Travel Cost Functions Research Articles

A novel route-based accessibility measure and its association with transit ridership

Transit systems play a key role in improving access to job opportunities and basic services such as health and education. Most studies in the literature calculate transit accessibility using traditional place-based indicators that measure accessibility at a given location. However, because transit routes are the main unit of analysis in most approaches for planning and operation of transit systems, these accessibility indicators provide limited information to inform transport planning at the route-level. In addition, previous studies have demonstrated the methodological limitations of traditional place-based accessibility metrics to study the association between accessibility and transit ridership. In this paper, we propose a novel route-based accessibility measure to fill the mentioned gaps. The indicator measures the average level of access to opportunities provided by a given transit route to the population in its extended catchment area. This indicator is flexible enough that it can be calculated using different travel cost functions and can be applied to measure access to different activity types for the whole population or for specific groups. To illustrate the applicability of the proposed indicator, we calculated the employment accessibility provided by all routes of the transit system of Fortaleza, Brazil. We also show that the proposed indicator has greater predictive power of transit ridership than other route-level accessibility measures found in the literature. This paper provides a methodological contribution that could help transport planners incorporate accessibility analysis into transit system redesign projects, and help practitioners anticipate what accessibility impacts and subsequent changes in transit ridership could be expected from route-level service changes, and to examine the influence of accessibility on transit ridership.

A System Optimization Approach for Trains’ Operation Plan with a Time Flexible Pricing Strategy for High-Speed Rail Corridors

Optimizing the train plan for high-speed rail systems should consider both the passengers’ demands and enterprise’s benefits. The choice of the departure time period is the most important factor affecting the passenger demand distribution. In this paper, the optimization problem of a train operation plan based on time period preference is studied for a high-speed rail corridor. First, according to the travel process of the passengers, the extended service network for a high-speed rail system is established. The main factors that influence the passengers’ travel choices are analyzed, and the departure time period preference, stop time and flexible pricing strategy based on the time period preference are put forward. The generalized travel cost function, including the convenience, ticket fare and stop time costs, is constructed, and a two-level programming model is established based on the function. The upper-level planning model is formulated as a mixed 0–1 programming problem that aims at maximizing the revenue of the railway enterprise. It is mainly constrained by passenger travel demand and solved by improved genetic algorithms. The lower-level model is a user equilibrium (UE) model. The Frank–Wolfe algorithm is used to allocate multiple groups of OD (origin and destination) passenger flows to each train so that the generalized travel expenses of all the passengers with the same OD are minimized and equal. Finally, the train operation plan is solved based on the Lan-xi (Lanzhou–Xi’an) high-speed rail data, and the validity of both the model and algorithm is verified.

Forwarding containers to dry ports in congested logistic networks

This work investigates the impact of container arrival flow rate on the port surrounding network and proposes a mixed integer programming model to optimize their forwarding towards dry port destinations. A novel efficient model with limited network capacity and time period dependent travel cost function is proposed. The aim is to give a decision support for operational planning with limited capacity of both the terminal yard and the logistic network, with respect to the quantity of containers transferred per time unit. The model considers time dependent costs and traveling times to reduce congestion. As a further novel issue of the model, arc costs and traveling times change during specific time slots. More precisely, new linear functions are derived as tangents to the nonlinear convex components of a classical traveling time function proposed in the literature. The aim is to produce a light model which can be effectively used for macro planning of forwarding operations. The model is proved to be fast in real case instances also if compared to classical literature approaches. The model is used to study the container dispatching process in a terminal which is going to be the main Italian container terminal equipped to manage mega-ship traffic. Results obtained from real-size instances are reported. We tested the behavior of the model under different scenarios. Our tests confirmed model efficiency and its of supporting the management of peak events also by controlling shut-down time slots to lower congestion.

