A combined trip distribution modal split and trip assignment model

We develop in this paper a trip distribution, modal split and trip assignment model. As is well known, the entropy type distribution model is equivalent to postulating a travel demand function where trips are proportional to a negative exponential function of the travel cost. We show that when two distribution models of this type are linked with route choice models based on Wardrop's “user optimized” principle, the mode choice is given by a logit model. We develop a solution algorithm that computes the resulting trip interchanges and route flows.     

The reliability of using the gravity model for forecasting trip distribution

The main purpose of this study is to assess the forecasting capability of the gravity model and to investigate the merit of including K-factors when using the model. Peak hour trip data was obtained for four study year periods 1962, 1971, 1976 and 1981 for the City of Winnipeg. Analysis of the calibration results indicated that the F-factors for the twenty year period were stable within a range of values. In general, however, the K-factors were found to be inconsistent from one prediction period to the next, and when used in forecasting trips they resulted in larger errors than without their use. The validity of using K-factors or the method which has been used to determine them is questionable. It was concluded that while K-factors are very meaningful in theory (as defined), they are not appropriate for use in predicting O-D matrices based on the method by which they are currently estimated (i.e. as a simple ratio). Further study is needed to investigate an alternative method of calibrating the gravity model such as the cell-by-cell regression method.     

A note on balancing procedures for trip distribution estimation

It is shown that the commonly used balancing procedure in trip distribution estimation is a simplified Newton method. One small numerical example is given.     

A schedule-based time-dependent trip assignment model for transit networks

A schedule-based time-dependent trip assignment model for transit networks is presented. First the transit network model is formulated using the schedule-based approach, in which the vehicles are assumed to arrive punctually in accordance with a scheduled time-table. Based on a previously developed time-dependent shortest path algorithm, an all-or-nothing network loading procedure is employed to assign the passenger trips onto the network. Both the passenger demand and scheduled time-table are time-varying. This provides a versatile tool for the evaluation of the performance of transit networks subject to peak period loading. A case study using the Mass Transit Railway System in Hong Kong is given to illustrate the potential applications of the model.     

Transit trip distribution model considering land use differences between catchment areas

Sustainable land use planning and advanced public transport system are believed to be effective solutions to traffic congestion. To this end, it is important to reveal the relationship between transit ridership and land use. However, current Direct Ridership Models only focus on the relationship between single station's boarding volume and the corresponding catchment area land use. This paper analyzed the ridership distribution between transit stations by considering the land use difference between catchment areas. Land use difference was calculated from point of interest (POI) data extracted from an electronic map of Beijing; transit trip distribution volume was obtained from ‘automatic fare collection’ facility. After data specification, a transit ridership distribution model was proposed and calibrated. The calibration results suggest that land use difference has a directly proportional correlation with transit ridership distribution. The research findings build a bridge between detailed urban form and public transport, which is of significance for the further research of sustainable urban planning. Copyright © 2016 John Wiley & Sons, Ltd.     

A probabilistic model for vehicle scheduling based on stochastic trip times

Vehicle scheduling plays a profound role in public transit planning. Traditional approaches for the Vehicle Scheduling Problem (VSP) are based on a set of predetermined trips in a given timetable. Each trip contains a departure point/time and an arrival point/time whilst the trip time (i.e. the time duration of a trip) is fixed. Based on fixed durations, the resulting schedule is hard to comply with in practice due to the variability of traffic and driving conditions. To enhance the robustness of the schedule to be compiled, the VSP based on stochastic trip times instead of fixed ones is studied. The trip times follow the probability distributions obtained from the data captured by Automatic Vehicle Locating (AVL) systems. A network flow model featuring the stochastic trips is devised to better represent this problem, meanwhile the compatibility of any pair of trips is redefined based on trip time distributions instead of fixed values as traditionally done. A novel probabilistic model of the VSP is proposed with the objectives of minimizing the total cost and maximizing the on-time performance. Experiments show that the probabilistic model may lead to more robust schedules without increasing fleet size.     

