On some traffic equilibrium theory paradoxes

We consider the asymmetric equilibrium problem with fixed demands in a transportation network where the travel cost on each link may depend on the flow on this as well as other links of the network and we study how the travellers' cost is affected by changes in the travel demand or addition of new routes. Assuming that the travel cost functions are strongly monotone, we derive formulas which express, under certain conditions, how a change in travel demand associated with a particular origin-destination (O / D) pair will affect the travelers' cost for any O / D pair. We then use these formulas to show that an increase in the travel demand associated with a particular O / D pair (all other remaining fixed) always results in an increase in the travelers' cost on that O / D pair, however, the travelers' cost on other O / D pairs may decrease. We then derive formulas yielding, under certain conditions, the change in travelers' cost on every O / D pair induced by the addition of a new path. These can be used to determine, whether Braess' paradox occurs in the network. We then show that when a new path is added, the travelers' cost associated with the particular O / D pair joined by this path will decrease (hence Braess' paradox does not occur) if a test matrix is positive semidefinite.     

Optimal starting location of an HOV lane for a linear monocentric urban area

This paper analyzes the optimal starting location of a high-occupancy-vehicle (HOV) lane for a linear monocentric urban area. Both travel time and carpooling costs are taken into account. The research proposes an analytical framework for the case with a continuum demand distribution along a highway corridor. The objective is assumed to maximize social welfare of the transportation system, which is the difference between the total user benefit and travel cost. Numerical analysis via simulation experiments was conducted to seek the existence of an optimal solution. Based on the results of a sensitivity analysis, we find a specific relationship between the carpooling cost and the optimal design of the starting point of an HOV lane.     

Optimal transit fare in a bimodal network under demand uncertainty and bounded rationality

This paper investigates the optimal transit fare in a simple bimodal transportation system that comprises public transport and private car. We consider two new factors: demand uncertainty and bounded rationality. With demand uncertainty, travelers are assumed to consider both the mean travel cost and travel cost variability in their mode choice decision. Under bounded rationality, travelers do not necessarily choose the travel mode of which perceived travel cost is absolutely lower than the one of the other mode. To determine the optimal transit fare, a bi‐level programming is proposed. The upper‐level objective function is to minimize the mean of total travel cost, whereas the lower‐level programming adopts the logit‐based model to describe users' mode choice behaviors. Then a heuristic algorithm based on a sensitivity analysis approach is designed to solve the bi‐level programming. Numerical examples are presented to illustrate the effect of demand uncertainty and bounded rationality on the modal share, optimal transit fare and system performance. Copyright © 2013 John Wiley & Sons, Ltd.     

The existence, uniqueness and computation of an arc-based dynamic network user equilibrium formulation

In this paper, a dynamic user equilibrium traffic assignment model with simultaneous departure time/route choices and elastic demands is formulated as an arc-based nonlinear complementarity problem on congested traffic networks. The four objectives of this paper are (1) to develop an arc-based formulation which obviates the use of path-specific variables, (2) to establish existence of a dynamic user equilibrium solution to the model using Brouwer's fixed-point theorem, (3) to show that the vectors of total arc inflows and associated minimum unit travel costs are unique by imposing strict monotonicity conditions on the arc travel cost and demand functions along with a smoothness condition on the equilibria, and (4) to develop a heuristic algorithm that requires neither a path enumeration nor a storage of path-specific flow and cost information. Computational results are presented for a simple test network with 4 arcs, 3 nodes, and 2 origin–destination pairs over the time interval of 120 periods.     

Spatiotemporal influence of land use and household properties on automobile travel demand

Understanding the patterns of automobile travel demand can help formulate policies to alleviate congestion and pollution. This study focuses on the influence of land use and household properties on automobile travel demand. Car license plate recognition (CLPR) data, point-of-interest (POI) data, and housing information data were utilized to obtain automobile travel demand along with the land use and household properties. A geographically and temporally weighted regression (GTWR) model was adopted to deal with both the spatial and temporal heterogeneity of travel demand. The spatial-temporal patterns of GTWR coefficients were analyzed. Also, comparative analyses were carried out between automobile and total person travel demand, and among travel demand of taxis, heavily-used private cars, and total automobiles. The results show that: (I) The GTWR model has significantly higher accuracy compared with the Ordinary Least Square (OLS) model and the Geographically Weighted Regression (GWR) model, which means the GTWR model can measure both the spatial and temporal heterogeneity with high precision; (II) The influence of built environment and household properties on automobile travel demand varies with space and time. In particular, the temporal distribution of regression coefficients shows significant peak phenomenon; and (III) Comparative analyses indicate that residents’ preference for automobiles over other travel modes varies with their travel purpose and destination. The above findings indicate that the proposed method can not only model spatial-temporal heterogeneous travel demand, but also provide a way to analyze the patterns of automobile travel demand.     