Modeling the Combined Effect of Travelers’ Contrarian Behavior, Learning and Inertia on the Day-to-Day Dynamics of Route Choice

Understanding the many facets of repeated route choice behavior in traffic networks is essential for obtaining accurate flow forecasts and enhancing the effectiveness of traffic management measures. This paper presents a model of the day-to-day evolution of route choices incorporating travelers’ contrarian behavior, learning and inertia. The model is formulated as a discrete-time nonlinear dynamical system, and its properties are investigated analytically and numerically with a focus on the effect of the fraction of individuals adopting a contrarian route choice behavior. The findings of the study indicate that the extent of contrarian behavior may have significant impacts on the attractiveness and stability of network equilibria as well as on global system performance. We show that a properly balanced combination of direct and contrarian subjects can protect the system from instabilities triggered by other behavioral and network features. Our results also suggest that the fixed point stability range may depend to a considerable extent on travelers’ inertia and memory of previous experiences, as well as on the form of the travel cost functions used in the model. The occurrence of contrarian behavior should be explicitly taken into account in the design of traffic management schemes involving the deployment of Advanced Traveler Information Systems (ATISs), as it may act as a mitigating factor against the concentration of choices on the recommended routes. The analytical framework proposed in this paper represents a novel contribution, since contrarian behavior in repeated route choice has been investigated mainly by means of empirical or simulation approaches thus far.

Collective and individual spatial equity measure in public transit accessibility based on generalized travel cost

This study devises a novel two-dimensional analysis framework for spatial equity in public transit accessibility. We incorporated door-to-door travel time and ticket price by public transit into a generalized travel cost function to measure utility-based accessibility following a log-sum formulation. Then, this study designed a Palma ratio of accessibility and a neighboring accessibility gap index to respectively examine the collective spatial equity and individual spatial equity of public transit. Finally, we took an empirical case of Kunming city, China to analyze the unity-based accessibility distribution and checked collective and individual spatial equity levels reaching business centers, transport hubs, and 3-A hospitals. The results show that the utility-based accessibility reaching transport hubs by public transit is less than 50% to business centers and 32% to 3-A hospitals. Collectively, the expected minimum generalized travel cost by public transit in the poorest 40% of traffic analysis zones is almost 2.5 times as much as in the richest 10% of traffic analysis zones, and the collective spatial equity in old blocks is superior to new blocks. Individually, the number of traffic analysis zones with no spatial inequity, slight inequity, and medium inequity in public transit accessibility respectively occupied almost 57%, 38%, and 5%. We also found individual spatial equity may be associated with the walking distance during taking public transit and the number of neighboring traffic analysis zones.

Stochastic ridesharing equilibrium problem with compensation optimization

In the urban traffic system with ridesharing programs, we develop a generalized stochastic user equilibrium model to formulate travelers’ mode and route choice behavior. To suit more general scenarios, the proposed model takes into consideration travelers’ heterogeneity in terms of car ownership and value of time, and travelers’ limited perceived information based on the stochastic user equilibrium principle instead of Wardrop’s user equilibrium principle. The proposed model is formulated as variational inequalities and an equivalent nonlinear mixed complementarity problem due to the inseparable and asymmetric travel cost functions. Furthermore, we address the decision-making problem of ridesharing compensation from the perspective of traffic managers and policy-makers who want to minimize the total travel cost and vehicular air pollution emissions simultaneously. A bi-objective optimization model and two single-objective optimization models are proposed to formulate this decision-making problem, in which travelers’ mode and route choice behavior has been respected. As a mathematical problem with complementarity constraints, the bi-objective optimization model is solved by an improved Non-Dominated Sorting Genetic Algorithm II to generate a set of Pareto-optimal solutions for policy-makers and allow them to choose desired solutions. Finally, several numerical experiments based on two different scales of networks are conducted to demonstrate the properties of the problem and the performance of the proposed model and algorithm. The results show that rational pricing of ridesharing compensation can indeed mitigate urban traffic congestion and pollution emissions simultaneously. Moreover, by integrating travelers’ choice behavior based on the stochastic user equilibrium principle instead of the user equilibrium principle in the ridesharing compensation optimization model, this study derives a series of more effective decision-making strategies for ridesharing compensation.

