Forecasting demand for high speed rail

It is sometimes argued that standard state-of-practice logit-based models cannot forecast the demand for substantially reduced travel times, for instance due to High Speed Rail (HSR). The present paper investigates this issue by reviewing the literature on travel time elasticities for long distance rail travel and comparing these with elasticities observed when new HSR lines have opened. This paper also validates the Swedish long distance model, Sampers, and its forecast demand for a proposed new HSR, using aggregate data revealing how the air–rail modal split varies with the difference in generalized travel time between rail and air. The Sampers long distance model is also compared to a newly developed model applying Box–Cox transformations. The paper contributes to the empirical literature on long distance travel, long distance elasticities and HSR passenger demand forecasts. Results indicate that the Sampers model is indeed able to predict the demand for HSR reasonably well. The new non-linear model has even better model fit and also slightly higher elasticities.     

Testing the stability of travel expenditures in Nigeria

A report is presented on a study carried out to develop a functional form for travel money expenditure in a Nigerian setting, and test its stability against energy policy change, specifically the fuel price increase of October 1994. The Box–Cox transformation regression approach was adopted in the modelling exercise in order to evolve a data-defined functional form and ensure a more rational basis for the stability test. The results of the modelling exercise show that while statistically significant functional forms were estimated for the “before” and “after” fuel price increase periods, the functional forms estimated are not stable across the periods. Thus “travel budget” is as yet not usable as a term for travel expenditures in Nigeria. The implication of this for travel demand modelling in Nigeria is that, at least till other evidences prove otherwise, there is as yet no basis for using the “Universal Mechanism Of Travel” model developed by Zahavi (The UMOT Project. Report No. DOT-RSPA-DPB-20-79-3; The UMOT Travel Model II Report No. DOT-RSPA-DPB-50-82-11). Of disposable income and total expenditure, the former has proved to be more appropriate for use as “available money” for the estimation of travel expenditures in Nigeria in the “before” energy policy change period, while total expenditure proved appropriate in the “after” period.     

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.     

A derived demand model of regional highway diesel fuel use

A regional, econometric model of heavy truck diesel fuel use is derived based on the theory of production. Input demand functions for new trucks and diesel fuel are specified and estimated. A simple, logistic scrappage model is estimated and used to estimate total heavy truck stocks and diesel-engine heavy truck stocks. Demand equations based on the AIDS almost ideal demand system flexible form cost function are estimated for new heavy truck demand and regional highway diesel fuel demand. New heavy truck demand is found to be elastic with respect to GNP, inelastic with respect to own price, and appears extremely sensitive to short term GNP trends. The short run price elasticity of diesel fuel demand is found to be very small.     

Road pricing for congestion control with unknown demand and cost functions

It is widely recognized that precise estimation of road tolls for various pricing schemes requires a few pieces of information such as origin–destination demand functions, link travel time functions and users’ valuations of travel time savings, which are, however, not all readily available in practice. To circumvent this difficulty, we develop a convergent trial-and-error implementation method for a particular pricing scheme for effective congestion control when both the link travel time functions and demand functions are unknown. The congestion control problem of interest is also known as the traffic restraint and road pricing problem, which aims at finding a set of effective link toll patterns to reduce link flows to below a desirable target level. For the generalized traffic equilibrium problem formulated as variational inequalities, we propose an iterative two-stage approach with a self-adaptive step size to update the link toll pattern based on the observed link flows and given flow restraint levels. Link travel time and demand functions and users’ value of time are not needed. The convergence of the iterative toll adjustment algorithm is established theoretically and demonstrated on a set of numerical examples.     

The treatment of uncertainty in the dynamic origin–destination estimation problem using a fuzzy approach

Regardless of existing types of transportation and traffic model and their applications, the essential input to these models is travel demand, which is usually described using origin–destination (OD) matrices. Due to the high cost and time required for the direct development of such matrices, they are sometimes estimated indirectly from traffic measurements recorded from the transportation network. Based on an assumed demand profile, OD estimation problems can be categorized into static or dynamic groups. Dynamic OD demand provides valuable information on the within-day fluctuation of traffic, which can be employed to analyse congestion dissipation. In addition, OD estimates are essential inputs to dynamic traffic assignment (DTA) models. This study presents a fuzzy approach to dynamic OD estimation problems. The problems are approached using a two-level model in which demand is estimated in the upper level and the lower level performs DTA via traffic simulation. Using fuzzy rules and the fuzzy C-Mean clustering approach, the proposed method treats uncertainty in historical OD demand and observed link counts. The approach employs expert knowledge to model fitted link counts and to set boundaries for the optimization problem by defining functions in the fuzzification process. The same operation is performed on the simulation outputs, and the entire process enables different types of optimization algorithm to be employed. The Box-complex method is utilized as an optimization algorithm in the implementation of the approach. Empirical case studies are performed on two networks to evaluate the validity and accuracy of the approach. The study results for a synthetic network and a real network demonstrate the robust performance of the proposed method even when using low-quality historical demand data.     

