Store-and-forward based methods for the signal control problem in large-scale congested urban road networks

The problem of designing network-wide traffic signal control strategies for large-scale congested urban road networks is considered. One known and two novel methodologies, all based on the store-and-forward modeling paradigm, are presented and compared. The known methodology is a linear multivariable feedback regulator derived through the formulation of a linear-quadratic optimal control problem. An alternative, novel methodology consists of an open-loop constrained quadratic optimal control problem, whose numerical solution is achieved via quadratic programming. Yet a different formulation leads to an open-loop constrained nonlinear optimal control problem, whose numerical solution is achieved by use of a feasible-direction algorithm. A preliminary simulation-based investigation of the signal control problem for a large-scale urban road network using these methodologies demonstrates the comparative efficiency and real-time feasibility of the developed signal control methods.     

Node modeling for congested urban road networks

First-order network flow models are coupled systems of differential equations which describe the build-up and dissipation of congestion along network road segments, known as link models. Models describing flows across network junctions, referred to as node models, play the role of the coupling between the link models and are responsible for capturing the propagation of traffic dynamics through the network. Node models are typically stated as optimization problems, so that the coupling between the link dynamics is not known explicitly. This renders network flow models analytically intractable. This paper examines the properties of node models for urban networks. Solutions to node models that are free of traffic holding, referred to as holding-free solutions, are formally defined and it is shown that flow maximization is only a sufficient condition for holding-free solutions. A simple greedy algorithm is shown to produce holding-free solutions while also respecting the invariance principle. Staging movements through nodes in a manner that prevents conflicting flows from proceeding through the nodes simultaneously is shown to simplify the node models considerably and promote unique solutions. The staging also models intersection capacities in a more realistic way by preventing unrealistically large flows when there is ample supply in the downstream and preventing artificial blocking when some of the downstream supplies are restricted.     

A new algorithm for optimal signal control in congested networks

Optimization of traffic lights in a congested network is formulated as a linear programming problem. The formulation adapted here takes into account particular capacity constraints for road links and for intersections. A necessary prerequisite for the determination of optimal green times is that representative a-priori information about the origin-destination and route choice pattern inside the network is available. Because any particular control strategy temporarily alters the effective turning rates at intersections, an iterative procedure is proposed here which accomplishes convergence of optimal signal control and resulting O-D flows. The efficiency of this optimization procedure is demonstrated in a case study for a network with fifteen intersections.     

Vulnerability analysis for large-scale and congested road networks with demand uncertainty

To assess the vulnerability of congested road networks, the commonly used full network scan approach is to evaluate all possible scenarios of link closure using a form of traffic assignment. This approach can be computationally burdensome and may not be viable for identifying the most critical links in large-scale networks. In this study, an “impact area” vulnerability analysis approach is proposed to evaluate the consequences of a link closure within its impact area instead of the whole network. The proposed approach can significantly reduce the search space for determining the most critical links in large-scale networks. In addition, a new vulnerability index is introduced to examine properly the consequences of a link closure. The effects of demand uncertainty and heterogeneous travellers’ risk-taking behaviour are explicitly considered. Numerical results for two different road networks show that in practice the proposed approach is more efficient than traditional full scan approach for identifying the same set of critical links. Numerical results also demonstrate that both stochastic demand and travellers’ risk-taking behaviour have significant impacts on network vulnerability analysis, especially under high network congestion and large demand variations. Ignoring their impacts can underestimate the consequences of link closures and misidentify the most critical links.     

On the distribution of urban road space for multimodal congested networks

Transport systems in real cities are complex with many modes of transport sharing and competing for limited road space. This work intends to understand how space distributions for modes and interactions among modes affect network traffic performance. While the connection between performance of transport systems and general land allocation is the subject of extensive research, space allocation for interacting modes of transport is an open research question. Quantifying the impact of road space distribution on the performance of a congested multimodal transport system with a dynamic aggregated model remains a challenge. In this paper, a multimodal macroscopic fundamental diagram (MFD) is developed to represent the traffic dynamics of a multimodal transport system. Optimization is performed with the objective of minimizing the total passenger hours traveled (PHT) to serve the total demand by redistributing road space among modes. Pricing strategies are also investigated to provide a higher demand shift to more efficient modes. We find by an application to a bi-modal two-region city that (i) the proposed model captures the operational characteristics of each mode, and (ii) optimal dynamic space distribution strategies can be developed. In practice, the approach can serve as a physical dynamic model to inform space distribution strategies for policy makers with different goals of mobility.     

