip generation and trip distribution models to produce a trip table for network assignment. This fixed table was divided into three trip types: external‐external trips, external‐internal trips, and internal‐internal trips. The methodology used to develop the new traffic assignment model assigned each of the trip types by varying the diversion of trips from the minimum path. External‐external trips were assigned on a minimum path routing and external‐internal trips were assigned with a slight diversion from the minimum path. Internal‐internal trips were assigned with more diversion than external‐internal trips and adjusted by utilizing iterative volume restraint and incremental link restraint.A statistical analysis indicated that assigning trips by trip types using trip diversion and volume and link restraint produces a significant improvement in the accuracy of the assigned traffic volumes.

Ridership estimation for short-range transit planning

The objective of this research was to develop a simple transit ridership estimation model system for short-range planning. The main feature of the model system is that it exploits knowledge of transit link volumes which are obtained readily from on-off counts. Extensive use is made of default values for model parameters, taken directly from the transportation literature. The remaining parameters can be derived easily from generally available land-use and socioeconomic data. Expensive household surveys and time-consuming model calibrations are not required. A sequence of simple trip generation, trip distribution and modal split models generate trip-purpose specific transit trip tables, denoted as “trial” trip tables. These trip tables and observed transit link volumes are used in a linear programming model which serves as a correction mechanism. The gain in accuracy is achieved by using the ridership information contained in the transit link volumes. The corrected trip tables may be used in a pivot-point analysis to estimate changes in ridership and revenue. The results of a test application of the model system indicate that it can generate accurate ridership estimates when reliable transit link volumes are available from on-off counts, and when the trial transit trip tables as derived from the first three component models are reasonably accurate.

Temporal versus other impacts upon trip distribution model parameter values

Southworth F. (1983) Temporal versus other impacts upon trip distribution model parameter values, Reg. Studies 17, 41–47. The change in trip distribution model travel impedence parameters, as a result of temporal changes in average in-vehicle travel times, are compared with parameter differences due to non-temporal disaggregations by trip purpose, income group and residence location. Goodness-of-fit tests on models using 1962 and 1971 Greater London car-owning household travel datas indicate the dominance of the travel impedence matrices used over model results. Spatial disaggregations of parameters cannot be expected to improve model forecasts, but may provide useful insights into regional travel pattern restructuring over time.

APPLICABILITY OF TRIP DISTRIBUTION MODELS

In this report, five trip-distribution models were applied to journey-to-work trips by road obtained from the six person-trip survey data of five cities in order to examine the applicability of models. The study is summarized as follows: In order to examine the reproducibility, correlation coefficients, and relative error indices were calculated. The effects of the sample size were studied. The effects of the parameter deviation from the optimal values on the estimated trip distribution were examined in six surveys. The effect of zoning composition was examined by applying the models to various zoning systems.

Occupational status and the journey-to-work

The importance of occupational status as an explanatory variable in the determination of work trip commuting flows has not been well studied in the literature. This paper addresses this issue by means of an empirical investigation of commuting patterns in the Toronto Census Metropolitan Area (CMA), using 1971 Census data. The analysis consists of three parts. First, a descriptive analysis of the work trip characteristics for six relatively homogeneous occupation groups is performed. Second, the employment and residential location distributions for these groups are briefly examined. Third, a series of work trip distribution models are calibrated and compared for each of the six occupation groups.

Spatial aggregation in gravity models; pt. 3, two-dimensional trip distribution and location models.

This is the third of four papers and in it the methodology for analysing spatial aggregation in gravity models outlined in the first paper is further elaborated. In the second paper, the methodology was applied to one-dimensional spatial interaction models of the population density type, with some success; and here it is proposed to apply the methodology to two-dimensional spatial interaction models using the same data base, the Reading (UK) region. Accordingly, the methodology is first stated for linking information in data measured by spatial entropy to the parameters of models generated from spatial entropy. The family of four spatial interaction models due to Cordey-Hayes and Wilson is then derived, the canonical forms of their associated spatial entropy functions presented, and the analytic properties of such models explored. These four models are then fitted to spatial aggregations of the Reading region, and various empirical relationships between their entropies and parameters described. The results are not as regular as those of the models in the second paper because of more variable model performance, but nevertheless a means of approximating scale parameters from data based on the work of Kirby is outlined. This enables estimates of the dispersion parameters to be made through the canonical forms. Although the results are poor because of model performance, the methodology outlined here serves as a basis for the more fully fledged application to be discussed in the final paper.

Maximum likelihood, entropy maximization, and the geometric programming approaches to the calibration of trip distribution models

Geometric programming is used to establish a formal primal-dual relationship between the maximum likelihood and the entropy maximization formulations of the trip distribution model. This relationship produces solution characteristics which agree with well known results. It provides an efficient procedure for interpreting and solving the model. A systematic method for conducting post-optimal sensitivity analysis is also available. The development is illustrated through a simple example.

Goodness of fit statistics for trip distribution models

Alternative goodness of fit statistics for comparing observed and model generated trip matrices are examined. The behaviour and appropriateness of the alternative statistics are tested by comparing trip matrices for eight Canadian cities with simulated trip matrices calculated by the introduction of progressively larger random errors in the trip cells. The tests suggested that the phi-statistic is the most appropriate to test goodness of fit of alternative trip distribution models. Evidence is also presented which illustrates that state-of-the-art work trip distribution models incorporating a negative exponential travel deterrence function have goodness of fit equivalent to a random error of from 75–100%.

Interval estimation in the calibration of certain trip distribution models

This paper argues for interval, rather than point, estimation when calibrating some variants of the trip distribution “gravity” models. Analytic expressions are derived for the approximate asymptotic covariances of least squares and maximum likelihood estimates of the parameters in the impedance function under a variety of conditions. A comparative numerical example, and an application using migration flows, are also presented.

Accessibility, entropy and the distribution and assignment of traffic—A comment

In an article in this journal Erlander (1977) has suggested an alternative way of interpreting the entropy maximizing approach when used to derive the gravity model formulation for trip distribution. Erlander views the optimization model as a planning model and for this purpose examines two alternative formulations, which are referred to as the efficiency and accessibility problems. In this comment we point out the similarities and dissimilarities between these formulations and the derivation of the trip distribution model on the basis of conventional neoclassical utility theory. We also question the meaningfulness of interpreting the entropy maximizing framework as a planning model.