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• Studies network Macroscopic Fundamental Diagram of urban network with hierarchical streets. • Presence of hierarchy leads to non-unimodal patterns in MFD when hierarchical streets present and users route according to UE principles. • Findings obtained with simple analytical model and confirmed with simulations and empirical data. Unimodal, concave relationships between average network productivity and accumulation or density aggregated across spatially compact regions of urban networks—so called network Macroscopic Fundamental Diagrams (MFDs)—have recently been shown to exist on homogeneous street networks. When present, MFD relationships facilitate the modeling of traffic congestion at a regional level and have led to the development of various regional traffic control strategies. However, real street networks are not homogeneous—they generally have a hierarchical structure where some streets (e.g., arterials) promote higher mobility than others (e.g., local roads). This paper examines how the presence of hierarchical roadway structures may potentially cause non-unimodal patterns in a network's MFD. These are observed using three types of tools: analytical models of simple network structures, simulations of various idealized roadway networks, and empirical data. The impacts of street hierarchy depend on how vehicles use different roadway types to move within the network; i.e., their routing strategy. The findings suggest that the presence of roadway hierarchies may lead to MFDs that have non-unimodal or non-concave patterns on the free-flow branch when vehicles route themselves according to user equilibrium principles, which is closest to what would be observed in realistic situations. Such patterns are contrary to what is traditionally assumed in most MFD-based modeling frameworks. However, the unimodal and concave MFD should be expected under system optimal routing conditions that maximize network productivity for a given traffic state. [ABSTRACT FROM AUTHOR]

This study presents a distributed gradient-based approach to solve system optimal dynamic traffic assignment (SODTA) formulated based on the cell transmission model. The algorithm distributes SODTA into local sub-problems, who find optimal values for their decision variables within an intersection. Each sub-problem communicates with its immediate neighbors to reach a consensus on the values of common decision variables. A sub-problem receives proposed values for common decision variables from all adjacent sub-problems and incorporates them into its own offered values by weighted averaging and enforcing a gradient step to minimize its objective function. Then, the updated values are projected onto the feasible region of the sub-problems. The algorithm finds high quality solutions in all tested scenarios with a finite number of iterations. The algorithm is tested on a case study network under different demand levels and finds solutions with at most a 5% optimality gap. [ABSTRACT FROM AUTHOR]

User equilibrium (UE) and system optimal (SO) are among the essential principles for solving the traffic assignment problem. Many studies have been performed on solving the UE and SO traffic assignment problem; however, the majority of them are either static (which can lead to inaccurate predictions due to long aggregation intervals) or analytical (which is computationally expensive for large-scale networks). Besides, most of the well-known micro/meso traffic simulators, do not provide a SO solution of the traffic assignment problem. To this end, this study proposes a new simulation-based dynamic system optimal (SB-DSO) traffic assignment algorithm for the SUMO simulator, which can be applied on large-scale networks. A new swapping/convergence algorithm, which is based on the logit route choice model, is presented in this study. This swapping algorithm is compared with the Method of Successive Average (MSA) which is very common in the literature. Also, a surrogate model of marginal travel time was implemented in the proposed algorithm, which was tested on real and abstract road networks (both on micro and meso scales). The results indicate that the proposed swapping algorithm has better performance than the classical swapping algorithms (e.g. MSA). Furthermore, a comparison was made between the proposed SB-DSO and the current simulation-based dynamic user equilibrium (SB-DUE) traffic assignment algorithm in SUMO. This proposed algorithm helps researchers to better understand the impacts of vehicles that may follow SO routines in future (e.g., Connected and Autonomous Vehicles (CAVs)).

In this study, we analyse the convergence and stability of dynamic system optimal (DSO) traffic assignment with fixed departure times. We first formulate the DSO traffic assignment problem as a strategic game wherein atomic users select routes that minimise their marginal social costs, called a 'DSO game'. By utilising the fact that the DSO game is a potential game, we prove that a globally optimal state is a stochastically stable state under the logit response dynamics, and the better/best response dynamics converges to a locally optimal state. Furthermore, as an application of DSO assignment, we examine characteristics of the evolutionary implementation scheme of marginal cost pricing. Through theoretical comparison with a fixed pricing scheme, we found the following properties of the evolutionary implementation scheme: (i) the total travel time decreases smoother to an efficient traffic state as congestion externalities are perfectly internalised; (ii) a traffic state would reach a more efficient state as the globally optimal state is stabilised. Numerical experiments also suggest that these properties make the evolutionary scheme robust in the sense that they prevent a traffic state from going to worse traffic states with high total travel times. • Convergence and stability of dynamic system optimal assignment are analysed. • An approach based on the potential game theory is presented. • Rigorous results on the stochastic stability of globally optimal states are obtained. • Characteristics of marginal cost pricing schemes are examined as an application. • An evolutionary pricing scheme is important for ensuring robustness of efficient states. [ABSTRACT FROM AUTHOR]