A theoretical and empirical model of trip chaining behavior

This paper addresses the theoretical and empirical issues involved in modeling complex travel patterns. Existing models have the shortcoming of not representing the interdependencies among trip links in trip chains with multiple non-home stops. A theoretical model based on utility theory and explicitly accounting for the trade-offs involved in the choice of multiple-stop chains is developed. Using this theoretical model, utility maximizing conditions for a household's choice of a daily travel pattern are derived. The optimum travel pattern is described in terms of the number of chairs (tours) traveled on a given day and in terms of the number of stops (sojourns) made on each of those chains. For a given household, the form of the optimum pattern is a function of the transportation expenditures (time, cost) required to reach potential destinations. Constraints on the conditions of optimality due to the limited and discrete nature of travel pattern alternatives are also considered. Parameters of the general utility function were estimated empirically using actual travel data derived from a home interview survey taken in Washington, D.C. The multinomial logit model is used to relate utility scores for the alternative travel patterns to choice probabilities. The resulting parameter estimates agree with theoretical expectations and with empirical results obtained in other studies. In order to demonstrate the empirical and theoretical implications of the model, forecasts for various transportation policies (e.g., gasoline price increases, transit fare reductions), as made by this model and by other less complex models, are compared. The results of these comparisons indicate the need for expanding the scope of existing travel forecasting models to explicit considerations of trip chaining behavior.     

Spatial aggregation bias in trip distribution probabilities: The case of the opportunity model

In estimating trip distribution probabilities by the opportunity model, the conventional method regards a region as a set of “point zones”, and hence inevitably yields a spatial aggregation bias. First, we show that the conventional method overestimates an intra-zone trip distribution probability and underestimates an inter-zone trip distribution probability. Second, it is presented that the inter-zone relative spatial aggregation bias depends only on an origin area, and that the spatial aggregation bias is independent of the spatial aggregation in the intermediate area. Finally we obtain the minimum number of zones required to ensure that a given level of bias is not exceeded.     

Empirical studies of work trip distribution models

The goodness of fit characteristics of three members of the Wilson-family of gravity models in explaining observed work trip interchanges are examined using an almost 100% sample of journey to work trips in Edmonton, Alberta. Model parameters of the three model types and several variants are estimated for four zone systems ranging in numbers from 22 to 234 zones. Changes in parameter magnitudes and model performance are examined across model types and spatial scales. It is concluded that current gravity models calibrated to cross-sectional data and using only trip end and aggregate travel cost constraints have inadequate explanatory power to justify their use in planning studies. Additional trip end constraints, such as socio-economic stratification, do not yield significant improvements and trip interchange constraints appear to offer the most productive improvement possibilities. The most important factor which is not captured by current cross-sectional models is the timing of urban development which can only reasonably be captured through trip interchange constraints.     

A flexible model structure approach for discrete choice models

Multi-dimensional discrete choice problems are usually estimated by assuming a single-choice hierarchical order for the entire study population or for pre-defined segments representing the behavior of an “average” person and by indicating either limited differences or a variety in choices among the study population. This study develops an integral methodological framework, termed the flexible model structure (FMS), which enhances the application of the discrete choice model by developing an optimization algorithm that segment given data and searches for the best model structure for each segment simultaneously. The approach is demonstrated here through three models that conceptualize the multi-dimensional discrete choice problem. The first two are Nested Logit models with a two-choice dimension of destination and mode; they represent the estimation of a fixed-structure model using pre-segmented data as is mostly common in multi-dimensional discrete choice model implementation. The third model, the FMS, includes a fuzzy segmentation method with weighted variables, as well as a combination of more than one model structure estimated simultaneously. The FMS model significantly improves estimation results, using fewer variables than do segmented NL models, thus supporting the hypothesis that different model structures may best describe the behavior of different groups of people in multi-dimensional choice models. The implementation of FMS involves presenting the travel behavior of an individual as a mix of travel behaviors represented by a number of segments. The choice model for each segment comprises a combination of different choice model structures. The FMS model thus breaks the consensus that an individual belongs to only one segment and that a segment can take only one structure.     

A note on the calculation and calibration of doubly constrained trip distribution models

The use of growth factor models for trip distribution has given way in the past to the use of more complex synthetic models. Nevertheless growth factor models are still used, for example in modelling external trips, in small area studies, in input-output analysis, and in category analysis. In this article a particular growth factor model, the Furness, is examined. Its application and functional form are described together with the method of iteration used in its operation. The expected information statistic is described and interpreted and it is shown that the Furness model predicts a trip distribution which, when compared with observed trips, has the minimum expected information subject to origin and destination constraints. An equivalent entropy maximising derivation is described and the two methods compared to show how the Furness iteration can be used in gravity models with specified deterrence functions. A trip distribution model explicitly incorporating information from observed trips, is then derived.It is suggested that if consistency is to be maintained between iteration, calibration, and the derivation of gravity models, then expected information should be used as the calibration statistic to measure goodness of fit. The importance of consistency in this respect is often overlooked.Lastly, the limitations of the models are discussed and it is suggested that it may be better to use the Furness iteration rather than any other, since it is more fully understood. In particular its ease of calculation makes it suitable for use in small models computed by hand.     