Robust network pricing and system optimization under combined long-term stochasticity and elasticity of travel demand

Network pricing serves as an instrument for congestion management, however, agencies and planners often encounter problems of estimating appropriate toll prices. Tolls are commonly estimated for a single-point deterministic travel demand, which may lead to imperfect policy decisions due to inherent uncertainties in future travel demand. Previous research has addressed the issue of demand uncertainty in the pricing context, but the elastic nature of demand along with its uncertainty has not been explicitly considered. Similarly, interactions between elasticity and uncertainty of demand have not been characterized. This study addresses these gaps and proposes a framework to estimate nearest optimal first-best tolls under long-term stochasticity in elastic demand. We show first that the optimal tolls under the deterministic-elastic and stochastic-elastic demand cases coincide when cost and demand functions are linear, and the set of equilibrium paths is constant. These assumptions are restrictive, so three larger networks are considered numerically, and the subsequent pricing decisions are assessed. The results of the numerical experiments suggest that in many cases, optimal pricing decisions under the combined stochastic-elastic demand scenario resemble those when demand is known exactly. The applications in this study thus suggest that inclusion of demand elasticity offsets the need of considering future demand uncertainties for first-best congestion pricing frameworks.     

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.     

Microeconomic theory and generalised cost

In a number of articles in this journal the use of generalised cost in travel demand analysis and transport planning has been subject to debate. However, some of the fundamental problems raised in these articles are left unanswered — e.g., the precise relationship between conventional microeconomic consumer demand theory and generalised cost, an issue with which this article is concerned. It is shown here that necessary and sufficient conditions for expressing travel demand in terms of generalised cost are that this cost, when measured in monetary units, is linear, and that the time variable is weighted by a constant marginal value of time. It is also shown that these conditions imply strong assumptions about the consumer's behaviour — e.g., that the willingness to pay to save time whilst travelling is not a function of real income.     

Itinerary choice and advance ticket booking for high-speed-railway network services

This paper formulates and examines the passenger flow assignment (itinerary choice) problem in high-speed railway (HSR) systems with multiple-class users and multiple-class seats, given the train schedules and time-varying travel demand. In particular, we take into account advance booking cost of travelers in the itinerary choice problem. Rather than a direct approach to model advance booking cost with an explicit cost function, we consider advance booking cost endogenously, which is determined as a part of the passenger choice equilibrium. We show that this equilibrium problem can be formulated as a linear programming (LP) model based on a three-dimension network representation of time, space, and seat class. At the equilibrium solution, a set of Lagrange multipliers for the LP model are obtained, which are associated with the rigid in-train passenger capacity constraints (limited numbers of seats). We found that the sum of the Lagrange multipliers along a path in the three-dimension network reflects the advance booking cost of tickets (due to advance/early booking to guarantee availability) perceived by the passengers. Numerical examples are presented to demonstrate and illustrate the proposed model for the passenger assignment problem.     

Inter-temporal variation in the travel time and travel cost parameters of transport models

The parameters for travel time and travel cost are central in travel demand forecasting models. Since valuation of infrastructure investments requires prediction of travel demand for future evaluation years, inter-temporal variation of the travel time and travel cost parameters is a key issue in forecasting. Using two identical stated choice experiments conducted among Swedish drivers with an interval of 13 years, 1994 and 2007, this paper estimates the inter-temporal variation in travel time and cost parameters (under the assumption that the variance of the error components of the indirect utility function is equal across the two datasets). It is found that the travel time parameter has remained constant over time but that the travel cost parameter has declined in real terms. The trend decline in the cost parameter can be entirely explained by higher average income level in the 2007 sample compared to the 1994 sample. The results support the recommendation to keep the travel time parameter constant over time in forecast models, but to deflate the travel cost parameter with the forecasted income increase among travellers and the relevant income elasticity of the cost parameter. Evidence from this study further suggests that the inter-temporal and the cross-sectional income elasticities of the cost parameter are equal. The average elasticity is found to be ?0.8 to ?0.9 in the present sample of drivers, and the elasticity is found to increase with the real income level, both in the cross-section and over time.     