Global convergence of the trial-and-error method for the traffic-restraint congestion-pricing scheme with day-to-day flow dynamics

The traffic-restraint congestion-pricing scheme (TRCPS) aims to maintain traffic flow within a desirable threshold for some target links by levying the appropriate link tolls. In this study, we propose a trial-and-error method using observed link flows to implement the TRCPS with the day-to-day flow dynamics. Without resorting to the origin–destination (O–D) demand functions, link travel time functions and value of time (VOT), the proposed trial-and-error method works as follows: tolls for the traffic-restraint links are first implemented each time (trial) and they are subsequently updated using observed link flows in a disequilibrium state at any arbitrary time interval. The trial-and-error method has the practical significance because it is necessary only to observe traffic flows on those tolled links and it does not require to wait for the network flow pattern achieving the user equilibrium (UE) state. The global convergence of the trial-and-error method is rigorously demonstrated under mild conditions. We theoretically show the viability of the proposed trial-and-error method, and numerical experiments are conducted to evaluate its performance. The result of this study, without doubt, enhances the confidence of practitioners to adopt this method.     

A network‐based model for estimating the market share of a new high‐speed rail system

This paper presents a novel application of static traffic assignment methods, but with a variable time value, for estimating the market share of high‐speed rail (HSR) in the northwest–southeast (NW–SE) corridor of Korea currently served by air, conventional rail and highway modes. The proposed model employs a time–space network structure to capture the interrelations among competing transportation modes, and to reflect their supply‐ and demand‐side constraints as well as interactions through properly formulated link‐node structures. The embedded cost function for each network link offers the flexibility for incorporating all associated factors, such as travel time and fare, in the model computation, and enables the use of a distribution rather than a constant to represent the time–value variation among all transportation mode users. To capture the value‐of‐time (VOT) of tripmakers along the target corridor realistically, this study has developed a calibration method with aggregate demand information and key system performance data from the NW–SE corridor.     

Mechanisms that govern how the Price of Anarchy varies with travel demand

Selfish routing, represented by the User-Equilibrium (UE) model, is known to be inefficient when compared to the System Optimum (SO) model. However, there is currently little understanding of how the magnitude of this inefficiency, which can be measured by the Price of Anarchy (PoA), varies across different structures of demand and supply. Such understanding would be useful for both transport policy and network design, as it could help to identify circumstances in which policy interventions that are designed to induce more efficient use of a traffic network, are worth their costs of implementation.This paper identifies four mechanisms that govern how the PoA varies with travel demand in traffic networks with separable and strictly increasing cost functions. For each OD movement, these are expansions and contractions in the sets of routes that are of minimum cost under UE and minimum marginal total cost under SO. The effects of these mechanisms on the PoA are established via a combination of theoretical proofs and conjectures supported by numerical evidence. In addition, for the special case of traffic networks with BPR-like cost functions having common power, it is proven that there is a systematic relationship between link flows under UE and SO, and hence between the levels of demand at which expansions and contractions occur. For this case, numerical evidence also suggests that the PoA has power law decay for large demand.     

A flexible gravity-opportunities model for trip distribution

This paper develops a flexible gravity-opportunities model for trip distribution in which standard forms of the gravity and opportunities models are obtained as special cases of a general opportunities (GO) model. Hence the question of choice between gravity or opportunities approaches is decided empirically and statistically by restrictions on parameters which control the global functional form of the trip distribution mechanism. The test for the gravity model is shown to be equivalent to a test of the IIA axiom where alternatives are destinations.The notational dichotomy between the two approaches is resolved by employing ordered trip matrices and transformations to permit row and column sum constraints to be applied. These constraints, often interpreted in various ways, are treated as normalisation terms and are therefore not strictly part of the form of the model. Doubly constrained, singly constrained and unconstrained versions of both models are developed throughout.A key step in the integration is the specification of an opportunity function which has as arguments destination-attribute variables such population, income or some other measure of opportunities and generalized cost/impedance-type variables relating origin and destination. This device obviates the mutual exclusiveness ordinarily required of these two sets of variables.The opportunity function is incorporated into a general proportionality factor which is defined by the difference in functions of cumulative opportunities; the latter are subjected to a convex combination of direct and inverse Box-Cox transformations. Different values of the parameters controlling these transformations generate contrasting families of models, notably the exponential and logarithmic intervening opportunities models and the gravity model. All models are shown to be embedded in a transformed triangular region over which likelihood function, response surface or simultaneous confidence interval contours may be plotted.These generalised gravity-opportunity concepts are applied to two well-known models: direct demand multimodal travel demand models, and the estimation of the OD matrix from link volumes. The second case is estimated empirically and here it is shown that a significant improvement is obtained over the gravity model, which is rejected, along with the logarithmic intervening opportunity model, in favour of a more general direct opportunities version.     

