Bayesian estimation of multinomial probit models of work trip choice

In this paper, we estimate a multinomial probit model of work trip mode choice in Seoul, Korea, using the Bayesian approach with Gibbs sampling. This method constructs a Markov chain Gibbs sampler that can be used to draw directly from the exact posterior distribution and perform finite sample likelihood inference. We estimate direct and cross-elasticities with respect to travel cost and the value of time. Our results show that travel demands are more sensitive to travel time than travel cost. The cross-elasticity results show that the bus has a greater substitute relation to the subway than the auto (and vice versa) and that an increase in the cost of an auto will increase the demand for bus transport more so than that of the subway.     

Aggregation with multinomial probit and estimation of disaggregate models with aggregate data: A new methodological approach

This paper describes an analytic aggregation procedure for disaggregate demand models similar to the one proposed in earlier publications by Westin (1974) and McFadden and Reid (1975). The technique, which uses a multivariate normal approximation for the distribution of the vector of attributes, is based on the multinomial profit algorithm proposed by Daganzo, Bouthelier and Sheffi (1977) and can be applied to an arbitrary number of alternatives. The procedure is computationally so efficient that it enables us to calibrate disaggregate models with aggregate data by maximum likelihood using the same or slightly modified codes developed for disaggregated data. The paper also contains a small scale numerical example intended to illustrate the important highlights of the aggregation-estimation problem.     

A note on goodness-of-fit statistics for probit and logit models

In the case of models designed to explain the choice among a finite set of alternatives, a number of goodness-of-fit statistics have been reported. This paper is primarily concerned with the properties of one of these statistics, the likelihood ratio index.By comparing the likelihood ratio index with some of the other statistics and by examining its mathematical properties, it is concluded that the index has desirable properties in binary and multinomial situations. However, the way in which the likelihood ratio index has been applied in many recent studies has led to results which are possibly unexpected. In these cases, the index was a measure of the extent to which a hypothesized model improved upon the explanatory power of a model with all coefficients, including the constant or the coefficients of alternative-specific dummies, equal to zero. It is shown that the minimum value of this likelihood ratio index depends on the relative proportions of sampled individuals selecting the various alternatives, contrary to the expectation of a zero minimum value. The dependence on the sampled proportions also prevents comparison of indices resulting from different samples.A simple adjustment alleviates these difficulties. This new definition makes the likelihood ratio index a measure of the extent to which the hypothesized model improves upon the explanatory of a model with only a constant or alternative-specific dummies. It is recommended that this index is more appropriate for assessing the value of choice models.A list of symbols used is given on page 387.     

Macroscopic Fundamental Diagrams: A cross-comparison of estimation methods

This paper aims to cross-compare existing estimation methods for the Macroscopic Fundamental Diagram. Raw data are provided by a mesoscopic simulation tool for two typical networks that mimic an urban corridor and a meshed urban center. We mainly focus on homogenous network loading in order to fairly cross-compare the different methods with the analytical reference. It appears that the only way to estimate the MFD without bias is to have the full information of vehicle trajectories over the network and to apply Edie’s definitions. Combining information from probes (mean network speed) and loop detectors (mean network flow) also provides accurate results even for low sampling rate (<10%). Loop detectors fail to provide a good estimation for mean network speed or density because they cannot capture the traffic spatial dynamics over links. This paper proposes a simple adjustment technic in order to reduce the discrepancy when only loop detectors are available.     

Discretised link travel time models based on cumulative flows: Formulations and properties

In the research area of dynamic traffic assignment, link travel times can be derived from link cumulative inflow and outflow curves which are generated by dynamic network loading. In this paper, the profiles of cumulative flows are piecewise linearized. Both the step function (SF) and linear interpolation (LI) are used to approximate cumulative flows over time. New formulations of the SF-type and LI-type link travel time models are developed. We prove that these two types of link travel time models ensure first-in-first-out (FIFO) and continuity of travel times with respect to flows, and have other desirable properties. Since the LI-type link travel time model does not satisfy the causality property, a modified LI-type (MLI-type) link travel time model is proposed in this paper. We prove that the MLI-type link travel time model ensures causality, strong FIFO and travel time continuity, and that the MLI-type link travel time function is strictly monotone under the condition that the travel time of each vehicle on a link is greater than the free flow travel time on that link. Numerical examples are set up to illustrate the properties and accuracy of the three models.     

