Bi-modal Transportation System Research Articles

Perimeter control in a mixed bimodal bathtub model

Perimeter control involves monitoring network-wide traffic and regulating traffic inflow to alleviate hypercongestion. Implementation of transit priority with perimeter control measures, which allow transit into a controlled area without queuing at the perimeter boundary, is an effective strategy in bimodal transportation systems. However, travelers’ behavior changes in response to perimeter control strategies, such as shifts in their departure times and transportation modes, have not been fully investigated. Therefore, important questions remain, such as the use of transit during perimeter control with transit priority. This paper examines the travelers’ behavior changes in response to perimeter control with transit priority in a mixed bimodal transportation system with cars and flexible route transit (FRT) vehicles. We model departure time and transportation mode choices in such a transportation system with hypercongestion and discomfort in FRT (called the mixed bimodal bathtub model). Initially, we investigate the properties of dynamic user equilibrium without perimeter control. Then, we study the equilibrium patterns during perimeter control with transit priority. Unlike existing works, we find that the number of FRT passengers decreases with time toward the desired arrival time and that FRT may not be used around the peak of rush hour. Furthermore, transit priority may not be sufficient to promote the use of FRT, and additional incentive such as subsidy for lower fares may be required to encourage FRT use during perimeter control. Finally, we show that operating many FRT vehicles does not always decrease the equilibrium cost, even under perimeter control with transit priority.

Optimal Fleet Deployment Strategy: Model the Effect of Shared E-Bikes on Bike-Sharing System

Following the bike-sharing system, the shared e-bike becomes increasingly popular due to the advantage in speed, trip distance, and so forth. However, limited research has investigated the impact of the introduction of shared e-bikes on the existing bike-sharing systems. This paper aims to study the effect of shared e-bikes on the traditional bike-sharing system and determine the optimal fleet deployment strategy under a bimodal transportation system. A stochastic multiperiod optimisation model is formulated to capture the demand uncertainty of travelers. The branch-and-bound algorithm is applied to solve problem. A 15-station numerical example is applied to examine the validity of the model and the effectiveness of the solution algorithm. The performance of integrated e-bike and bike-sharing system has been compared with the traditional bike-sharing system. The impacts of the charging efficiency, fleet size, and pricing strategy of e-bike-sharing system on the traditional bike-sharing system have been examined.

Learning and managing stochastic network traffic dynamics with an aggregate traffic representation

This study estimates and manages the stochastic traffic dynamics in a bi-modal transportation system, and gives hints on how increasing data availability in transport and cities can be utilized to estimate transport supply functions and manage transport demand simultaneously. In the bi-modal system, travelers’ mode choices are based on their perceptions of the two travel modes: driving or public transit. Some travelers who have access to real-time road (car) traffic information may shift their mode based on the information received (note that real-time information about public transit departures/arrivals is not considered here). For the roadway network, the within-day traffic evolution is modeled through a Macroscopic Fundamental Diagram (MFD), where the flow dynamics exhibits a certain level of uncertainty. A non-parametric approach is proposed to estimate the MFD. To improve traffic efficiency, we develop an adaptive pricing mechanism coupled with the learned MFD. The adaptive pricing extends the study of Liu and Geroliminis (2017) to the time-dependent case, which can better accommodate temporal demand variations and achieve higher efficiency. Numerical studies are conducted on a one-region theoretical city network to illustrate the dynamic evolution of traffic, the MFD learning framework, and the efficiency of the adaptive pricing mechanism.

Mode choice and railway subsidy in a congested monocentric city with endogenous population distribution

The objective of this paper is to provide new insights into commuters’ mode choice behavior in a monocentric closed city with endogenous population distribution, where a congested highway and a crowded railway provide commuting services for residents on a linear urban corridor. We first explore the typical equilibrium mode-choice patterns with exogenous city boundary and population distribution, and then incorporate the residents’ mode choice into an urban spatial equilibrium model, in which the residents’ household consumption, the residential location choice and the property developers’ housing production are also explicitly modeled. Using comparative static analysis, we find that the urban corridor expands with the increase of railway fare if there is no congestion in the bimodal transportation system, but it’s not necessarily the case if highway congestion and transit crowding cannot be ignored. We provide numerical evidence to show that the urban corridor possibly shrinks with the increase of railway fare once congestion effects are considered. We also discuss the changes of urban form, utility level of residents and social welfare with different railway fare and subsidy policies. Numerical results show that the distance-based fare policy with low subsidy should be preferred because it can realize the Pareto-improved social welfare and utility level of residents.