Development of a transit network from a street map database with spatial analysis and dynamic segmentation

This paper presents an integrated transit-oriented travel demand modeling procedure within the framework of geographic information systems (GIS). Focusing on transit network development, this paper presents both the procedure and algorithm for automatically generating both link and line data for transit demand modeling from the conventional street network data using spatial analysis and dynamic segmentation. For this purpose, transit stop digitizing, topology and route system building, and the conversion of route and stop data into link and line data sets are performed. Using spatial analysis, such as the functionality to search arcs nearest from a given node, the nearest stops are identified along the associated links of the transit line, while the topological relation between links and line data sets can also be computed using dynamic segmentation. The advantage of this approach is that street map databases represented by a centerline can be directly used along with the existing legacy urban transportation planning systems (UTPS) type travel modeling packages and existing GIS without incurring the additional cost of purchasing a full-blown transportation GIS package. A small test network is adopted to demonstrate the process and the results. The authors anticipate that the procedure set forth in this paper will be useful to many cities and regional transit agencies in their transit demand modeling process within the integrated GIS-based computing environment.     

First-best marginal cost toll for a traffic network with stochastic demand

First-best marginal cost pricing (MCP) in traffic networks has been extensively studied with the assumption of deterministic travel demand. However, this assumption may not be realistic as a transportation network is exposed to various uncertainties. This paper investigates MCP in a traffic network under stochastic travel demand. Cases of both fixed and elastic demand are considered. In the fixed demand case, travel demand is represented as a random variable, whereas in the elastic demand case, a pre-specified random variable is introduced into the demand function. The paper also considers a set of assumptions of traveler behavior. In the first case, it is assumed that the traveler considers only the mean travel time in the route choice decision (risk-neutral behavior), and in the second, both the mean and the variance of travel time are introduced into the route choice model (risk-averse behavior). A closed-form formulation of the true marginal cost toll for the stochastic network (SN-MCP) is derived from the variational inequality conditions of the system optimum and user equilibrium assignments. The key finding is that the calculation of the SN-MCP model cannot be made by simply substituting related terms in the original MCP model by their expected values. The paper provides a general function of SN-MCP and derives the closed-form SN-MCP formulation for specific cases with lognormal and normal stochastic travel demand. Four numerical examples are explored to compare network performance under the SN-MCP and other toll regimes.     

Morning commute in a single-entry traffic corridor with no late arrivals

This paper analyzes a model of early morning traffic congestion, that is a special case of the model considered in Newell (1988). A fixed number of identical vehicles travel along a single-lane road of constant width from a common origin to a common destination, with LWR flow congestion and Greenshields’ Relation. Vehicles have a common work start time, late arrivals are not permitted, and trip cost is linear in travel time and time early. The paper explores traffic dynamics for the social optimum, in which total trip cost is minimized, and for the user optimum, in which no vehicle’s trip cost can be reduced by altering its departure time. Closed-form solutions for the social optimum and quasi-analytic solutions for the user optimum are presented, along with numerical examples, and it is shown that this model includes the bottleneck model (with no late arrivals) as a limit case where the length of the road shrinks to zero.     

A direct demand model for downtown work trips

This article documents the development of a direct travel demand model for bus and rail modes. In the model, the number of interzonal work trips is dependent on travel times and travel costs on each available mode, size and socioeconomic characteristics of the labor force, and the number of jobs. In estimating the models’ coefficients constraints are imposed to insure that the travel demand elasticities behave according to the economic theory of consumer behavior. The direct access time elasticities for both transit modes are estimated to be approximately minus two, and the direct linehaul time elasticities approximately minus one. The cross-elasticities with respect to the travel time components are estimated to be less than the corresponding direct elasticities. In general, the time cross-elasticities are such that rail trip characteristics but not car trip characteristics affect bus travel, and car trip characteristics but not bus trip characteristics affect rail travel. The cost elasticities lie between zero and one-half. Thus, the success of mass transit serving a strong downtown appears to depend on good access arrangements. This success can be confirmed with competitive linehaul speeds. The cost of travel appears to assume a minor role in choice of mode and tripmaking decisions. In the paper, a comparison is also made between the predictive performance of the models developed and that of a traditional transit model. The results indicate that the econometric models developed attain both lower percent error and lower variation of the error than the traditional model.     

Estimating origin‐destination matrices from link volume counts: a simple intercity auto travel demand model for Sri Lanka

The cost of nation wide travel surveys is high. Hence in many developing countries, planners have found it difficult to develop intercity transportation plans due to the non availability of origin‐destination trip matrices. This paper will describe a method for the intercity auto travel estimation for Sri Lanka with link traffic volume data.

The paper outlines the rationale of selecting the district capitals of Sri Lanka as its “cities,” the methodology for selecting the intercity road network, determination of link travel times from express bus schedules and the location of link volume counting positions.

Initially, the total auto travel demand model is formulated with various trip purpose sub‐models. This model is finally modified to a simple demand model with district urban population and travel times between city pairs as the exogenous variables, to overcome statistical estimation difficulties. The final demand model has statistics within the acceptable regions.

