Lane‐based optimization of traffic equilibrium settings for area traffic control

Area traffic control is an important element in Intelligent Transportation System (ITS). This paper extends the lane‐based optimization method to a traffic equilibrium network, which improves the operational performance of signal‐controlled network. We formulate a decomposition approach to simultaneously optimize the lane markings and signal settings for a signal‐controlled network that comprises two levels of optimization. At the junction level, the lane markings, control sequence, and other aspects of the signal settings are optimized for individual junctions, whereas at the network level, the group‐based signal settings are optimized to take into account the re‐routing characteristics of travelers and signal coordination effects that are based on a TRANSYT traffic model, which is a well‐known procedure for evaluating the performance of signal‐controlled networks. We use a numerical example to demonstrate the effectiveness of the proposed methodology.     

Optimal offsets for traffic signal systems in urban networks

The paper proposes a binary integer programming model for the computation of optimal traffic signal offsets for an urban road network. The basic theoretical assumptions for the computation of delay on the network are those employed by the main models developed during the last few years. The set of input data coincides with that needed for the Combination Method and its extensions. The model is solved through a branch-and-backtrack method and allows the obtaining of optimal offsets for condensable or uncondensable networks without introducing any special assumption on delay-offset functions, contrary to what occurs within other mathematical programming formulations of the problem. A reduced memory dimension is required by the developed algorithm, which promptly supplies during the computation better and better sub-optimal solutions, very interesting in view of the possible application of the method to real-time control problems. The tests performed show that the method can be applied to networks of practical size.     

An equilibrium algorithm for the spatial aggregation problem of traffic assignment

Present traffic assignment methods require that all possible origins and destinations of trips taking place within a study area be represented as if they were taking place to and from a small set of points or centroids. Each centroid is supposed to represent the location of all trip-ends within a given zone, and this necessarily misrepresents points located at the edges of the zone.In order to alleviate this problem (which we refer to as the spatial aggregation problem) one could use smaller zones and more centroids, but existing traffic assignment algorithms cannot efficiently handle many centroids.This paper introduces an algorithm procedure which is designed to handle a substantially larger number of centroids. In the paper that follows, the technique is further developed to take into account a continuous distribution of population.     

The impact of speed limits on traffic equilibrium and system performance in networks

Speed limits are usually imposed on roads in an attempt to enhance safety and sometimes serve the purpose of reducing fuel consumption and vehicular emissions as well. Most previous studies up to date focus on investigation of the effects of speed limits from a local perspective, while network-wide traffic reallocation effects are overlooked. This paper makes the first attempt to investigate how a link-specific speed limit law reallocates traffic flow in an equilibrium manner at a macroscopic network level. We find that, although the link travel time–flow relationship is altered after a speed limit is imposed, the standard traffic assignment method still applies. With the commonly adopted assumptions, the uniqueness of link travel times at user equilibrium (UE) remains valid, and the UE flows on links with non-binding speed limits are still unique. The UE flows on other links with binding speed limits may not be unique but can be explicitly characterized by a polyhedron or a linear system of equalities and inequalities. Furthermore, taking into account the traffic reallocation effects of speed limits, we compare the capability of speed limits and road pricing for decentralizing desirable network flow patterns. Although from a different perspective for regulating traffic flows with a different mechanism, a speed limit law may play the same role as a toll charge scheme and perform better than some negative (rebate) toll schemes under certain conditions for network flow management.     

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.     

An application of shock wave theory to traffic signal control

A real time control policy minimizing total intersection delays subject to queue length constraints at an isolated signalized intersection is developed in this paper. The policy is derived from a new traffic model which describes the simultaneous evolution of queue lengths of two conflicting traffic streams, controlled by a traffic light, in both time and space. The model is based on the examination of shock waves generated upstream of the stop lines by the intermittent service of traffic at the signal. The proposed policy was tested against the existing pre-timed control policy at a high volume intersection and it was found superior, especially when demands increase well above the saturation level.     

Real-time network-wide traffic signal optimization considering long-term green ratios based on expected route flows

We propose a novel real-time network-wide traffic signal control scheme which is (1) applicable under modern data technologies, (2) flexible in response to variations of traffic flows due to its non-cyclic feature, (3) operable on a network-wide and real-time basis, and (4) capable of considering expected route flows in the form of long-term green time ratios for intersection movement. The proposed system has a two-level hierarchical architecture: (1) strategy level and (2) control level. Considering the optimal states for a long-term period found in the strategy level, the optimal signal timings for a short-term period are calculated in the control level which consists of two steps: (1) queue weight update and (2) signal optimization. Based on the ratio of the cumulative green time to the desired green time is the first step to update the queue weights, which are then used in the optimization to find signal timings for minimum total delay. A parametric queue weight function is developed, discussed and evaluated. Two numerical experiments were given. The first demonstrated that the proposed system performs effectively, and the second shows its capability in a real-world network.     