Traffic dynamics in a bi-modal transportation network with information provision and adaptive transit services

This paper has two major components. The first one is the day-to-day evolution of travelers’ mode and route choices in a bi-modal transportation system where traffic information (predicted travel cost) is available to travelers. The second one is a public transit operator adjusting or adapting its service over time (from period to period) based on observed system conditions. Particularly, we consider that on each day both travelers’ past travel experiences and the predicted travel cost (based on information provision) can affect travelers’ perceptions of different modes and routes, and thus affect their mode choice and/or route choice accordingly. This evolution process from day to day is formulated by a discrete dynamical model. The properties of such a dynamical model are then analyzed, including the existence, uniqueness and stability of the fixed point. Most importantly, we show that the predicted travel cost based on information provision may help stabilize the dynamical system even if it is not fully accurate. Given the day-to-day traffic evolution, we then model an adaptive transit operator who can adjust frequency and fare for public transit from period to period (each period contains a certain number of days). The adaptive frequency and fare in one period are determined from the realized transit demands and transit profits of the previous periods, which is to achieve a (locally) maximum transit profit. The day-to-day and period-to-period models and their properties are also illustrated by numerical experiments.

Day-to-day modal choice with a Pareto improvement or zero-sum revenue scheme

We investigate the day-to-day modal choice of commuters in a bi-modal transportation system comprising both private transport and public transit. On each day, commuters adjust their modal choice, based on the previous day's perceived travel cost and intraday toll or subsidy of each mode, to minimize their perceived travel cost. Meanwhile, the transportation authority sets the number of bus runs and the tolls or subsidies of two modes on each day, based on the previous day's modal choice of commuters, to simultaneously reduce the daily total actual travel cost of the transportation system and achieve a Pareto improvement or zero-sum revenue target at a stationary state. The evolution process of the modal choice of commuters, associated with the strategy adjustment process of the authority, is formulated as a dynamical system model. We analyze several properties of the dynamical system with respect to its stationary point and evolutionary trajectory. Moreover, we introduce new concepts of Pareto improvement and zero-sum revenue in a day-to-day dynamic setting and propose the two targets’ implementations in either a prior or a posterior form. We show that, although commuters have different perceived travel costs for using the same travel mode, the authority need not know the probability distribution of perceived travel costs of commuters to achieve the Pareto improvement target. Finally, we give a set of numerical examples to show the properties of the model and the implementation of the toll or subsidy schemes.

Interactive travel choices and traffic forecast in a doubly dynamical system with user inertia and information provision

This study models the joint evolution (over calendar time) of travelers’ departure time and mode choices, and the resulting traffic dynamics in a bi-modal transportation system. Specifically, we consider that, when adjusting their departure time and mode choices, travelers can learn from their past travel experiences as well as the traffic forecasts offered by the smart transport information provider/agency. At the same time, the transport agency can learn from historical data in updating traffic forecast from day to day. In other words, this study explicitly models and analyzes the dynamic interactions between transport users and traffic information provider. Besides, the impact of user inertia is taken into account in modeling the traffic dynamics. When exploring the convergence of the proposed model to the dynamic bi-modal commuting equilibrium, we find that appropriate traffic forecast can help the system converge to the user equilibrium. It is also found that user inertia might slow down the convergence speed of the day-to-day evolution model. Extensive sensitivity analysis is conducted to account for the impacts of inaccurate parameters adopted by the transport agency.

Tradable credits scheme and transit investment optimization for a two‐mode traffic network

SummaryThis paper proposes an optimization model to minimize the “system costs” and guide travelers' behavior by exploring the optimal bus investment and tradable credits scheme design in a bimodal transportation system. Travelers' transport mode choice behavior (car or bus) and the modal equilibrium conditions between these two forms of transport are studied in the tradable credits scheme. Public transport priority is highlighted by charging car travelers credits only. The economies of scale presented by the transit system under the tradable credit scheme are analyzed by comparing the marginal cost and average cost. Numerical examples are presented to demonstrate the model. Furthermore, the effects of tradable credits schemes on bus investment and travelers' modal choice behavior are explored based on scenario discussions. Copyright © 2016 John Wiley & Sons, Ltd.

Dynamics of modal choice of heterogeneous travelers with responsive transit services

In this paper, we investigate travelers’ day-to-day modal choice in a bi-modal transportation system with responsive transit services under various economic objectives. A group of travelers with heterogeneous preferences adjust their modal choice each day based on their perceived travel cost of each mode, aiming to minimize their travel cost. Meanwhile, the transit operator sets frequency each period according to the realized transit demand and previous frequency, trying to achieve different profit targets. For a given profit target, the fixed point of equilibrium may not be unique. We establish the condition for existence of multiple fixed points and examine the stability of the fixed points in each case. Furthermore, in view of a socially desirable mode choice, we also investigate the impacts of total travel demand and bus size on the convergence of the system to various fixed points associated with different targeted mode split. Finally, we use several numerical examples to illustrate the theoretical results and their practical implications for the transit operator to design appropriate transit schemes in a dynamic transportation environment.

