Multimodal Network Equilibrium Research Articles

A multi-modal network equilibrium model considering captive travelers and mode correlation

A multi-modal network equilibrium model considering captive travelers and mode correlation

A station location design problem in a bike-sharing system with both conventional and electric shared bikes considering bike users’ roaming delay costs

Bike-sharing systems (BSSs) have emerged in many cities worldwide. One key issue regarding the strategic design of BSSs is the deployment of bike stations. Innovations in technology have enabled new types of bikes, such as shared e-bikes, to work alongside conventional shared bikes. However, existing studies on bike station location design mainly focus on single bike type, and there is a lack of a theoretical model to determine the optimal bike station locations for a BSS where both conventional shared bikes and e-bikes are considered. This study investigates the station location design problem in a BSS with conventional shared bikes and e-bikes. The design problem is formulated as a bi-level optimization problem. The upper-level problem is to determine the optimal station locations with the objective of maximizing social welfare, and the lower-level problem is a multi-period multi-modal network equilibrium problem with pick-up and drop-off constraints. The upper-level problem is solved using the Genetic Algorithm, while the rolling horizon method is used to decompose the lower-level problem into multiple period-specific subproblems. Each subproblem is solved via a block Gauss-Seidel decomposition approach coupled with the revised simplex method and column generation. Numerical examples are given to demonstrate the properties of the problem, illustrate the performance of the solution algorithm, and offer key insights into the planning of BSSs.

Location of transit-oriented development stations based on multimodal network equilibrium: Bi-level programming and paradoxes

The unique relationship between the value capture mechanism (VCM) and transit-oriented development (TOD) stations and their peripheral areas, which progressively develops an expanded multimodal network, is well acknowledged in the transport industry. However, in regards to the location of TOD stations, insufficient attention has been paid to user travel behaviours and the operating mechanism of the multimodal network. To bridge this research gap, we develop a bi-level programming model for the location of TOD stations that analyses user travel behaviour in the multimodal network. The VCM and transit priority are the objectives of the upper level of this multi-objective optimization model. And the lower level of the model is a modified multimodal network equilibrium based on the Davidson function. Using a simple numerical simulation, this study proposes explanations for some traffic paradoxes from the perspective of a multimodal network equilibrium. We also illustrate competition and collaboration between rail and bus transport systems. Finally, this study uses an empirical case to describe the feasibility and applicability of the model. The results demonstrate that the location of TOD stations is not only one of the keys to the competitiveness of public transport but is also relevant to implementing its VCM.

Location of Transit-Oriented Development Stations Based on Multimodal Network Equilibrium: Bi-Level Programming and Paradoxes

Location of Transit-Oriented Development Stations Based on Multimodal Network Equilibrium: Bi-Level Programming and Paradoxes

An Activity-Based Multimodal Network Equilibrium Model with Interacting Mobility Service Providers' Strategies

An Activity-Based Multimodal Network Equilibrium Model with Interacting Mobility Service Providers' Strategies

A multi-modal network equilibrium model with captive mode choice and path size logit route choice

Abstract In this paper, we consider captive mode travelers (those who have no other choices but rely on one specific travel mode for daily commuting trips) in a multi-modal network equilibrium (MMNE) problem. Specifically, the dogit model is adopted to account for captive mode travelers in the modal split problem, and the path-size logit (PSL) model is used to capture route overlapping effects in the traffic assignment problem. The dogit-PSL MMNE model is formulated as an equivalent entropy-based mathematical programming (MP) problem, which admits solution existence and uniqueness. Three numerical examples are provided. The first example examines the effects of mode captivity and route overlapping on network performances and observes that accounting for captive mode travelers would produce different equilibrium states and hence the network performance indicators. The second example applies the dogit-PSL MMNE model for evaluating the exclusive bus lane (EBL) expansion plans, in which a consistent synthetic proportional index is proposed. Numerical results show that considering mode captivity may produce substantial impacts on the odds (up to 50 percent of odds in the given scenarios) of making different EBL line expansion decisions. The third example implements the dogit-PSL MMNE model in the Seoul network to show the applicability of the dogit-PSL MMNE model in a real-size multi-modal system.

