Hai-Jun Huang

THE MULTI-CLASS, MULTI-CRITERIA TRAFFIC NETWORK EQUILIBRIUM AND SYSTEMS OPTIMUM PROBLEM

It is well known that in the standard traffic network equilibrium model with a single value of time (VOT) for all users, a so-called marginal-cost toll can drive a user equilibrium flow pattern to a system optimum. This result holds when either cost (money) or time units are used in expressing the objective function of the system optimum and the criterion for user equilibrium. This paper examines the multi-criteria or the cost-versus-time network equilibrium and system optimum problem in a network with a discrete set of VOTs for several user classes. Specifically, the following questions are investigated: Are the user-optimal flows dependent upon the unit (time or money) used in measuring the travel disutility in the presence of road pricing? Are there any uniform link tolls across all individuals (link tolls that are identical for all user classes) that can support a multi-class user equilibrium flow pattern as a system optimum when the system objective function is measured by either money or time units? What are the general properties of the valid toll set?

Modeling and solving the dynamic user equilibrium route and departure time choice problem in network with queues

Abstract This paper considers a simultaneous route and departure (SRD) time choice equilibrium assignment problem in network with queues. The problem is modeled on discrete-time basis and formulated as an equivalent “zero-extreme value” minimization problem, in which the first-in-first-out (FIFO) behavior at intersection is guaranteed by proper formulation of the dynamic link travel times. A heuristic solution algorithm is proposed, which simulates a normal day-to-day dynamic system by a route/time-swapping process, thereby reaching to an extreme point of the minimization problem. The existence of discrete-time dynamic user-equilibrium (UE) solutions is investigated. The iteration-to-iteration stability of the proposed algorithm is discussed, together with numerical results on two example networks.

Principle of marginal-cost pricing: how does it work in a general road network?

Most previous theoretical arguments on congestion pricing are based on the fundamental economic principle of marginal-cost pricing, and are entirely concerned with abstract travel demand-supply models. There exists in the literature considerable confusion on analysis of congestion which needs to be clarified. There are also many interesting, and important issues to be explored when detailed network modeling is involved. This paper makes a theoretical investigation into how this classical economic principle would work in a general congested road network. Some new explanations of the marginal-cost pricing and its implications under different equilibrium conditions are presented.

Analysis of the time-varying pricing of a bottleneck with elastic demand using optimal control theory

In this paper, a time-varying pricing model of a road bottleneck with elastic traffic demand is formulated using the optimal control theory. It is assumed that the optimal use of the bottleneck is achieved when social benefit over the whole time horizon of study is maximized. The necessary conditions for optimal solution are derived and their economic interpretations are given. Different from conventional analyses, queuing is not pre-assumed to be zero when obtaining the optimal time-varying toll, and the exit capacity of the bottleneck is assumed either to be constant or to vary with queue length. An approximate iterative algorithm is proposed for solving the model in a discrete time version. Three numerical examples are presented to demonstrate the applications of the proposed model and algorithm.

A multiclass, multicriteria logit-based traffic equilibrium assignment model under ATIS

This paper presents a multiclass, multicriteria (cost versus time) logit-based traffic equilibrium assignment model in road networks served by advanced traveler information systems (ATIS). All users are differentiated by their own value of time (VOT) that follows some probability distribution. Users of each class, having their own VOT, are further divided into two groups, equipped and unequipped with ATIS respectively. The travel disutility received by each user is defined as a linear bi-criteria combination of travel time and monetary travel cost. It is assumed that all users make their route choices in a logit-based stochastic manner, but the equipped users have lower perception variation on the travel disutility than the unequipped due to the ATIS service. The model is formulated as a fixed-point problem and solved by the method of successive averages in conjunction with logit assignment. Numerical results show that the traditional single-class and/or single-criterion models may overestimate or underestimate the benefit from ATIS services. 2005 Elsevier B.V. All rights reserved.

Carpooling and congestion pricing in a multilane highway with high-occupancy-vehicle lanes

High-occupancy-vehicle (HOV) lanes and toll differentiation have been used as efficient measures to address growing traffic congestion problems by providing priority treatment for buses and carpools. This paper deals with carpooling behavior and optimal congestion pricing in a multilane highway with or without HOV lanes. It is shown that in the absence of HOV lanes, a uniform toll for all vehicles (independent of their number of occupants) should be charged to achieve a first-best social optimum. However, in the presence of HOV lanes, first-best pricing for a social optimum requires differentiating the toll per vehicle across segregated lanes. In the case where toll differentiation cannot be applied, the optimal uniform toll for the second-best solution in the presence of HOV lanes should be set to be a weighted average of the marginal external congestion costs between non-carpooling and carpooling commuters. Our theoretical observations have strong practical implications for combined implementation of HOV lanes and congestion pricing.

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

Abstract 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.

Dynamic User Optimal Traffic Assignment Model for Many to One Travel Demand

A freeway or expressway corridor where all vehicles travel to the same destination such as the city centre is considered in this article, similar to the morning commute problem. A continuous time optimal control model that deals with the dynamic user optimal assignment for multiple origins and single destination is proposed. The splitting rates of traffic flows at each network node are defined as the control variables in this model. The optimality conditions are proved to be equivalent to the dynamic user optimal principle or user equilibrium of instantaneous travel cost. In order not to solve the complicated two-point boundary-value problem with substantial computational times for obtaining the optimal control solution, a steady state-costate solution algorithm is developed that generates an approximate solution to the network optimal control problem. This algorithm exploits advantage of the embedded network structure of the problem and would be computationally efficient. A numerical example with two peak period traffic demands which was drawn from the road network problem between Hong Kong and several adjacent cities of inland China is used to demonstrate the performance of the proposed algorithm.

Modeling Park-and-Ride Services in a Multimodal Transport Network with Elastic Demand

With the rapid development of metro systems in large Asian cities, such as Hong Kong and Shanghai, China, local authorities are developing park-and-ride (P&R) schemes to encourage commuters to reach the cities’ central areas by transferring from private cars to metro at stations with P&R facilities. A network equilibrium formulation can be used to model P&R services in a multimodal transportation network with elastic demand. It is assumed that commuters can complete their journeys by three options: auto mode, walk–metro mode, and P&R mode. The proposed model simultaneously considered commuters’ travel choices on travel mode, route–path, and transfer point, as well as their parking choice behavior. The effects of elastic travel demand, together with passengers’ discomfort in metro vehicles, were explicitly incorporated. The resultant problem can be formulated as an equivalent variational inequality problem. Numerical results showed that the introduction of P&R schemes could bring a positive, neutral, or even negative social welfare increment, and its efficiency depends greatly on the parking charging level and the number of parking spaces supplied at the P&R site and in the urban central area, as well as the metro dispatching frequency and fare.

Multiclass multicriteria mixed equilibrium on networks and uniform link tolls for system optimum

In this paper, we consider a unified framework of multiclass multicriteria mixed equilibrium, and the existence of uniform link tolls supporting such a mixed equilibrium as a system optimum. The network users are divided into different classes, and each class of traveler perceives his/her disutility associated with a route as a combination of two criteria given, respectively, by the travel time disutility and the time-irrelevant travel disutility. And users in a common class follow either user equilibrium (UE) principle or Cournot-Nash (CN) principle. A variational inequality model characterizing the multiclass multicriteria UE-CN mixed equilibrium behavior is developed. By utilizing the dual theory, we establish the existence of uniform link tolls supporting such mixed equilibrium as a system optimum.