Can day-to-day dynamic model be solved analytically? New insights on portraying equilibrium and accommodating autonomous vehicles

This paper develops a new approach to portray the equilibrium and analyze the appropriate lane policy during different deployment stages of autonomous vehicles (AVs) by innovatively integrating Vickrey's bottleneck model into the day-to-day dynamic model. The travel cost function in the classical bottleneck model is described by considering the impact of AVs’ value of time (VOT) reduction and AV gain. The evolution of lane choice behaviors is described using the first-order and second-order day-to-day dynamic model. Furthermore, three lane policies are proposed to accommodate AVs’ development, and the properties for the endogenous market penetration of AVs and travel cost under three lane policies are examined to recognize which policy is more suitable at different development stages of AVs. The results demonstrate that such equilibrium solutions as traffic flow, total travel cost, the convergence time are all analytically solvable and thus can perfectly answer the problem of stability and convergence involved in the day-to-day dynamic model. Finally, the numerical analysis is conducted to verify the previous findings and get some intuitive insights on system performance. This work not only provides new insights on the evolutionary process of AVs’ and regular vehicles (RVs)’ lane choice behaviors, but also recognizes appropriate lane policy to accommodate AVs from a novel perspective.

Research on the Deployment of Joint Dedicated Lanes for CAVs and Buses

CAVs (Connected Autonomous Vehicles) can be effective in improving the efficiency of transportation, but heterogeneous multi-modal traffic flows may hinder this efficiency. This paper addresses the issue of heterogeneous traffic flows affecting the efficiency of transportation when CAVs enter the market and proposes a joint dedicated lane for CAVs and buses. In the bi-level program model for the joint dedicated lane, the lower-level is aimed at the multi-modal traffic assignment problem, while the upper-level is aimed at system optimality. For the lower-level, the paper examines the characteristics of various traffic flows in a mixed traffic flow, investigates the impact of CAV mixing on the road link’s capacity, calculates the travel time of various traffic modes accordingly, and generates a generalized travel cost function for each mode, which is solved using the diagonalized weighted successive averaging method (MSWA) algorithm. The upper-level issue considers the continuity of dedicated and non-dedicated road segments, and the goal is to reduce the overall cost for all travelers by utilizing the dedicated road deployment scheme as the decision variable, which is addressed using a genetic algorithm. Finally, numerical examples and sensitivity analyses are designed accordingly. The numerical example demonstrates that the joint dedicated lane not only lowers the overall cost of the system, but also enhances the efficiency of CAV and bus travel, optimizing the road network and promoting bus and CAV travel modes. The sensitivity analysis shows that in order to set up a joint dedicated lane, the frequency of bus departures and the penetration of CAVs are conditions that must be considered, and that the benefits of a joint dedicated lane can only be fully realized if the frequency of bus departures and the penetration of CAVs are appropriate.

Research on Passenger Flow Assignment of Integrated Cross-Line and Skip-Stop Operation between State Railway and Suburban Railway

The passenger flow assignment in the rail transit network is the basis for determining the passenger spatiotemporal distribution and train operation organization plan. In previous studies, the passenger flow assignment problem mainly focused on lines within the same rail system. Few studies focus on lines with the integrated mode of cross-line and skip-stop operation between state and suburban railway due to fewer cases in practice. In this study, passenger congestion and fare policy are taken into account in the generalized travel cost function, and a passenger flow assignment model based on the path-sized logit (PSL) model considering train capacity is proposed. Meanwhile, a schedule-based spatiotemporal digraph is established to search for the shortest spatiotemporal travel path. Furthermore, an improved method of successive averages (MSA) algorithm is designed to solve the proposed model. The proposed model is verified by a numerical example. The sensitivities of three main parameters which influence the results are also analyzed. The results show that the assignment model based on PSL is practicable in integrated operation mode. The higher the passenger’s familiarity with network information, the more accurate the assignment results. State trains are more attractive when the fare is lower than 0.5 CNY/km or the hourly wage is higher than 50 CNY/h.

General attraction analysis on high-speed rail and aviation between Beijing and Shanghai, China

High-speed rail and aviation are the two most popular modes of transportation between Beijing and Shanghai. Based on the existing literature, this paper summarized seven key influencing factors of the high-speed rail and civil aviation comprehensive attraction from the Beijing-Shanghai corridor. Furthermore, we constructed five single index models to quantify them. By analysing the logical relationships among various indicators, the generalized travel cost function with different modes of transportation and different user types under different seasons is finally obtained. To ensure the reliability of the analysis results, the collected data were used to calibrate most of the parameters of the generalized cost function model. After that, a series of sensitivity analysis are conducted. The results show that the attractiveness ranking of these two transportation modes is influenced by the purpose of the trip, the characteristics of the passengers, and changes in the season. This paper may offer some valuable references for aviation and railway transport companies.

