General stochastic user equilibrium traffic assignment problem with link capacity constraints

This paper addresses a general stochastic user equilibrium (SUE) traffic assignment problem with link capacity constraints. It first proposes a novel linearly constrained minimization model in terms of path flows and then shows that any of its local minimums satisfies the generalized SUE conditions. As the objective function of the proposed model involves path‐specific delay functions without explicit mathematical expressions, its Lagrangian dual formulation is analyzed. On the basis of the Lagrangian dual model, a convergent Lagrangian dual method with a predetermined step size sequence is developed. This solution method merely invokes a subroutine at each iteration to perform a conventional SUE traffic assignment excluding link capacity constraints. Finally, two numerical examples are used to illustrate the proposed model and solution method.     

Dynamic user equilibrium with side constraints for a traffic network: Theoretical development and numerical solution algorithm

This paper investigates a traffic volume control scheme for a dynamic traffic network model which aims to ensure that traffic volumes on specified links do not exceed preferred levels. The problem is formulated as a dynamic user equilibrium problem with side constraints (DUE-SC) in which the side constraints represent the restrictions on the traffic volumes. Travelers choose their departure times and routes to minimize their generalized travel costs, which include early/late arrival penalties. An infinite-dimensional variational inequality (VI) is formulated to model the DUE-SC. Based on this VI formulation, we establish an existence result for the DUE-SC by showing that the VI admits at least one solution. To analyze the necessary condition for the DUE-SC, we restate the VI as an equivalent optimal control problem. The Lagrange multipliers associated with the side constraints as derived from the optimality condition of the DUE-SC provide the traffic volume control scheme. The control scheme can be interpreted as additional travel delays (either tolls or access delays) imposed upon drivers for using the controlled links. This additional delay term derived from the Lagrange multiplier is compared with its counterpart in a static user equilibrium assignment model. If the side constraint is chosen as the storage capacity of a link, the additional delay can be viewed as the effort needed to prevent the link from spillback. Under this circumstance, it is found that the flow is incompressible when the link traffic volume is equal to its storage capacity. An algorithm based on Euler’s discretization scheme and nonlinear programming is proposed to solve the DUE-SC. Numerical examples are presented to illustrate the mechanism of the proposed traffic volume control scheme.     

Study on road section environmental traffic capacity model and algorithm under double constraints

The coordinated development of city traffic and environment is a key research content in traffic field in twenty-first Century. Among them, road section environmental traffic capacity analysis is one of the important research issues. It can provide solid theoretical basis and reliable data support for road network traffic optimization control, road traffic pollution control and city traffic structure optimization. This paper analyzed main factors which impacted environmental traffic capacity from two aspects, including road capacity constraint conditions and road traffic pollution control constraint conditions. Then, road section environmental traffic capacity optimization model was established, and method of improved augmented Lagrange function was used to solve the model. Case study showed that, (1) The environmental traffic capacity optimal model and methodology were effective; (2) In order to ensure road section environmental traffic capacity greater than (or equal to) road capacity, some measures could be taken including adjusting motor vehicle type proportion as well as improving emission characteristics of motor vehicles exhausting pollutants.     

Joint optimization of freight facility location and pavement infrastructure rehabilitation under network traffic equilibrium

Establishment of industry facilities often induces heavy vehicle traffic that exacerbates congestion and pavement deterioration in the neighboring highway network. While planning facility locations and land use developments, it is important to take into account the routing of freight vehicles, the impact on public traffic, as well as the planning of pavement rehabilitation. This paper presents an integrated facility location model that simultaneously considers traffic routing under congestion and pavement rehabilitation under deterioration. The objective is to minimize the total cost due to facility investment, transportation cost including traffic delay, and pavement life-cycle costs. Building upon analytical results on optimal pavement rehabilitation, the problem is formulated into a bi-level mixed-integer non-linear program (MINLP), with facility location, freight shipment routing and pavement rehabilitation decisions in the upper level and traffic equilibrium in the lower level. This problem is then reformulated into an equivalent single-level MINLP based on Karush–Kuhn–Tucker (KKT) conditions and approximation by piece-wise linear functions. Numerical experiments on hypothetical and empirical network examples are conducted to show performance of the proposed algorithm and to draw managerial insights.     