Multimodal Network Equilibrium with Stochastic Travel Times

The private car, unlike public traffic modes (e.g., subway, trolley) running along dedicated track-ways, is invariably subject to various uncertainties resulting in travel time variation. A multimodal network equilibrium model is formulated that explicitly considers stochastic link capacity variability in the road network. The travel time of combined-mode trips is accumulated based on the concept of the mean excess travel time (METT) which is a summation of estimated buffer time and tardy time. The problem is characterized by an equivalent VI (variational inequality) formulation where the mode choice is expressed in a hierarchical logit structure. Specifically, the supernetwork theory and expansion technique are used herein to represent the multimodal transportation network, which completely represents the combined-mode trips as constituting multiple modes within a trip. The method of successive weighted average is adopted for problem solutions. The model and solution method are further applied to study the trip distribution and METT variations caused by the different levels of the road conditions. Results of numerical examples show that travelers prefer to choose the combined travel mode as road capacity decreases. Travelers with different attitudes towards risk are shown to exhibit significant differences when making travel choice decisions.

A Model for Evaluation of Transport Policies in Multimodal Networks with Road and Parking Capacity Constraints

This paper presents a model for evaluation of transport policies in multimodal networks with road and parking capacity constraints. The proposed model simultaneously considers choices of travelers on route, parking location and mode between auto and transit. In the proposed model, it is assumed that auto drivers make a simultaneous route and parking location choice in a user equilibrium manner, and the modal split between auto and transit follows a multinomial logit formulation. A mathematical programming model with capacity constraints on road link and parking facilities is proposed that generates optimality conditions equivalent to the requirements for multimodal network equilibrium. An augmented Lagrangian dual algorithm embedded by partial linearization approach is developed to solve the proposed model. Numerical results on two example networks are presented to illustrate the proposed methodology. The results show that the service level of transit, parking charges, road link and parking capacities, and addition of a new parking location may bring significant impacts on travelers’ behavior and network performance. In addition, transport policies may result in paradoxical phenomenon.

Network Performance Evaluation Model for HOV Facilities

A model to assess the impacts of major high-occupancy vehicle (HOV) facilities on regional levels of energy consumption and vehicle air pollution emissions in urban areas is developed and applied. This model can be used to forecast and compare the impacts of alternative HOV facility design and operation plans on traffic patterns, travel costs, mode choice, travel demand, energy consumption, and vehicle emissions. The model is designed to show differences in the overall impacts of alternative HOV facility types, locations, and operation plans, rather than to serve as a tool for detailed engineering design and traffic planning studies. The Network Performance Evaluation Model (NETPREM) combines several urban transportation planning models into a multimodal network equilibrium framework, including a module with which to define the type, location, and operation of the HOV facility to be tested, and an evaluation module with which to assess the impacts of this facility. As an example application, potential impacts of three different HOV lane/ramp facilities, when added to a major expressway in the Pittsburgh metropolitan area, are forecasted. The results of these example runs and potential improvements to the model are discussed.

Isomorphic multiclass spatial price and multimodal traffic network equilibrium models

In this paper, we first show that a multiclass spatial price equilibrium model can be formulated as an equivalent multimodal traffic network equilibrium model with special structure. This connection allows us to obtain, for the multiclass spatial price equilibrium model, in a routine manner, any information that is currently available in the well developed theory of the general multimodal network equilibrium model, and moreover, to strengthen a number of these results taking advantage of the special structure of the equivalent multimodal traffic network model.

Relaxation Algorithms for the General Asymmetric Traffic Equilibrium Problem

In this paper we establish the convergence of two relaxation algorithms designed to solve, respectively, the extended single-mode and the general multimodal network equilibrium problems. Both algorithms are shown to converge linearly; the first under the assumption that the cost functions are not too asymmetric; the second under the assumption that the cost interaction among the different modes is relatively weak.

The general multimodal network equilibrium problem with elastic demand

AbstractIn this article, we consider the general multimodal traffic equilibrium model with elastic demands. The link travel costs may depend upon the entire load pattern and the travel demands associated with each origin‐destination pair and mode may depend upon travel costs associated with every origin‐destination pair and every mode of transportation. For this model, we define the concepts of user‐optimality and equilibrium. We establish, by means of a constructive proof motivated by the theory of variational inequalities, the existence of a unique equilibrium under appropriate monotonicity conditions. We then show that the existence proof induces an algorithm for the computation of equilibrium traffic patterns. The algorithm proceeds by iteration, each step of which amounts to computing the equilibrium pattern for a single modal linear traffic equilibrium problem with elastic demands. We derive estimates for the speed of convergence.