This work studies the user equilibrium (UE) state and the system optimal (SO) state in vehicular communication networks that support both V2V and V2I communication. Each user in this network is assumed to make route choice that optimizes a utility function that involves the traditional travel cost and the data communication utility. The overall social cost is minimized when the network is in the SO state. However, the rational and selfish user behavior brings the network to the UE state. It is well known that, in general, the UE state does not necessarily coincide with the SO state. In this paper, we leverage the data communication aspect of the decision making to influence the users’ route choices, driving the UE state to the SO state. We provide a guideline for the system operator on how to drive the network towards the SO state using the V2I bandwidth allocation scheme developed in the paper. The model and the proposed algorithm are validated using Veins simulation under IEEE 802.11p protocol. In the simulation, we also show that the system cost can be lowered compared with the UE state if the bandwidth allocation is close to the optimal solution under the proposed algorithm. [ABSTRACT FROM AUTHOR]

Control of conventional transportation networks aims at bringing the state of the network (e.g., the traffic flows in the network) to the system optimal (SO) state. This optimum is characterized by the minimality of the social cost function, i.e., the total cost of travel (e.g., travel time) of all drivers. On the other hand, drivers are assumed to be rational and selfish, and make their travel decisions (e.g., route choices) to optimize their own travel costs, bringing the state of the network to a user equilibrium (UE). A classic approach to influence users’ route choice is using congestion tolls. In this paper, we study the SO and UE of future connected vehicular transportation networks, where users consider both the travel cost and the utility from data communication, when making their travel decisions. We leverage the data communication aspect of the decision making to influence the user route choices, driving the UE state to the SO state. We assume the cache-enabled vehicles can communicate with other vehicles via vehicle-to-vehicle (V2V) connections. We propose an algorithm for calculating the values of the data communication utility that drive the UE to the SO. This result provides a guideline on how the system operator can adjust the parameters of the communication network (e.g., data pricing and bandwidth) to achieve the optimal social cost. We discuss the insights that the results shed on a secondary optimization that the operator can conduct to maximize its own utility without deviating the transportation network state from the SO. We validate the proposed communication model via Veins simulation. The simulation results also show that the system cost can be lowered even if the bandwidth allocation does not exactly match the optimal allocation policy under 802.11p protocol. [ABSTRACT FROM AUTHOR]

Traditionally, transit network assignment is modelled based on the user equilibrium principle, according to which individual passengers are assumed to select paths that minimize their travel disutility. Models that follow this principle result in sub-optimal system performance when the transit lines become overcrowded. This study presents a new framework for the transit assignment problem to address the system performance of an overcrowded transit network while integrating individual travel needs. It proposes a novel approach, called System Optimal Re-Routing Transit Assignment Heuristic (SORTAH), which produces a user-constrained system optimal solution by reducing the number of overcrowded segments and spreading out the demand to better utilize routes that are under capacity. SORTAH minimizes the overall congestion effects of a transit network and leads to a better performing solution than that of a user equilibrium model, while simultaneously guaranteeing superior fairness compared to the pure system optimal model. A large-scale real-world application was conducted on the Toronto Transit Commission (TTC) network. SORTAH was capable of reducing the number of overcrowded routes on the TTC network without adversely affecting the total travel time. Critical systemic gaps that need to be addressed in order to reduce the overall network congestion were uncovered. The study also revealed that realistic passenger paths are bounded by existing network design and capacity.