Selection of expert system shells for traffic signal design

Although the use of expert systems (ESs) as a problem-solving tool is relatively new in the transportation profession, it has been recognized that a well-designed ES can contribute in areas where the knowledge domain requires an integration of expertise from various disciplines or is very complex and difficult to quantify. To minimize the effort involved in developing essential ES mechanisms, researchers often prefer to use ES shells which provide a standard inference procedure, knowledge representation, and a user-friendly design environment. However, commercial ES shells tend to be designed for only certain classes of problems, and are not as general and flexible as programming languages. More than 150 commercial ES shells are available in the microcomputer market. Most ES shells are usually claimed by their vendors to be usable for almost any conceivable applications, but such claims have often proved to be extravagant. Hence, the selection of an efficient yet costeffective commercial shell is one of the most critical tasks in ES development. In reviewing the vital task of ES shell selection, this paper presents our experience in evaluating more than 30 ES shells for developing an ES for signal design. The proposed ES includes signal settings, phasing plans, controllers, and detector locations.     

A phenomenological model for dynamic traffic flow in networks

A macroscopic model for dynamic traffic flow is presented. The main goal of the model is the real time simulation of large freeway networks with multiple sources and sinks. First, we introduce the model in its discrete formulation and consider some of its properties. It turns out, that our non-hydrodynamical ansatz for the flows results in a very advantageous behavior of the model. Next the fitting conditions at junctions of a traffic network are discussed. In the following sections we carry out a continuous approximation of our discrete model in order to derive stationary solutions and to consider the stability of the homogeneous one. It turns out, that for certain conditions unstable traffic flow occurs. In a subsequent section, we compare the stability of the discrete model and the corresponding continuous approximation. This confirms in retrospection the close similarities of both model versions. Finally we compare the results of our model with the results of another macroscopic model, that was recently suggested by Kerner and Konhäuser [Phys. Rev. E 48, 2335–2338 (1993)].     

On the degradation of performance for traffic networks with oblivious users

We consider the problem of characterizing user equilibria and optimal solutions for routing in a given network. We extend the known models by considering users oblivious to congestion in the following sense: While in the typical user equilibrium setting the users follow a strategy that minimizes their individual cost by taking into account the (dynamic) congestion due to the current routing pattern, an oblivious user ignores congestion altogether; instead, he or she decides his routing on the basis of cheapest routes on a network without any flow whatsoever. These cheapest routes can be, for example, the shortest paths in the network without any flow. This model tries to capture the fact that a certain percentage of travelers base their route simply on the distances they observe on a map, without thinking (or knowing, or caring) about the delays experienced on this route due to their fellow travelers. In this work we study the effect of such users using as the measure of network performance its price of anarchy, i.e., the ratio of the total latency experienced by the users (oblivious or not) at equilibrium over the social optimum.     

A dual decomposition method for sector capacity constrained traffic flow optimization

An aggregate air traffic flow model based on a multicommodity network is used for traffic flow management in the National Airspace System. The problem of minimizing the total travel time of flights in the National Airspace System of the United States, subject to sector capacity constraints, is formulated as an Integer Program. The resulting solution achieves optimal delay control. The Integer Program implemented for the scenarios investigated has billions of variables and constraints. It is relaxed to a Linear Program for computational efficiency. A dual decomposition method is applied to solve the large scale Linear Program in a computationally tractable manner. A rounding algorithm is developed to map the Linear Program solution to a physically acceptable result, and is implemented for the entire continental United States. A 2-h traffic flow management problem is solved with the method.     

Trial-and-error method for congestion pricing scheme under side-constrained probit-based stochastic user equilibrium conditions

A toll pattern that can restrict link flows on the tolled links to some predetermined thresholds is named as effective toll solution, which can be theoretically obtained by solving a side-constraint traffic assignment problem. Considering the practical implementation, this paper investigates availability of an engineering-oriented trial-and-error method for the effective toll pattern of cordon-based congestion pricing scheme, under side-constrained probit-based stochastic user equilibrium (SUE) conditions. The trial-and-error method merely requires the observed traffic counts on each entry of the cordon. A minimization model for the side-constrained probit-based SUE problem with elastic demand is first proposed and it is shown that the effective toll solution equals to the product of value of time and optimal Lagrangian multipliers with respect to the side constraints. Then, employing the Lagrangian dual formulation of the minimization method, this paper has built a convergent trial-and-error method. The trial-and-error method is finally tested by a numerical example developed from the cordon-based congestion pricing scheme in Singapore.     

Network equilibrium for congested multi‐mode networks with elastic demand

This paper proposes an elastic demand network equilibrium model for networks with transit and walking modes. In Hong Kong, the multi‐mode transit system services over 90% of the total journeys and the demand on it is continuously increasing. Transit and walking modes are related to each other as transit passengers have to walk to and from transit stops. In this paper, the multi‐mode elastic‐demand network equilibrium problem is formulated as a variational inequality problem where the combined mode and route choices are modeled in a hierarchical logit structures and the total travel demand for each origin‐destination pair is explicitly given by an elastic demand function. In addition, the capacity constraint for transit vehicles and the effects of bi‐directional flows on walkways are considered in the proposed model. All these congestion effects are taken into account for modeling the travel choices. A solution algorithm is developed to solve the multi‐mode elastic‐demand network equilibrium model. It is based on a Block Gauss‐Seidel decomposition approach coupled with the method of successive averages. A numerical example is used to illustrate the application of the proposed model and solution algorithm.     