An aggregate demand model for intercity passenger travel in Sri Lanka

Inspite of the inherent weaknesses in aggregate demand models, they continue to be used in everyday applications, especially in developing countries. The largely data intensive disaggregate model preclude its application in many cases. This paper attempts the formulation and calibration of an aggregate total demand model for estimating inter-district passenger travel by public transport in Sri Lanka. In its process, an investigation is made of the common problems in the aggregate approach while examining possible remedial measures to improve the accuracy and (hence) the usability of the aggregate model. It is argued that commonly used variables and functional forms are inappropriate for making accurate estimates in developing countries. Consequently, the model calibration is shown to incorporate variables representing urbanisation, under-development, transfers, a mode-abstract cost function and intrinsic features. The necessity for functional form for each variable to be based on behavioral assumptions that are tested using the Box-Cox transformation for ensuring the best fit of the data is also observed. Although, the model form was calibrated for Sri Lanka, the model is generalised in order for its applications to other countries as well as, both, inter-district and intercity travel demand estimation.     

Transportation policy analysis with a geographic information system: The virtual network of freight transportation in Europe

This paper presents a multi-modal freight transportation model based on a digitized geographic network. A systematic analysis and decomposition of all the transport operations i.e. moving, loading and unloading, transshipping and transiting, leads to the development of a virtual network where each virtual link corresponds to a specific operation, and all transportation modes and means are inter-linked. Software, called NODUS, automatically generates the virtual network so that the model can be conveniently applied to large networks. The analytical structure of the links notation makes it easy to attach specific cost functions to each virtual link. The model is applied to the trans-European freight network of roads, railways and inland waterways for the transportation of wood. Cost functions are built up for each operation by each mode/means combination. A detailed point-to-point origin-destination matrix, calibrated on Eurostat statistics, is generated by a Monte-Carlo technique. Then, the total transportation cost is minimized with respect to the choices of routes, modes and means. This provides estimations of transportation services demands as well as modal splits, to the extent that the two hypotheses of demand based on generalized cost minimization and market contestability are accepted. A sensitivity analysis on the relative road cost is made, which provides measures of arc-elasticities.     

Privatisation and the quality of rail services

Using the concept of generalised costs to reflect quality in rail services, we consider the level of provision and quality of these services in the various forms they may take in a privatised environment within a model where we assume linear and separable demand and cost functions for analytical simplicity. Using the Pareto-efficient output and quality outcomes under a fully integrated system for reference (as well as those for a fully integrated profit-maximising monopolist) we show that if either bilateral monopoly or complementary monopoly emerge as a market structure the output of train services and their quality will generally fall. In the case of the emergence of both bilateral monopoly and complementary monopoly our analysis again suggests poor welfare outcomes. The implication that can be drawn from our analysis is that a regulator of a privatised rail system faces some severe problems if she is to attain the appropriate welfare targets.     

The marginal cost taxation of a transportation network

The paper shows that if the cost and demand functions satisfy certain weak smoothness conditions then the marginal cost taxation of a transportation network is optimal in the usual local sense. Interactions between the cost of travel along a link and flow along other links and between the demand for travel along a route and flow along other routes are permitted.     

Network design: selection and design of links and facility location

In this paper we introduce new network design problems. A network of potential links is given. Each link can be either constructed or not at a given cost. Also, each constructed link can be constructed either as a one-way or two-way link. The objective is to minimize the total construction and transportation costs. Two different transportation costs are considered: (i) traffic is generated between any pair of nodes and the transportation cost is the total cost for the users and (ii) demand for service is generated at each node and a facility is to be located on a node to satisfy the demand. The transportation cost in this case is the total cost for a round trip from the facility to each node and back. We will consider two options in regard to the links between nodes. They can either be two-way only, or mixed, with both two-way and one-way (in either direction) allowed. When these options are combined with the two objective functions, four basic problems are created. These problems are solved by a descent algorithm, simulated annealing, tabu search, and a genetic algorithm. Extensive computational results are presented.     