• Linear program for integrating shared autonomous vehicles with transit. • Traffic flow modeled through the link transmission model. • Rolling horizon algorithm for application to larger networks. • Integration with transit reduces total person travel time. • Transit is especially useful with low headways or small autonomous vehicle fleets. Use of shared autonomous vehicles (SAVs) for last-mile transportation can improve transit use and reduce road congestion. We investigate the problem of optimal integration of SAVs with transit. By optimal, we mean that transit should be used instead of or to complement SAVs only when it reduces the total system travel time. Although greater use of transit reduces congestion, transit often increases travel time due to frequent stops and transfers. By using a continuous approximation to passenger and vehicle movements, we formulate the problem as a linear program using the link transmission model for traffic flow. One of the main challenges is associating passenger movement with vehicles that can have different destinations (e.g. a transit stop). Although the mathematical program is linear, it nevertheless has a large number of variables. We find a suboptimal solution using a rolling horizon method, which greatly reduces the required computation time. We also demonstrate an example of a possibly unfair passenger-to-vehicle ordering, and propose a first-come-first-served greedy algorithm to match passengers. A suite of experimental results on the Sioux Falls network show that using transit decreases total system travel time, especially when SAV fleet sizes are small. Transit also decreases the time travelers spend waiting, but tends to increase in-vehicle travel time. The methodology could be useful both for future SAV operators and for planners seeking to predict the effects of SAVs on traffic congestion. [ABSTRACT FROM AUTHOR]

This study investigates the impact of a tradable credit scheme (TCS) on managing morning commute congestion by considering commuters' value-of-time and schedule delay heterogeneities, and loss aversion behavior in purchasing credits. It illustrates that total value of traded credits and credit price approach zero as commuters' loss sensitivity increases. Further, the initial credit allocation method can impact the credit price and commuters' departure rate. The study insights show that if commuters' loss sensitivity is not considered, the system-optimal TCS design can lead to a less effective scheme to minimize the total system travel cost. [ABSTRACT FROM AUTHOR]

Fully automated vehicles could have a significant share of the road network traffic in the near future. Several commercial vehicles with full-range Adaptive Cruise Control (ACC) systems or semi-autonomous functionalities are already available on the market. Many research studies aim at leveraging the potential of automated driving in order to improve the fuel efficiency of vehicles. However, in the vast majority of those, fuel efficiency is isolated to the driving dynamics between a single follower-leader pair, hence overlooking the complex nature of traffic. Consequently fuel efficiency and the efficient use of the roadway capacity are framed as conflicting objectives, leading to fuel-economy control models that adopt highly conservative driving styles. This formulation of the problem could be seen as a user-optimal approach, where in spite of delivering savings for individual vehicles, there is the side-effect of the deterioration of traffic flow. An important point that is overlooked is that the inefficient use of roadway capacity gives rise to congested traffic and traffic breakdowns, which in return increases energy costs within the system. The optimisation methods used in these studies entail high computational costs and, therefore, impose a strict constraint on the scope of problem. In this study, the use of car-following models and the limitation of the search space of optimal strategies to the parameter space of these is proposed. The proposed framework enables performing much more comprehensive optimisations and conducting more extensive tests on the collective impacts of fuel-economy driving strategies. The results show that, as conjectured, a “short-sighted” user-optimal approach is unable to deliver overall fuel efficiency. Conversely, a system-optimal formulation for fuel efficient driving is presented, and it is shown that the objectives of fuel efficiency and traffic flow are in fact not only non-conflicting, but also that they could be viewed as one when the global benefits to the network are considered. [ABSTRACT FROM AUTHOR]

This paper sets out to model an efficient and fair transportation system accounting for both departure time choice and route choice of a general multi-OD network within a dynamic traffic assignment environment. Firstly, a bi-level optimization formulation is introduced based on the link-based traffic flow model. The upper level of the formulation minimizes the total system travel time, whereas the lower level captures traffic flow propagation and the user equilibrium constraints. Then the bi-level formulation is relaxed to a linear programming formulation that produces a lower bound of an efficient and fair system state. An efficient iterative algorithm is proposed to obtain the exact solution. It only requires solving one linear program in one iteration. Further, it is shown that the number of iterations is bounded, and the output traffic flow pattern is efficient and fair. Finally, two numerical cases (including a single OD network and a multi-OD network) are conducted to demonstrate the performance of the algorithm. The results consistently show that the departure rate pattern generated from the algorithm leads to an efficient and fair system state, and the algorithm converges within two iterations across all test scenarios. [ABSTRACT FROM AUTHOR]