A bi-objective bi-level signal control policy for transport of hazardous materials in urban road networks

A bi-objective bi-level signal control optimization for hazardous material (hazmat) transport is considered to assess trade-offs between travel cost and environment impacts such as public risk exposure. A least maxi-sum risk model with explicit signal delay is presented to determine generalized travel cost for hazmat carriers. Since the bi-level signal control problem is generally a non-convex program, a bundle method using generalized gradients is proposed. A bounding strategy is developed to stabilize solutions of the bi-level program and reduce relative gaps between iterations. Numerical comparisons are made with other risk-averse models. The results indicate that the proposed bi-objective bi-level model becomes even amiable to signal control policy makers since provides flexible solutions whilst is acceptable to carriers since takes account of travel delay at signal-controlled junctions. Moreover, the trade-offs between public risk and generalized travel costs are empirically investigated among different risk models with a variety of weights. As a result, the proposed model consistently exhibits highly considerable advantage on mitigation of public risk whilst incurred less cost loss as compared to other alternatives.     

Dynamic modeling and control of taxi services in large-scale urban networks: A macroscopic approach

Taxis are increasingly becoming a prominent mobility mode in many major cities due to their accessibility and convenience. The growing number of taxi trips and the increasing contribution of taxis to traffic congestion are cause for concern when vacant taxis are not distributed optimally within the city and are unable to find unserved passengers effectively. A way of improving taxi operations is to deploy a taxi dispatch system that matches the vacant taxis and waiting passengers while considering the search friction dynamics. This paper presents a network-scale taxi dispatch model that takes into account the interrelated impact of normal traffic flows and taxi dynamics while optimizing for an effective dispatching system. The proposed model builds on the concept of the macroscopic fundamental diagram (MFD) to represent the dynamic evolution of traffic conditions. The model considers multiple taxi service firms operating in a heterogeneously congested city, where the city is assumed to be partitioned into multiple regions each represented with a well-defined MFD. A model predictive control approach is devised to control the taxi dispatch system. The results show that lack of the taxi dispatching system leads to severe accumulation of unserved taxi passengers and vacant taxis in different regions whereas the dispatch system improves the taxi service performance and reduces traffic congestion by regulating the network towards the undersaturated condition. The proposed framework demonstrates sound potential management schemes for emerging mobility solutions such as fleet of automated vehicles and demand-responsive transit services.     

Modeling residential location choice in relation to housing location and road tolls on congested urban highway networks

We present a reformulation of the residential location submodel of the Integrated Model of Residential and Employment Location as a network equilibrium problem, thereby making travel costs by auto endogenous. The location of housing supply is examined as a welfare maximization problem for both user-optimal and system-optimal travel costs using concepts of bilevel programming. Finally, we briefly discuss how the employment submodel can be reformulated, and the entire model solved as a variational inequality problem.     

A predictive dynamic traffic assignment model in congested capacity-constrained road networks

In this paper, a predictive dynamic traffic assignment model in congested capacity-constrained road networks is formulated. A traffic simulator is developed to incrementally load the traffic demand onto the network, and updates the traffic conditions dynamically. A time-dependent shortest path algorithm is also given to determine the paths with minimum actual travel time from an origin to all the destinations. The traffic simulator and time-dependent shortest path algorithm are employed in a method of successive averages to solve the dynamic equilibrium solution of the problem. A numerical example is given to illustrate the effectiveness of the proposed method.     

New technology and the modeling of risk-taking behavior in congested road networks

Intelligent transport systems provide various means to improve traffic congestion in road networks. Evaluation of the benefits of these improvements requires consideration of commuters’ response to reliability and/or uncertainty of travel time under various circumstances. Various disruptions cause recurrent or non-recurrent congestion on road networks, which make road travel times intrinsically fluctuating and unpredictable. Confronted with such uncertain traffic conditions, commuters are known to develop some simple decision-making process to adjust their travel choices. This paper represents the decision-making process involved in departure-time and route choices as risk-taking behavior under uncertainty. An expected travel disutility function associated with commuters’ departure-time and route choices is formulated with taking into account the travel delay (due the recurrent congestion), the uncertainty of travel times (due to incident-induced congestion) and the consequent early or late arrival penalty. Commuters are assumed to make decision on the departure-time and route choices on the basis of the minimal expected travel disutility. Thus the network will achieve a simultaneous route and departure-time user equilibrium, in which no commuter can decrease his or her expected disutility by unilaterally changing the route or departure-time. The equilibrium is further formulated as an equivalent nonlinear complementarity problem and is then converted into an unconstrained minimization problem with the use of a gap function suggested recently. Two algorithms based on the Nelder–Mead multidimensional simplex method and the heuristic route/time-swapping approach, are adapted to solve the problem. Finally, numerical example is given to illustrate the application of the proposed model and algorithms.     