An expert system for air traffic flow management

An expert system for the air traffic flow management (ATFM) problem is presented. Two main prototypes have been constructed, one for timetable rescheduling that attempts to modify airline timetables to smooth traffic peaks at airports during rush-hours and another for centralized flow control that works to forecast the place, time and magnitude of the congestion and to propose mitigative actions. Simulations for the Brazilian ATFM, including the principal 14 airports, show the potential usefulness of the expert system.     

A technique for the investigation of scheme benefits in large-scale transport networks

Existing methods of evaluating large-scale transport networks involve the use of mathematical models of traffic flow which are generally both large and complex. However, the time and cost involved in the use of these models normally restricts their use for the detailed forecasting of traffic flows and costs to the assessment of a relatively small number of alternative patterns of overall investment. In order to evaluate the individual projects and groups of projects which go to make up an overall investment plan, it is, therefore, usually necessary to make simplifying assumptions about the influence of any one project on the overall traffic pattern, so as to isolate it from the influence of neighbouring projects. These assumptions generally result in the loss of a certain amount of the detail normally available from a standard model, and the task of assessing the relative value of different projects and the amount of interaction between them is made more difficult.This paper describes a new technique, designed to permit the evaluation of individual projects whilst still retaining the level of detail available from a full-scale mathematical model. The aim has been to produce a cheap and easy-to-use technique, capable of producing substantially the same results as a standard model. The technique uses newly developed computer algorithms which short-cut the full-scale model by forecasting the changes in an existing travel pattern resulting from the influence of a particular project. Initial tests suggest that approaching the problem in this way can save up to 70% of the computing time and costs involved in the use of a standard model for the evaluation of individual projects.The technique as described here is envisaged as a tool for aiding strategic investment decisions. It can, however, provide data for more detailed investigations, and could, with modifications, carry out these investigations on smaller problems than those for which it was originally designed.Crown copyright reserved, 1973     

An adaptive information fusion model to predict the short-term link travel time distribution in dynamic traffic networks

As intelligent transportation systems (ITS) approach the realm of widespread deployment, there is an increasing need to robustly capture the variability of link travel time in real-time to generate reliable predictions of real-time traffic conditions. This study proposes an adaptive information fusion model to predict the short-term link travel time distribution by iteratively combining past information on link travel time on the current day with the real-time link travel time information available at discrete time points. The past link travel time information is represented as a discrete distribution. The real-time link travel time is represented as a range, and is characterized using information quality in terms of information accuracy and time delay. A nonlinear programming formulation is used to specify the adaptive information fusion model to update the short-term link travel time distribution by focusing on information quality. The model adapts good information by weighing it higher while shielding the effects of bad information by reducing its weight. Numerical experiments suggest that the proposed model adequately represents the short-term link travel time distribution in terms of accuracy and robustness, while ensuring consistency with ambient traffic flow conditions. Further, they illustrate that the mean of a representative short-term travel time distribution is not necessarily a good tracking indicator of the actual (ground truth) time-dependent travel time on that link. Parametric sensitivity analysis illustrates that information accuracy significantly influences the model, and dominates the effects of time delay and the consistency constraint parameter. The proposed information fusion model bridges key methodological gaps in the ITS deployment context related to information fusion and the need for short-term travel time distributions.     

An optimization framework for workplace charging strategies

The workplace charging (WPC) has been recently recognized as the most important secondary charging point next to residential charging for plug-in electric vehicles (PEVs). The current WPC practice is spontaneous and grants every PEV a designated charger, which may not be practical or economic when there are a large number of PEVs present at workplace. This study is the first research undertaken that develops an optimization framework for WPC strategies to satisfy all charging demand while explicitly addressing different eligible levels of charging technology and employees’ demographic distributions. The optimization model is to minimize the lifetime cost of equipment, installations, and operations, and is formulated as an integer program. We demonstrate the applicability of the model using numerical examples based on national average data. The results indicate that the proposed optimization model can reduce the total cost of running a WPC system by up to 70% compared to the current practice. The WPC strategies are sensitive to the time windows and installation costs, and dominated by the PEV population size. The WPC has also been identified as an alternative sustainable transportation program to the public transit subsidy programs for both economic and environmental advantages.     

An improved cellular automata model for heterogeneous work zone traffic

This paper aims to develop an improved cellular automata (ICA) model for simulating heterogeneous traffic in work zone. The proposed ICA model includes the forwarding rules to update longitudinal speeds and positions of work zone vehicles. The randomization probability parameter used by the ICA is formulated as a function of the activity length, the transition length and the volumes of different types of vehicles traveling across work zone. Compared to the existing cellular automata models, the ICA model possesses a novel and realistic lateral speed and position updating rule so that the simulation of vehicle’s lateral movement in work zone is close to the reality. The ICA model is calibrated and validated microscopically and macroscopically by using the real work zone data. Comparisons of field data and ICA for trajectories, speed and speed–flow relationship in work zone show very close agreement. Finally, the proposed ICA model is applied to estimate traffic delay occurred in work zone.     

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.