New models for financing and managing highways: asset-based road corporations in China

The China International Engineering Consulting Corporation undertook, in 1997, the study of Viability of Asset Based Road Corporations in China as part of the World Bank's transport sector program review. The purpose was to investigate, in a case study format, road administration in China with two specific objectives: to compare (toll) road management in different provinces and to investigate the financial viability of China's toll roads.This paper shows that the three case projects studied, each having different management structures, are all financially viable given the present financing arrangements. However, should the projects be immediately subject to market interest rates and loan maturities prevailing in China today, their financial viability would be uncertain.In a broader context, the World Bank's lending program has enabled China to experiment with different kinds of toll road management structures. These models have both advantages and disadvantages and seem to fit that province's political economic environment in which they are employed. The toll roads and, especially, the impacts of the toll road management and financing arrangements on road administration present challenges to road administration rarely faced even in the developed countries. The challenges involve questions of the congruence of public good and private interest, as well as the role of planning and public accountability – all serious questions as China moves forward in development. These questions are raised in the context of the case studies.     

Error and optimism bias in toll road traffic forecasts

Traffic forecasts are employed in the toll road sector, inter alia, by private sector investors to gauge the bankability of candidate investment projects. Although much is written in the literature about the theory and practice of traffic forecasting, surprisingly little attention has been paid to the predictive accuracy of traffic forecasting models. This paper addresses that shortcoming by reporting the results from the largest study of toll road forecasting performance ever conducted. The author had access to commercial-in-confidence documentation released to project financiers and, over a 4-year period, compiled a database of predicted and actual traffic usage for over 100 international, privately financed toll road projects. The findings suggest that toll road traffic forecasts are characterised by large errors and considerable optimism bias. As a result, financial engineers need to ensure that transaction structuring remains flexible and retains liquidity such that material departures from traffic expectations can be accommodated.

Multi-class percentile user equilibrium with flow-dependent stochasticity

Travelers often reserve a buffer time for trips sensitive to arrival time in order to hedge against the uncertainties in a transportation system. To model the effects of such behavior, travelers are assumed to choose routes to minimize the percentile travel time, i.e. the travel time budget that ensures their preferred probability of on-time arrival; in doing so, they drive the system to a percentile user equilibrium (UE), which can be viewed as an extension of the classic Wardrop equilibrium. The stochasticity in the supply of transportation are incorporated by modeling the service flow rate of each road segment as a random variable. Such stochasticity is flow-dependent in the sense that the probability density functions of these random variables, from which the distribution of link travel time are constructed, are specified endogenously with flow-dependent parameters. The percentile route travel time, obtained by directly convolving the link travel time distributions in this paper, is not available in closed form in general and has to be numerically evaluated. To reveal their structural properties, percentile UE solutions are examined in special cases and verified with numerical results. For the general multi-class percentile UE traffic assignment problem, a variational inequality formulation is given and solved using a route-based algorithm. The algorithm makes use of the diagonal elements in the Jacobian of percentile route travel time, which is approximated through recursive convolution. Preliminary numerical experiments indicate that the algorithm is able to achieve highly precise equilibrium solutions.     

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.     

Nonlinear pricing on private roads with congestion and toll collection costs

Nonlinear pricing (a form of second-degree price discrimination) is widely used in transportation and other industries but it has been largely overlooked in the road-pricing literature. This paper explores the incentives for a profit-maximizing toll-road operator to adopt some simple nonlinear pricing schemes when there is congestion and collecting tolls is costly. Users are assumed to differ in their demands to use the road. Regardless of the severity of congestion, an access fee is always profitable to implement either as part of a two-part tariff or as an alternative to paying a toll. Use of access fees for profit maximization can increase or decrease welfare relative to usage-only pricing for profit maximization. Hence a ban on access fees could reduce welfare.     