Route recommendation based on temporal–spatial metric

The acquisition and analysis of large amounts of mobile trajectory data promote the rapid development of mobile recommender systems, which can essentially recommend a series of positions to the mobile users. In this paper, we concentrate on the mobile sequential recommendation problem by considering both the distance and time factors, the objective of which is to recommend an optimal driving route consisting of a sequence of pick-up locations for the drivers. Firstly, we formulate this problem and develop a potential travel cost function to comprehensively evaluate each candidate route. Then we propose an efficient and effective Route recommendation based on Temporal-Spatial metric scheme called RTS, which adopts the simulated annealing algorithm and can achieve real-time route recommendation without severely sacrificing the recommendation performance. The extensive experiments based on both the real-world and synthetic data are conducted, the results of which demonstrate the efficiency and effectiveness of the proposed RTS scheme.

On Stochastic-User-Equilibrium-Based Day-to-Day Dynamics

Researchers have proposed many different concepts and models to study day-to-day dynamics. Some models explicitly model travelers’ perceiving and learning on travel costs, and some other models do not explicitly consider the travel cost perception but instead formulate the dynamics of flows as the functions of flows and measured travel costs (which are determined by flows). This paper investigates the interconnection between these two types of day-to-day models, in particular, those models whose fixed points are a stochastic user equilibrium. Specifically, a widely used day-to-day model that combines exponential-smoothing learning and logit stochastic network loading (called the logit-ESL model in this paper) is proved to be equivalent to a model based purely on flows, which is the logit-based extension of the first-in-first-out dynamic of Jin [Jin W (2007) A dynamical system model of the traffic assignment problem. Transportation Res. Part B Methodological 41(1):32–48]. Via this equivalent form, the logit-ESL model is proved to be globally stable under nonseparable and monotone travel cost functions. Moreover, the model of Cantarella and Cascetta is shown to be equivalent to a second-order dynamic incorporating purely flows and is proved to be globally stable under separable link cost functions [Cantarella GE, Cascetta E (1995) Dynamic processes and equilibrium in transportation networks: Towards a unifying theory. Transportation Sci. 29(4):305–329]. Further, other discrete choice models, such as C-logit, path-size logit, and weibit, are introduced into the logit-ESL model, leading to several new day-to-day models, which are also proved to be globally stable under different conditions.

Participation in Shared Mobility: An Analysis of the Influence of Walking and Public Transport Accessibility to Vehicles on Carsharing Membership in Montreal, Canada

In the context of sustainable mobility policies, carsharing services have gained importance as an alternative to personal vehicles. In an effort to increase the adherence to and use of such services, several studies have explored the key factors that determine use and membership. Although the ease with which individuals can access shared vehicles appears to be a central determinant, few studies have specifically investigated how to measure station and vehicle accessibility. To fill this gap, this study seeks to systematically assess and compare the contribution of different accessibility indicators to modeling carsharing membership rate, using 2016 data from the Montreal carsharing company Communauto and from the Canadian census. Three indicators of accessibility to in-station vehicles are generated: walking only, public transport only, and multimodal accessibility (walking and public transport), considering a variety of travel time thresholds and cost functions. A linear regression model is then generated to assess the contribution of the different indicators to modeling membership rates, while controlling for socio-economic and commuting characteristics. The results show that walking accessibility, within 20 minutes, and public transport accessibility, within 40 minutes, are both key determinants of membership rate and in a complementary manner. The influence of public transport accessibility is positive and highest when walking accessibility is low. The results also demonstrate that the use of a cumulative or weighted-opportunity indicator is equally sound from an empirical perspective. The study is of relevance to researchers and planners wishing to better understand and model the influence of vehicle accessibility.

Will We Fly Again? Modeling Air Travel Demand in light of COVID-19 through a London Case Study.