The advantages of a simple model are discussed and possible extensions are proposed.     

Estimating performance of traffic signals based on link travel times

Recent advances in communication and computing technology have made travel time measurements more available than ever before. In urban signalized arterials, travel times are strongly influenced by traffic signals. This study presents a novel method based on well‐known principles to estimate traffic signal performance (or more precisely their major “through” movements) based on travel time measurements. The travel times were collected between signals in the field by using point‐to‐point travel time measurement technologies. Closed‐circuit television cameras and signal databases were used to collect traffic demand and signal timings, respectively. Then, the volume/capacity ratio of major downstream signal movements was computed based on demand and signal timings. This volume/capacity ratio was then correlated with travel times on the relevant intersection approach. The best volume‐delay function was found, along with many other functions, to fit the field data. This volume‐delay function was then used to estimate volume/capacity ratios and, indirectly, a few other signal performance metrics. The method, called travel time‐based signal performance measurements, was automated and displayed on a Google Map. The findings show that the proposed method is accurate and robust enough to provide necessary information about signal performance. A newly developed volume‐delay function was found to work just slightly better than the Bureau of Public Roads curve. Several issues, which may reduce the accuracy of the proposed method, are identified, and their solutions are proposed for future research. Copyright © 2016 John Wiley & Sons, Ltd.     

The role of the passenger train in the United States: A cost comparison of the common carriers

The objective of this article is to establish whether the train has a role to play in the market for intercity passenger travel in the United States. To accomplish this objective, we compare the common carriers on the basis of thier cost effectiveness in moving a given flow of passengers between two points a specified distance apart. The comparisons are based on cost models which highlight the technological differences between the modes and eliminate distortions caused by public policy choices. By varying the size of the passenger flow and trip distance, we develop a notion of each common carrier's ideal operating environment. We find that the cost of the right-of-way is the major factor limiting the range of travel situations in which the train is cost competitive with the other common carriers. More specifically, our results indicate that Amtrak's service in the Northeast Corridor should be continued in the short run. In the long run, the possibility of upgrading Amtrak's service in the Northeast Corridor to high-speed service should be investigated. Outside the Northeast Corridor, we find that high-speed train service should be able to cover its operating costs but not its capital costs.     

The analysis of regulation on private highway investment under a build-operate-transfer scheme

The build-operate-transfer (BOT) approach has become an attractive instrument for public facility provision, especially for a project that faces difficulty with public finance. This study analyzes the regulation alternatives on private highway investment under a BOT scheme and their impacts on traffic flows, travel costs, toll, capacity, and social welfare (total user-benefit in the traffic system including congestion). For comparison, five cases are analyzed: (1) No BOT with maximizing welfare, (2) No BOT with breaking even on finance, (3) BOT without regulation, (4) BOT with a minimum flow constraint (the total users will not be less than those in Case 1), and (5) BOT with a maximum travel cost constraint (the travel cost for users on a non-tolled road will not exceed the maximum tolerance). After each case is modeled and simulated on some functional forms, we find that the case of BOT with regulations performs between the cases of maximizing welfare and that of maximizing profit. From the perspective of the government, regulation has less power in a project with low elastic demand. Furthermore, even when the regulation is strict, a high cost-efficient firm with BOT could result in a higher level of social welfare than that without a BOT scheme.     

Do travel cost models value transportation properly?

This paper examines whether travel cost models value transportation properly. It uses contingent behavior and contingent pricing analyses to explore the valuation of transport costs within the context of recreation demand. The contingent behavior analysis poses hypothetical increases in travel costs––travel distance and access fees––and examines the demand responses. In contrast, the ‘contingent pricing’ analysis asks respondents to state the increase in travel costs that is consistent with certain reductions in recreation demand, in this case, reductions that eliminate demand. By comparing distance-related responses to fee-related responses, the two analyses estimate factors for testing and improving the valuation of transport costs. To achieve these ends, the two analyses also explore the valuation of time costs.     

A dynamic station strategy to improve the performance of flex-route transit services

As an innovative combination of conventional fixed-route transit and demand responsive service, flex-route transit is currently the most popular type of flexible transit services. This paper proposes a dynamic station strategy to improve the performance of flex-route transit in operating environments with uncertain travel demand. In this strategy, accepted curb-to-curb stops are labeled as temporary stations, which can be utilized by rejected requests for their pick-up and drop-off. The user cost function is defined as the performance measure of transit systems. Analytical models and simulations are constructed to test the feasibility of implementing the dynamic station strategy in flex-route transit services. The study over a real-life flex-route service indicates that the proposed dynamic station strategy could reduce the user cost by up to 30% without any additional operating cost, when an unexpectedly high travel demand surpasses the designed service capacity of deviation services.