A combined activity/travel choice model for congested road networks with queues

This paper presents a combined activity/travel choice model and proposes a flow-swapping method for obtaining the model's dynamic user equilibrium solution on congested road network with queues. The activities of individuals are characterized by given temporal utility profiles. Three typical activities, which can be observed in morning peak period, namely at-home activity, non-work activity on the way from home to workplace and work-purpose activity, will be considered in the model. The former two activities always occur together with the third obligatory activity. These three activities constitute typical activity/travel patterns in time-space dimension. At the equilibrium, each combined activity/travel pattern, in terms of chosen location/route/departure time, should have identical generalized disutility (or utility) experienced actually. This equilibrium can be expressed as a discrete-time, finite-dimensional variational inequality formulation and then converted to an equivalent "zero-extreme value" minimization problem. An algorithm, which iteratively adjusts the non-work activity location, corresponding route and departure time choices to reach an extreme point of the minimization problem, is proposed. A numerical example with a capacity constrained network is used to illustrate the performance of the proposed model and solution algorithm.     

Modeling urban taxi services in road networks: Progress,problem and prospect

Traditionally, many economists have examined the models and economics of urban taxi services under various types of regulation such as entry restriction and price control in an aggregate way. Only recently have we modeled urban taxi services in a network context. A realistic method has been proposed to describe vacant and occupied taxi movements in a road network and taxi drivers' search behavior for customers. A few extensions have been made to deal with demand elasticity and congestion effects together with development of efficient solution algorithms. Calibration and validation of the network taxi service models have been conducted towards their practical applications. This paper presents an overview of the research that has been carried out by the authors to develop network equilibrium models and solution algorithms for urban taxi services, and offers perspectives for future researches.     

On the fundamental diagram and supply curves for congested urban networks

Macroscopic fundamental diagrams (MFD) of traffic for some networks have been shown to have similar shape to those for single links. They have erroneously been used to help estimate the level of travel in congested networks. We argue that supply curves, which track vehicles in their passage through congested networks, are needed for this purpose, and that they differ from the performance curves generated from MFD. We use a microsimulation model, DRACULA and two networks, one synthesizing the network for Cambridge, England, and one of the city of York, England, to explore the nature of performance curves and supply curves under differing patterns of demand.We show that supply curves differ from performance curves once the onset of congestion is reached, and that the incorrect use of performance curves to estimate demand can thus seriously underestimate traffic levels, the costs of congestion, and the value of congestion relief measures. We also show that network aggregated supply curves are sensitive to the temporal distribution of demand and, potentially, to the spatial distribution of demand. The shape of the supply curve also differs between origin–destination movements within a given network.We argue that supply curves for higher levels of demand cannot be observed in normal traffic conditions, and specify ways in which they can be determined from microsimulation and, potentially, by extrapolating observed data. We discuss the implications of these findings for conventional modelling of network management policies, and for these policies themselves.     

Controller design for gating traffic control in presence of time-delay in urban road networks

Recent studies demonstrated the efficiency of feedback-based gating control in mitigating congestion in urban networks by exploiting the notion of macroscopic or network fundamental diagram (MFD or NFD). The employed feedback regulator of proportional-integral (PI)-type targets an operating NFD point of maximum throughput to enhance the mobility in the urban road network during the peak period, under saturated traffic conditions. In previous studies, gating was applied directly at the border of the protected network (PN), i.e. the network part to be protected from over-saturation. In this work, the recently developed feedback-based gating concept is applied at junctions located further upstream of the PN. This induces a time-delay, which corresponds to the travel time needed for gated vehicles to approach the PN. The resulting extended feedback control problem can be also tackled by use of a PI-type regulator, albeit with different gain values compared to the case without time-delay. Detailed procedures regarding the appropriate design of related feedback regulators are provided. In addition, the developed feedback concept is shown to work properly with very long time-steps as well. A large part of the Chania, Greece, urban network, modelled in a microscopic simulation environment under realistic traffic conditions, is used as test-bed in this study. The reported results demonstrate a stable and efficient behaviour and improved mobility of the overall network in terms of mean speed and travel time.     