The COVID-19 pandemic and associated travel restrictions have created an unprecedented challenge for the air transport industry, which before the pandemic was facing almost the exact opposite set of problems. Instead of the growing demand and need for capacity expansion warring against environmental concerns, the sector is now facing a slump in demand and the continuing uncertainty about the impacts of the pandemic on people's willingness to fly. To shed light on consumer attitudes toward air travel during and post the pandemic, this study presents an analysis that draws on recently collected survey data (April-July 2020), including both revealed and stated preference components, of 388 respondents who traveled from one of the six London, U.K., airports in 2019. Several travel scenarios considering the circumstances and attitudes related to COVID-19 are explored. The data is analyzed using a hybrid choice model to integrate latent constructs related to attitudinal characteristics. The analysis confirms the impact of consumers' health concerns on their willingness to travel, as a function of travel characteristics, that is, cost and number of transfers. It also provides insights into preference heterogeneity as a function of sociodemographic characteristics. However, no significant effects are observed concerning perceptions of safety arising from wearing a mask, or concerns over the necessity to quarantine. Results also suggest that some respondents may perceive virtual substitutes for business travel, for example video calls and similar software, as only a temporary measure, and seek to return to traveling as soon as it is possible to do so safely.

Dynamic user equilibrium for departure time choice in the basic trip-based model

Recent research indicates that the trip-based models can perform more accurately for capturing network hyper-congestion than the conventional macroscopic fundamental diagram (MFD) dynamics, especially during transient phases. However, due to the complex mathematical structure of the trip-based models, deriving analytical properties of the dynamic user equilibrium (DUE) of departure time choice with the trip-based models is still a challenge. This paper investigates the DUE problem of departure time choice in an isotropic urban network with identical travelers. Traffic dynamics is captured by the basic trip-based model using a speed-MFD that maps the traffic accumulation to the space-mean speed of the network. Necessary conditions for dynamic user equilibrium with and without inflow capacity constraint are derived, respectively. Under dynamic user equilibrium condition, no traveler can reduce her/his travel cost by changing the departure time. The analysis reveals the significant difference between the basic trip-based model and the conventional MFD models regarding the information support involved in the departure time choice. The derivation does not rely on some common assumptions in the literature such as linear travel cost function, no late arrivals, or linear speed-MFD. The numerical example indicates that the inflow capacity constraint can help prevent two peaks in the departure profile and the vehicle accumulation.

Extracting the Relationship and Evolutionary Rule Connecting Residents' Travel Demand and Traffic Supply Using Multisource Data.

Urban rail transit (URT) systems are often regarded as the backbone of their respective city. The evolutionary features of URT systems have attracted much attention in recent years, but their evolution and their distinct function in contrast to other transit modes have seldom been investigated, especially quantitatively from the perspective of work–residence separation. Accordingly, we propose a framework for exploring the evolution of URT topological networks and demand-weighted networks, comparing the different impacts of all transit modes on work–residence separation. In this study, a URT passenger flow assignment model was formulated on the basis of travel cost function and an improved logit model was proposed that takes into account the heterogeneity of passengers. This model was used to generate a section load, which is regarded as a weight and able to reflect the residents’ demand for travel by URT. Then, the fractal dimensions for a non-weighted network and demand-weighted network are proposed and their indications for transportation explained. Finally, the Beijing Subway System (BSS) is used as a case study by employing fifty years of network data and ten years of smart card data. Using fractal approaches, the different characteristics illustrated by the two networks were investigated and the reasons behind the observed patterns explained. In addition, the spatial features of the rail network, in terms of fractal indictors, were compared with population distribution and urban mobility for all modes, extracted from phone data as a proxy. Thus, the relationship between the residents’ travel demand and traffic supply can be revealed to some extent. The main finding of this work is that demand must be taken into account when analyzing the fractal features of a transport network, lest the demand side be separated from the supply and important issues missed such as inconsistencies between demand and supply. Additionally, the role of rail transit in work–home imbalance can be investigated in the context of urban mobility for an entire city.