Timetable optimization models and methods for minimizing passenger waiting time at public transit terminals

This paper focuses on developing mathematical optimization models for the train timetabling problem with respect to dynamic travel demand and capacity constraints. The train scheduling models presented in this paper aim to minimize passenger waiting times at public transit terminals. Linear and non-linear formulations of the problem are presented. The non-linear formulation is then improved through introducing service frequency variables. Heuristic rules are suggested and embedded in the improved non-linear formulation to reduce the computational time effort needed to find the upper bound. The effectiveness of the proposed train timetabling models is illustrated through the application to an underground urban rail line in the city of Tehran. The results demonstrate the effectiveness of the proposed demand-oriented train timetabling models, in terms of decreasing passenger waiting times. Compared to the baseline and regular timetables, total waiting time is reduced by 6.36% and 10.55% respectively, through the proposed mathematical optimization models.     

Treatment of seasonal tickets for public transport in estimation and application of mode/destination choice models

A new model system dealing with trips of length up to 100 km has recently been developed in Norway. A new way of dealing with seasonal passes for public transport is used in the travel-to-work model. The objective was to account for the fact that a respondent that posses a seasonal pass for public transport may behave as if public transport is free on the day they report a travel diary. On the other hand, we can not assume that public transport is free for respondents that used other modes of transport or that public transport is free to alternative destinations. This problem was solved by defining seasonal pass as a separate alternative in the form of a nest that included all modes of travel. The cost of a seasonal pass is a common cost for all modes in the nest and will thus not affect the choice within the nest. The estimation of this specification is compared with the more common approach of assigning an average cost per day based on the cost of a monthly pass and the number of workdays in a month. The comparison indicates that the “average cost per day” approach may produce biased estimates for several parameters. It also turns out that the cost parameter for seasonal pass is higher than the parameter for “out of pocket” cost, probably reflecting that there will be some uncertainty with respect to the actual use of a seasonal pass.     

Constrained nested logit model: formulation and estimation

A model of traveller behaviour should recognise the exogenous and endogenous factors that limit the choice set of users. These factors impose constraints on the decision maker, which constraints may be considered implicitly, as soft constraints imposing thresholds on the perception of changes in attribute values, or explicitly as hard constraints. The purpose of this paper is twofold: (1) To present a constrained nested logit-type choice model to cope with hard constraints. This model is derived from the entropy-maximizing framework. (2) To describe a general framework to deal with (dynamic) non-linear utilities. This approach is based on Reproducing Kernel Hilbert Spaces. The resulting model allows the dynamic aspect and the constraints on the choice process to be represented simultaneously. A novel estimation procedure is introduced in which the utilities are viewed as the parameters of the proposed model instead of attribute weights as in the classical linear models. A discussion on over-specification of the proposed model is presented. This model is applied to a synthetic test problem and to a railway service choice problem in which users choose a service depending on the timetable, ticket price, travel time and seat availability (which imposes capacity constraints). Results show (1) the relevance of incorporating constraints into the choice models, (2) that the constrained models appear to be a better fit than the counterpart unconstrained choice models; and (3) the viability of the approach, in a real case study of railway services on the Madrid–Seville corridor (Spain).     

Air traffic management: Optimization models and algorithms

Current air traffic control systems are mainly conceived to ensure the safety of flights by means of tactical interventions, because of the difficulty of accurately foreseeing the traffic evolution. In fact, in real traffic conditions, planes are often penalized since sometimes safety standards are redundant. Today, this management philosophy is no longer valid because of congestion phenomena which often occur in the most important terminal areas. Therefore, as to future control systems it is necessary to introduce not only more automated procedures to keep adequate safety levels, but also planning functions in order to increase the system capacity and to improve system efficiency. In recent years several studies have been carried out, new control concepts have been introduced and some optimization models and algorithms developed to improve air traffic management. In this paper a survey of our early works in this field is reported and a multilevel model of air traffic management is proposed and discussed. The functions corresponding to the on-line control, that is flow control, strategic control of flights and aircraft sequencing in a terminal area, are examined and the optimization models and solution algorithms are illustrated. Finally, relevant problems coped by recent research are mentioned and new trends are indicated.     