Modelling trip distribution with fuzzy and genetic fuzzy systems

This paper explores the potential capabilities of fuzzy and genetic fuzzy system approaches in urban trip distribution modelling with some new features. First, a simple fuzzy rule-based system (FRBS) and a novel genetic fuzzy rule-based system [GFRBS: a fuzzy system improved by a knowledge base learning process with genetic algorithms (GAs)] are designed to model intra-city passenger flows for Istanbul. Subsequently, their accuracy, applicability and generalizability characteristics are evaluated against the well-known gravity- and neural network (NN)-based trip distribution models. The overall results show that: traditional doubly constrained gravity models are still simple and efficient; NNs may not show expected performance when they are forced to satisfy trip constraints; simply-designed FRBSs, learning from observations and expertise, are both efficient and interpretable even if the data are large and noisy; and use of GAs in fuzzy rule-based learning considerably increases modelling performance, although it brings additional computation cost.     

Comparing decision tree algorithms to estimate intercity trip distribution

Traditional trip distribution models usually ignore the fact that destination choices are made individually in addition to aggregated factors, such as employment and average travel costs. This paper proposes a disaggregated analysis of destination choices for intercity trips, taking into account aggregated characteristics of the origin city, an impedance measurement and disaggregated variables related to the individual, by applying nonparametric Decision Tree (DT) algorithms. Furthermore, each algorithm’s performance is compared with traditional gravity models estimated from a stepwise procedure (1) and a doubly constrained procedure (2). The analysis was based on a dataset from the 2012 Origin-Destination Survey carried out in Bahia, Brazil. The final selected variables to describe the destination choices were population of the origin city, GDP of the origin city and travel distances at an aggregated level, as well as the variables: age, occupation, level of education, income (monthly), number of cars per household and gender at a disaggregated one. The comparison of the DT models with gravity models demonstrated that the former models provided better accuracy when predicting the destination choices (trip length distribution, goodness-of-fit measures and qualitative perspective). The main conclusion is that Decision Tree algorithms can be applied to distribution modeling to improve traditional trip distribution approaches by assimilating the effect of disaggregated variables.     

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.     

Developing an activity-based trip generation model for small/medium size planning agencies

The primary shortcoming of traditional four-step models is that they cannot capture derived travel demand behaviors. However, travel demand modeling (TDM) is an essential input for urban transportation planning. TDM needs to be highly precise and accurate by integrating the accurate base year estimation along with suitable alternatives. Currently, activity-based models (ABMs) have been developed mostly for large metropolitan planning organizations (MPO), whereas smaller/medium-sized MPOs typically lack these models. The main reason for this disparity in ABM development is the complexity of the models and the cost and data requirements needed. We posit however that smaller MPOs could develop ABMs from traditional travel surveys. Therefore, the specific aim of this paper is to develop a probabilistic home-based destination activity trip generation model considering travel time behavior. Results show that the developed model can significantly capture the actual number of trip generations.     

A joint trip timing store-type choice model for grocery shopping,including inventory effects and nonparametric control for omitted variables

In principle, stochastic modelling methods are ideally suited to the analysis and forecasting of discretionary travel; they formalise both the capriciousness and continuity which are empirically typical of recurrent choice. In practice, the development of theoretically justifiable but tractable stochastic models has appeared to be an illusive goal in transportation research and stochastic models have found little favour. Recent statistical results on the nonparametric characterisation of mixing distributions now enable stochastic models to simultaneously represent a much greater variety of behaviour while, at the same time, actually reducing problems over tractability. The consequent case for reappraisal is illustrated by the development and calibration of a new joint timing/choice model for shopping travel. This model has sound theoretical underpinnings, permits complex variation in the frequency and regularity of shopping due to both observed and unobserved characteristics and constraints, and yet is readily calibrated from diary data.     

The effect of round-off error on computed solutions of trip distribution problems

Round-off error analyses of two versions of the Kruithof method are given. It is shown than an alternative implementation is numerically superior to the usual implementation. Since it also has the advantage of requiring less writing in secondary memory, and requires the same number of arithmetic operations, the case for always using the alternative implementation seems indisputable.