Model and algorithm of stochastic dynamic traffic assignment based on dynamic rainfall intensity

Frequent occurrence of urban rainy weather, especially rainstorm weather, affects transportation operation and safety, so it is essential that effective intervention measures to recover disordered traffic be adopted and then analyzed for their influence on the dynamic network. Therefore, models and algorithm to show dynamic traffic flow of traffic network in rainy weather are a fundamental need and have drawn great interest from governments and scholars. In this paper, innovative content contains a travel cost function considering rainfall intensity; considering the travel cost function, a dynamic traffic assignment model based on dynamic rainfall intensity is built. Then a corresponding algorithm is designed. Moreover, this study designs three scenarios under rainfall and analyzes the influence of the rainfall on an example network. The results show that rainfall has a significant effect on traffic flow. The finding proved the proposed models and algorithm can express the development trend of path flow rate on a dynamic network under rainfall.

Enforcing fuel-optimal traffic patterns

Traffic Assignment (TA) models route choices of users of a road transport network assuming a known relationship between traffic flow and travel cost, and fixed demand between origin and destination points in the network. In this paper, we consider the case where the users’ travel cost function is a weighted sum of travel time, fuel consumption, and tolls. We show the existence of speed limits and tolls whose combination induces a traffic pattern with minimum total fuel consumption as a user equilibrium. This result holds both in the case where all tolls are required to be non-negative as well as in the case where negative tolls (subsidies) are allowed but network-wide revenue neutrality of the toll scheme is required. With respect to the speed limits, arbitrary non-negative values are allowed in our model, but we additionally analyze the more realistic scenario in which only a discrete set of speed limits (e.g., integer multiples of ten) is available. While this restriction of the available speed limits may lead to an increase in the total fuel consumption achievable in a user equilibrium, we prove upper bounds showing that the increase is very small for real-world TA instances.

Comparison of Contingent Valuation and Travel Cost Methods to Estimate Outdoor Recreation Value of Recreation, Tourism and Aesthetic Function of Bamou National Park

Background and Objective: Valuation of functions and Non-Market services of environment are important for many reasons such as identifying and understanding the environmental and ecological benefits by humans, presentation of environmental issues to decision makers and planners, providing link between economic policies and natural revenues and assess the role and importance of environmental resources in support of human welfare and sustainable development. Methods: In this study, recreational value of Bamou Park is estimated and measured with using two methods of contingent value and travel cost. For this purpose, 315 questionnaires from visitor to extract the required data have been matched. Findings: Based on estimated results, variables: inhabitance, distance from park, first visit, number of visit, Deontologist, education, travel cost, visitors income, museum existence, and existence of Animal species such as deer, wolf, wild ram and cinereous vulture is effective variable on willingness to pay of visitor in 2011. Results show that monthly expected willingness to pay of consequentialist and deontologist visitors is 51397 and 61028 Rial respectively. Finally, recreational value of Bamou Park estimated in 2 methods is 1.085 and 1.975 Billion Rial respectively in 2011. Discussion and Conclusion: Since that travel cost method used market price information and revealed willingness to pay and also 90.7 percentages of visitors are Zone inhabitance and travel cost function was ideal form econometrics theoretical aspect, preferred using travel cost method instead of contingent value method to valuating the Bamou National Park in 2011.

Dynamic System Optimum Analysis of Multi-Region Macroscopic Fundamental Diagram Systems With State-Dependent Time-Varying Delays

This paper investigates the dynamic system optimum (DSO) problem with simultaneous route and departure time assignments for a general traffic network partitioned into multiple regions. Regional traffic congestion is modeled with a well-defined macroscopic fundamental diagram (MFD) mapping the trip completion rate to the vehicular accumulation. To overcome the limitation of inconsistent flow propagation between region boundaries and the corresponding travel time, the state-dependent regional travel time function is explicitly incorporated in the flow propagation of the conventional MFD dynamics. From a systems perspective, the traffic dynamics within a region can be regarded as a dynamic system with an endogenous time-varying delay depending on the system state. Equilibrium condition for the DSO problem is analytically derived through the lens of Pontryagin minimum principle and is compared against the static SO counterpart. The structure of path specific marginal cost is analyzed regarding the path travel cost and early-late penalty function. In contrast to existing analytical methods, the proposed method is applicable for general MFD systems without linearization of the MFD dynamics. Neither approximation of the equilibrium solution nor constant regional delay assumption is required. Numerical examples are conducted to illustrate the characteristics of DSO traffic equilibrium and the corresponding marginal cost together with other dynamic external costs.