GIS and network models: Issues for three potential applications

Geographic Information Systems (GISs) are now being developed for urban transportation planning and modeling. Supporting other recent work, this paper demonstrates the combination of GIS and network-based, urban transportation planning (UTP) modeling software to create powerful tools for the analysis of policies and plans. Following a literature review and informal survey identifying GIS and UTP modeling software in use at transportation agencies, three applications of GIS for network modeling and relevant issues are discussed: 1) developing or modifying UTP models, 2) incorporating network data into a GIS framework, and 3) creating and using a high-speed interactive system suitable for providing near real-time alternatives and policy analysis. Some specific suggestions are made related to the use of two software products, and extensions to other platforms are noted. Conclusions allude to the potential of such systems while realistically pointing to the present difficulties and magnitude of effort that will be required.     

Capacitated maximum covering location models: Formulations and solution procedures

This paper presents two formulations and two solution procedures for a capacitated maximum covering location problem. In the first formulation, the problem is presented as a mixed-interger linear programming model which maximizes covered demand. In the second model, the objective function maximizes the weighted covered demand while at the same time minimizing the average distance from the uncovered demands to the located facilities. The second formulation attempts to account for the assignment of the demand which is not “covered” to located facilities which have excess capacity. This assignment is very important, especially for locating emergency service facilities. Two heuristic procedures are proposed to solve these models. These are based on greedy adding technique and Lagrangian relaxation. At each iteration, the demands are allocated to the facilities using an out-of-kilter method. The performance of the solution techniques are compared to the optimal solutions in a variety of test problems.     

Cost and time damping: evidence from aggregate rail direct demand models

There is a significant body of evidence from both disaggregate choice modelling literature and practical travel demand forecasting that the responsiveness to cost and possibly to time diminishes with journey length. This has, in Britain at least, been termed ‘Cost Damping’, and is recognised in guidance issued by the UK Department for Transport. However, the consistency of the effect across modes and data types has not been established. Cost damping, if it exists, affects both the forecasting of demand and our understanding of behaviour. This paper aims to investigate the evidence for cost and time damping in rail demand using aggregate rail ticket sales data. The rail ticket sales data in Britain has, for many years, formed the basis of analysis of a wide range of impacts of rail demand. It records the number of tickets sold between station pairs, and it is generally felt to provide a reasonably accurate reflection of travel demand. However, the consistency of these direct demand models with choice modelling and highway demand model structures has not been investigated. Rail direct demand models estimated by ticket sales data indicate only slight variation in the fare elasticity with distance, as is evidenced in the largest meta-analysis of price elasticities conducted to date (Wardman in J Transp Econ Policy 48(3):367–384, 2014). This study of UK elasticities shows strong variation between urban and inter-urban trips, presumably a segmentation at least in part by purpose, but less remaining variation by trip length. A lack of variation by length supports the hypothesis of cost damping, because constant cost sensitivity would imply that fare elasticity would increase strongly with distance, because of the increasing impact of higher fares at longer distances. In this paper we indicate that rail direct demand models have some consistency of behavioural paradigm with utility based choice models used in highway planning. We go on to use rail demand data to estimate time and fare elasticities in the context of various cost damping functions. Our empirical contribution is to estimate time elasticities on a basis directly comparable with cost elasticities and to show that the phenomenon of cost damping is strongly present in ticket sales data. This finding implies that cost damping should be included in models intended for multimodal analysis, which may otherwise give incorrect predictions.     

Telecommunications and travel demand and supply: Aggregate structural equation models for the US