A Bimodal Transportation Model for Steam Coal Exportation Based on Magdalena River as Main Waterway

The aim of this work is to offer a new alternative to allow the release of the Colombian coal transportation system that nowadays is under a saturation state. For this reason it is proposed, the option of making the exportation of the surplus production granted by the thermic coal mining activity focused on the Cesar department, through a bimodal transportation system that will highlight on the Magdalena River as the most important way for the logistic development of the country. As main key and support tool, the Discrete Event Simulation (DES) methodology was used for conducting experiments based on information which has given the characterization of the proposed system. Hence, the establishment of the conceptual model that determinated and limit the system, a simulation in the software Rockwell Arena was implemented which results were tested and analyzed to study the performance of itself.

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

SUMMARYThis 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.

Modeling intermodal equilibrium for bimodal transportation system design problems in a linear monocentric city

This paper investigates the intermodal equilibrium, road toll pricing, and bus system design issues in a congested highway corridor with two alternative modes – auto and bus – which share the same roadway along this corridor. On the basis of an in-depth analysis of the demand and supply sides of the bimodal transportation system, the mode choice equilibrium of travelers along the continuum corridor is first presented and formulated as an equivalent variational inequality problem. The solution properties of the bimodal continuum equilibrium formulation are analytically explored. Two models, which account for different infrastructure/system regulatory regimes (public and private), are then proposed. In the public regulatory model, the road toll location and charge level are simultaneously optimized together with the bus service fare and frequency. In the private regulatory model, the fare and frequency of bus services, which are operated by a profit-driven private operator, are optimized for exogenously given toll pricing schemes. Finally, an illustrative example is given to demonstrate the application of the proposed models. Sensitivity analysis of residential/household distribution along the corridor is carried out together with a comparison of four different toll pricing schemes (no toll, first best, distance based, and location based). Insightful findings are reported on the interrelationships among modal competition, market regulatory regimes, toll pricing schemes, and urban configurations as well as their implications in practice.

Integration of Traffic Management and Traveller Information Systems: Basic Principles and Case Study in Intermodal Transport System Management

As they involve many interacting agents behaving in numerous ways that are extremely difficult to predict, urban transportation systems are complex in nature. The development of intermodal passenger transportation solutions to address the mobility issues constitutes a major thrust area of urban transport policies. But, to offer citizens comprehensive seamless mobility, intermodal transportation system management (ITSM) requires the integration of two major components. The traffic regulation support system, to help the operator responsible for the regulation tasks: coordination of timetables, synchronising arrival and departure times between the different transportation modes, and the traveller information system, giving customers access to information and using a comprehensive set of information tools. In this paper, a generic model of a transport management system, integrating these two components is proposed. This generic model is then used to elaborate a traffic regulation system in the case of a bimodal transportation system (tram-bus). The traffic regulation support system, based on the decision model of an operator, and the traveler information system are described.

Pricing and logit-based mode choice models of a transit and highway system with elastic demand

The objective of this paper is to enhance the insights into transport pricing mechanism and the corresponding mode choice behavior in a simple bi-modal transportation system with elastic demand. This system comprises a mass transit parallel to a bottleneck-constrained highway between a residential area and a workplace. We derive and compare three pricing schemes: the arbitrarily fixed pricing, the first-best pricing for a social optimum of the system, and the second-best pricing in the case of incapability of road toll. It is shown that the first-best pricing requires to implement a road toll and a transit fare simultaneously, and the optimal transit fare for the second-best solution should be set to be a weighted sum of the marginal external costs between auto and transit commuters. A numerical example is presented to illustrate how the pricing policies affect the demand implementation, the mode choice behavior and the efficiency of the whole transportation system.

Self-reinforcing motorization: can travel demand management take us out of the social trap?

Motorization is a self-reinforcing process, which involves positive feedback. Using a simple model of bi-modal transportation system, it is shown that a transportation system may eventually be dominated by the automobile, or may equilibrate at a grossly inefficient point due to social dilemmas associated with automobile use. Furthermore, in areas with well-developed public transit, road capacity addition can be detrimental not only to the public transit but also to the automotive transportation. Travel demand management (TDM) measures are conceived in this study as mechanisms to prevent the divergence of the motorization process away from a social optimum due to its positive feedback and social dilemmas. A simple model of bi-modal transportation system and a cellular automata model of individuals’ TDM compliance behavior are combined in the study to see how TDM measures that rely on individuals’ voluntary cooperation may be effective. Results of simulation analyses based on the model are presented.