Emergence of cooperation in congested road networks using ICT and future and emerging technologies: A game-based review

Information and communications technologies (ICT) and future and emerging technologies (FET) are expected to revolutionize transportation in the next generation. Travelers’ behavioral adaptation is a key to their success. We discuss the notion of managing traffic congestion by enhancing cooperation in road networks enabled with ICT and FET. Cooperation is an emergent social state related to the dynamics and complexity of road traffic and reinforced learning. Game theory and research in behavioral economics show that cooperation can be leveraged to efficiently solve social dilemmas similar to traffic congestion. We review the applicability of behavioral economics and game theory concepts to route, mode and departure time choice problems. Beyond advancing theory, research on cooperation in the context of transportation is still in its infancy. We discuss state-of-the-art methodologies and their weaknesses and review the unexplored opportunities inherent in game-based methodologies. A behavioral-technological research agenda for FET is also discussed.     

The multi-criteria road network design problem in an urban area

In this paper, urban network design is analysed through a heuristic multi-criteria technique based on genetic algorithms. Both network layout and link capacity (link layout and traffic lights) are optimised. Different optimisation criteria are included for users, non-users and public system managers. Demand is considered elastic with respect to mode choice; both morning and afternoon peak periods are taken into account. In addition, choice of parking location is simulated. The procedure is applied to a test and to a real transportation system.     

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.     

A quantum evolutionary algorithm for the second-best congestion pricing problem in urban traffic networks

This paper investigates the congestion pricing problem in urban traffic networks. A first-best strategy, a second-best strategy for toll leveling in closed cordons and a second-best strategy for determining both toll levels and toll points are considered. The problem is known to be a mixed integer programming model and formulated as a bi-level optimization problem, with an objective of maximizing the social welfare. A method is presented to solve the problem, based on a novel metaheuristic algorithm, namely quantum evolutionary algorithm (QEA). To verify the proposed method, the widely used genetic algorithm (GA) is also applied to solve the problem. The problem is solved for a medium-size urban traffic network and the results of the QEA are compared against the conventional GA. Computational results show that the QEA outperforms the GA in solution quality.     

The impacts of time of day pricing on the behavior of freight carriers in a congested urban area: Implications to road pricing

This paper describes the key findings from a major research project aimed at assessing the impacts of the Port Authority of New York and New Jersey’s time of day pricing initiative on the behavior of commercial carriers. The paper, believed by the authors to be the first comprehensive study on the subject, highlights key implications for road pricing policy.One of the most interesting findings is that carriers respond to time of day pricing by implementing multi-dimensional responses involving Productivity increases, Cost transfers, and Change in facility usage. This implies a more nuanced response than suggested by micro-economic theory, which would only predict a change in facility usage. In fact, no carrier was found to have responded by implementing only changes in facility usage, which leads to the authors to believe that this is a last resort alternative.In terms of numerical importance, three combinations of strategy groups represent almost 90% of the cases: Productivity increases (42.79%), followed by Changes in facility usage and Cost transfers (27.60%) and Productivity increases and Changes in facility usage and Cost transfers (19.32%). The fact that some of these responses impact only the carrier (i.e., Productivity increases) while others mostly impact the receivers (Changes in facility usage and Cost transfers) lead the authors to believe that the nature of the response is determined by the balance of power between carriers and receivers. If carriers dominate the relationship, then it is likely that policies that mostly impact receivers are implemented; otherwise, the carriers have no choice but implementing strategies that help them cope with the impacts of pricing without impacting their customers, i.e., productivity increases. In this context, the authors’ conjecture is that carriers consider changes in facility usage to be a very disruptive alternative that forces them—and more importantly their customers—to alter their shipping/delivery patterns. It should be pointed out that, although carriers stand to benefit from working during the off-peak hours, they could only do so if their customers are willing to work during the off-peak hours.The data indicate that 36 carriers (20.2%) changed behavior because of the time of day pricing initiative. This number includes 17 carriers (9.0%) that reacted by increasing shipping charges to receivers, which illustrates the need to find out more about how receivers reacted to the time of day pricing initiative. If the carriers that only increased shipment charges are excluded, 15.3% of carriers changed behavior because of time of day pricing.     

Equilibrium analysis of the scheduling of tours in congested networks

In this paper, we develop a model of travel in tours that joins several locations by travel through a congested network. We develop a microscopic analysis in continuous time of individual benefits obtained by spending time at each of the locations and costs incurred through travel between them. This is combined with a continuous time macroscopic equilibrium model of travel during congested peak periods to show how individuals' travel choices are influenced by the congestion that result from corresponding choices made by others. We show how different travellers can achieve identical net utilities by making different combinations of choices within the equilibrium. The resulting model can be used to investigate the effect on travel behaviour and individual utility of various transport interventions, and we illustrate this by considering the effect of a peak‐period charge that eliminates congestion.