The nonlinear equation system approach to solving dynamic user optimal simultaneous route and departure time choice problems

Dynamic user optimal simultaneous route and departure time choice (DUO-SRDTC) problems are usually formulated as variational inequality (VI) problems whose solution algorithms generally require continuous and monotone route travel cost functions to guarantee convergence. However, the monotonicity of the route travel cost functions cannot be ensured even if the route travel time functions are monotone. In contrast to traditional formulations, this paper formulates a DUO-SRDTC problem (that can have fixed or elastic demand) as a system of nonlinear equations. The system of nonlinear equations is a function of generalized origin-destination (OD) travel costs rather than route flows and includes a dynamic user optimal (DUO) route choice subproblem with perfectly elastic demand and a quadratic programming (QP) subproblem under certain assumptions. This study also proposes a solution method based on the backtracking inexact Broyden–Fletcher–Goldfarb–Shanno (BFGS) method, the extragradient algorithm, and the Frank-Wolfe algorithm. The BFGS method, the extragradient algorithm, and the Frank-Wolfe algorithm are used to solve the system of nonlinear equations, the DUO route choice subproblem, and the QP subproblem, respectively. The proposed formulation and solution method can avoid the requirement of monotonicity of the route travel cost functions to obtain a convergent solution and provide a new approach with which to solve DUO-SRDTC problems. Finally, numeric examples are used to demonstrate the performance of the proposed solution method.     

Sequential optimization approach for the multi‐class user equilibrium problem in a continuous transportation system

We consider a city region with several facilities that are competing for customers of different classes. Within the city region, the road network is dense, and can be represented as a continuum. Customers are continuously distributed over space, and they choose a facility by considering both the transportation cost and market externalities. More importantly, the model takes into account the different transportation cost functions and market externalities to which different customer classes are subjected. A logit‐type distribution of demand is specified to model the decision‐making process of users' facility choice. We develop a sequential optimization approach to decompose the complex multi‐class and multi‐facility problem into a series of smaller single‐class and single‐facility sub‐problems. An efficient solution algorithm is then proposed to solve the resultant problem. A numerical example is given to demonstrate the effectiveness and potential applicability of the proposed methodology.     

Modeling a rail transit alignment considering different objectives

An optimization model for station locations for an on-ground rail transit line is developed using different objective functions of demand and cost as both influence the planning of a rail transit alignment. A microscopic analysis is performed to develop a rail transit alignment in a given corridor considering a many-to-one travel demand pattern. A variable demand case is considered as it replicates a realistic scenario for planning a rail transit line. A Genetic Algorithm (GA) based on a Geographical Information System (GIS) database is developed to optimize the station locations for a rail transit alignment. The first objective is to minimize the total system cost per person, which is a function of user cost, operator cost, and location cost. The second objective is to maximize the ridership or the service coverage of the rail transit alignment. The user cost per person is minimized separately as the third objective because the user cost is one of the most important decision-making factors for planning a transit system from the users’ perspective. A transit planner can make an informed decision between various alternatives based on the results obtained using different objective functions. The model is applied in a case study in the Washington, DC area. The optimal locations and sequence of stations obtained using the three objective functions are presented and a comparative study between the results obtained is shown in the paper. In future works we will develop a combinatorial optimization problem using the aforementioned objectives for the rail transit alignment planning and design problem.     

Continuous formulations and analytical properties of the link transmission model

The link transmission model (LTM) has great potential for simulating traffic flow in large-scale networks since it is much more efficient and accurate than the Cell Transmission Model (CTM). However, there lack general continuous formulations of LTM, and there has been no systematic study on its analytical properties such as stationary states and stability of network traffic flow. In this study we attempt to fill the gaps. First we apply the Hopf–Lax formula to derive Newell’s simplified kinematic wave model with given boundary cumulative flows and the triangular fundamental diagram. We then apply the Hopf–Lax formula to define link demand and supply functions, as well as link queue and vacancy functions, and present two continuous formulations of LTM, by incorporating boundary demands and supplies as well as invariant macroscopic junction models. With continuous LTM, we define and solve the stationary states in a road network. We also apply LTM to directly derive a Poincaré map to analyze the stability of stationary states in a diverge-merge network. Finally we present an example to show that LTM is not well-defined with non-invariant junction models. We can see that Newell’s model and continuous LTM complement each other and provide an alternative formulation of the network kinematic wave theory. This study paves the way for further extensions, analyses, and applications of LTM in the future.     

Stochastic capacity expansion models for airport facilities

It is important and also challenging to plan airport facilities to meet future traffic needs in a rapidly changing environment, which is characterized by various uncertainties. One key issue in airport facility development is that facility performance functions (delay levels as functions of capacity utilization rates) are nonlinear, which complicates the solution method design. Potential demand fluctuations in a deregulated aviation market add another dimension to the decision making process. To solve this problem, a deterministic total cost minimization model is proposed and then extended into stochastic programs, by including uncertainties in traffic forecasts. After the exploration of properties of the delay cost function, an Outer-Approximation (OA) technique which is superior to the existing discrete approximation is designed. After model enhancements, an efficient solution framework based on the OA technique is used to solve the model to its global optimality by interactively generating upper and lower bounds to the objective. Computational tests demonstrate the validity of developed models and efficiency of proposed algorithms. The total cost is reduced by 18.8% with the stochastic program in the numerical example.