Disaggregate studies of the impacts of telecommunications applications (e.g. telecommuting) on travel have generally found a net substitution effect. However, such studies have all been short-term and small-scale, and there is reason to believe that when more indirect and longer-term effects are accounted for, complementarity is the likely outcome. At least two aggregate studies have focused on the relationships between telecommunications and travel from economic perspectives (consumer and industry). However, both use the monetary value of consumption or transactions rather than actual activity measures (e.g. miles, number of calls), and neither fully explains the direct and indirect causal relationships between the two. The purpose of this study is to develop a conceptual model in a comprehensive framework, considering causal relationships among travel, telecommunications, land use, economic activity, and socio-demographics, and to explore the aggregate relationships between telecommunications and travel, using structural equation modeling of national time series data spanning 1950–2000 in the US. In this paper we focus on number of telephone calls as the measure of telecommunications, and passenger vehicle–miles traveled as the measure of transportation. Future research will investigate additional measures of these two constructs. Our empirical results strongly support the hypothesis that telecommunications and travel are complementary. That is, as telecommunications demand increases, travel demand increases, and vice versa. These results offer a more realistic picture to policy makers and transportation planners than has been available till now, and suggest useful directions for them to develop transportation or telecommunications strategies designed to reduce traffic congestion, air pollution, and energy consumption.     

Link choice proportions from trip distribution and assignment models: An overview and comparison

A number of estimation procedures have been suggested for the situation where a prior estimate of an origin-destination matrix is to be updated on the basis of recently-acquired traffic counts. These procedures assume that both the link flows and the proportionate usage of each link made by each origin-destination flow (referred to collectively as the link choice proportions) are known. This paper examines the possibility and methods for estimating the link choice proportions. Three methods are presented: (1) using ad hoc iteration between trip distribution and traffic assignment; (2) combining trip distribution and assignment in one step; (3) solving a new optimization problem in which the path flows are directly considered as variables and its optimal solution is governed by a logit type formula. The algorithms, covergencies and computational efficiencies of these methods are investigated. Results of testing the three methods on example networks are discussed.     

Probe vehicle data sampled by time or space: Consistent travel time allocation and estimation

A characteristic of low frequency probe vehicle data is that vehicles traverse multiple network components (e.g., links) between consecutive position samplings, creating challenges for (i) the allocation of the measured travel time to the traversed components, and (ii) the consistent estimation of component travel time distribution parameters. This paper shows that the solution to these problems depends on whether sampling is based on time (e.g., one report every minute) or space (e.g., one every 500 m). For the special case of segments with uniform space-mean speeds, explicit formulae are derived under both sampling principles for the likelihood of the measurements and the allocation of travel time. It is shown that time-based sampling is biased towards measurements where a disproportionally long time is spent on the last segment. Numerical experiments show that an incorrect likelihood formulation can lead to significantly biased parameter estimates depending on the shapes of the travel time distributions. The analysis reveals that the sampling protocol needs to be considered in travel time estimation using probe vehicle data.     

New models for financing and managing highways: asset-based road corporations in China

The China International Engineering Consulting Corporation undertook, in 1997, the study of Viability of Asset Based Road Corporations in China as part of the World Bank's transport sector program review. The purpose was to investigate, in a case study format, road administration in China with two specific objectives: to compare (toll) road management in different provinces and to investigate the financial viability of China's toll roads.This paper shows that the three case projects studied, each having different management structures, are all financially viable given the present financing arrangements. However, should the projects be immediately subject to market interest rates and loan maturities prevailing in China today, their financial viability would be uncertain.In a broader context, the World Bank's lending program has enabled China to experiment with different kinds of toll road management structures. These models have both advantages and disadvantages and seem to fit that province's political economic environment in which they are employed. The toll roads and, especially, the impacts of the toll road management and financing arrangements on road administration present challenges to road administration rarely faced even in the developed countries. The challenges involve questions of the congruence of public good and private interest, as well as the role of planning and public accountability – all serious questions as China moves forward in development. These questions are raised in the context of the case studies.     

Optimal shipment decisions for an airfreight forwarder: Formulation and solution methods

We study the freight forwarder’s shipment planning problem in an airfreight forwarding network where a set of cargo shipments have to be transported to given destinations. We provide mixed integer programming formulations that use piecewise-linear cargo rates and account for volume and weight constraints, flight departure/arrival times, as well as shipment-ready times.After exploring the solution of such models using CPLEX, we devise two solution methodologies to handle large problem sizes. The first is based on Lagrangian relaxation, where the problems decompose into a set of knapsack problems and a set of network flow problems. The second is a local branching heuristic that combines branching ideas and local search. The two approaches show promising results in providing good quality heuristic solutions within reasonable computational times, for difficult and large shipment consolidation problems.