Multi-modal traffic signal control with priority,signal actuation and coordination

Both coordinated-actuated signal control systems and signal priority control systems have been widely deployed for the last few decades. However, these two control systems are often conflicting with each due to different control objectives. This paper aims to address the conflicting issues between actuated-coordination and multi-modal priority control. Enabled by vehicle-to-infrastructure (v2i) communication in Connected Vehicle Systems, priority eligible vehicles, such as emergency vehicles, transit buses, commercial trucks, and pedestrians are able to send request for priority messages to a traffic signal controller when approaching a signalized intersection. It is likely that multiple vehicles and pedestrians will send requests such that there may be multiple active requests at the same time. A request-based mixed-integer linear program (MILP) is formulated that explicitly accommodate multiple priority requests from different modes of vehicles and pedestrians while simultaneously considering coordination and vehicle actuation. Signal coordination is achieved by integrating virtual coordination requests for priority in the formulation. A penalty is added to the objective function when the signal coordination is not fulfilled. This “soft” signal coordination allows the signal plan to adjust itself to serve multiple priority requests that may be from different modes. The priority-optimal signal timing is responsive to real-time actuations of non-priority demand by allowing phases to extend and gap out using traditional vehicle actuation logic. The proposed control method is compared with state-of-practice transit signal priority (TSP) both under the optimized signal timing plans using microscopic traffic simulation. The simulation experiments show that the proposed control model is able to reduce average bus delay, average pedestrian delay, and average passenger car delay, especially for highly congested condition with a high frequency of transit vehicle priority requests.     

Cooperative traffic control of a mixed network with two urban regions and a freeway

Currently most optimization methods for urban transport networks (i) are suited for networks with simplified dynamics that are far from real-sized networks or (ii) apply decentralized control, which is not appropriate for heterogeneously loaded networks or (iii) investigate good-quality solutions through micro-simulation models and scenario analysis, which make the problem intractable in real time. In principle, traffic management decisions for different sub-systems of a transport network (urban, freeway) are controlled by operational rules that are network specific and independent from one traffic authority to another. In this paper, the macroscopic traffic modeling and control of a large-scale mixed transportation network consisting of a freeway and an urban network is tackled. The urban network is partitioned into two regions, each one with a well-defined Macroscopic Fundamental Diagram (MFD), i.e. a unimodal and low-scatter relationship between region density and outflow. The freeway is regarded as one alternative commuting route which has one on-ramp and one off-ramp within each urban region. The urban and freeway flow dynamics are formulated with the tool of MFD and asymmetric cell transmission model, respectively. Perimeter controllers on the border of the urban regions operating to manipulate the perimeter interflow between the two regions, and controllers at the on-ramps for ramp metering are considered to control the flow distribution in the mixed network. The optimal traffic control problem is solved by a Model Predictive Control (MPC) approach in order to minimize total delay in the entire network. Several control policies with different levels of urban-freeway control coordination are introduced and tested to scrutinize the characteristics of the proposed controllers. Numerical results demonstrate how different levels of coordination improve the performance once compared with independent control for freeway and urban network. The approach presented in this paper can be extended to implement efficient real-world control strategies for large-scale mixed traffic networks.     

Complementarity formulations for the cell transmission model based dynamic user equilibrium with departure time choice, elastic demand and user heterogeneity

In this paper we formulate the dynamic user equilibrium problem with an embedded cell transmission model on a network with a single OD pair, multiple parallel paths, multiple user classes with elastic demand. The formulation is based on ideas from complementarity theory. The travel time is estimated based on two methods which have different transportation applications: (1) maximum travel time and (2) average travel time. These travel time functions result in linear and non-linear complementarity formulations respectively. Solution existence and the properties of the formulations are rigorously analyzed. Extensive computational experiments are conducted to demonstrate the benefits of the proposed formulations on various test networks.     

Modeling the evolutions of day‐to‐day route choice and year‐to‐year ATIS adoption with stochastic user equilibrium

Suppose that in an urban transportation network there is a specific advanced traveler information system (ATIS) which acts for reducing the drivers' travel time uncertainty through provision of pre‐trip route information. Because of the imperfect information provided, some travelers are not in compliance with the ATIS advice although equipped with the device. We thus divide all travelers into three groups, one group unequipped with ATIS, another group equipped and in compliance with ATIS advice and the third group equipped but without compliance with the advice. Each traveler makes route choice in a logit‐based manner and a stochastic user equilibrium with multiple user classes is reached for every day. In this paper, we propose a model to investigate the evolutions of daily path travel time, daily ATIS compliance rate and yearly ATIS adoption, in which the equilibrium for every day's route choice is kept. The stability of the evolution model is initially analyzed. Numerical results obtained from a test network are presented for demonstrating the model's ability in depicting the day‐to‐day and year‐to‐year evolutions.