We study the shared autonomous vehicle (SAV) routing problem while considering congestion. SAVs essentially provide a dial-a-ride service to travelers, but the large number of vehicles involved (tens of thousands of SAVs to replace personal vehicles) results in SAV routing causing significant congestion. We combine the dial-a-ride service constraints with the linear program for system optimal dynamic traffic assignment, resulting in a congestion-aware formulation of the SAV routing problem. Traffic flow is modeled through the link transmission model, an approximate solution to the kinematic wave theory of traffic flow. SAVs interact with travelers at origins and destinations. Due to the large number of vehicles involved, we use a continuous approximation of flow to formulate a linear program. Optimal solutions demonstrate that peak hour demand is likely to have greater waiting and in-vehicle travel times than off-peak demand due to congestion. SAV travel times were only slightly greater than system optimal personal vehicle route choice. In addition, solutions can determine the optimal fleet size to minimize congestion or maximize service. [ABSTRACT FROM AUTHOR]

The basic design concept of most advanced traveler information systems (ATIS) is to present generic information to travelers, leaving travelers to react to the information in their own way. This “passive” way of managing traffic by providing generic traffic information makes it difficult to predict the outcome and may even incur an adverse effect, such as overreaction (also referred to as the herding effect). Active traffic and demand management (ATDM) is another approach that has received continual attention from both academic research and real-world practice, aiming to effectively influence people's travel demand, provide more travel options, coordinate between travelers, and reduce the need for travel. The research discussed in this article deals with how to provide users with a travel option that aims to minimize the marginal system impact that results from this routing. The goal of this research is to take better advantage of the available real-time traffic information provided by ATIS, to further improve the system level traffic condition from User Equilibrium (UE), or a real-world traffic system that is worse than UE, toward System Optimal (SO), and avoid passively managing traffic. A behaviorally induced, system optimal travel demand management model is presented to achieve this goal through incremental routing. Both analytical derivation and numerical analysis have been conducted on Tucson network in Arizona, as well as on the Capital Area Metropolitan Planning Organization (CAMPO) network in Austin, TX. The outcomes of both studies show that our proposed modeling framework is promising for improving network traffic conditions toward SO, and results in substantial economic savings. [ABSTRACT FROM PUBLISHER]

Tailpipe emissions in the road transportation system are a major source of air pollution and greenhouse gases. One of the possible approaches is to influence drivers' routing decisions such that the emissions and fuel consumption is minimized. In order to evaluate such condition, we develop environmental traffic assignment (E-TA) models based on user equilibrium (UE) and system optimal (SO) behavioral principles. Extending the traditional travel time-based UE and SO principles to E-TA is not straightforward because, unlike travel time, the rate of emissions increases with the increase in vehicle speed beyond a certain point. The results of various TA models show a network-wide traffic control strategy in which vehicles are routed according to SO-based E-TA, can reduce system-wide emissions. However, a system in which drivers make routing decisions to minimize their own emissions (E-UE system) results in a paradoxical situation of increased individual as well as system-wide emissions. [ABSTRACT FROM AUTHOR]

When optimising the overall commuting pattern for a city or a region, there are often winners and losers among commuters at the subdivision level. Losers are those who are burdened with longer commutes than before the optimisation. Knowing who or where losers are is of interest to both researchers and policy-makers. The information would help them efficiently locate losers and compensate them. Few, however, pay attention to such losers. By revisiting ‘excess commuting’ in the economic framework, we show that optimising the commuting pattern is comparable to restoring Pareto optimality in commuting. Using Beijing as a case study, we identify and geo-visualise the losers when the city’s bus commuting pattern is optimised. We examine the severity of the loss among the losers, the spatial pattern of the losers and their influencing factors. We find that most losers are located around the epicenter. The severity of the loss is independent of jobs/housing ratio but is associated with the commute distance before the optimisation. Workers whose commute distance is less than the global average are more likely to become losers. Places where losers reside have significantly lower employment density in a few industries than where non-losers reside. A low jobs/housing ratio in individual subareas does not necessarily increase the average trip length of commuters therein. A low jobs/housing ratio of one or several subareas, however, could influence the average trip length of all the commuters in the area. Locating diverse jobs and housing opportunities around or along transit corridors could compensate the losers and reduce the overall commuting cost. [ABSTRACT FROM AUTHOR]

This study formulates a program for simultaneous traffic signal optimization and system optimal traffic assignment for urban transportation networks with added degree of realism. The formulation presents a new objective function, i.e., weighted trip maximization, and explicit constraints that are specifically designed to address oversaturated conditions. This formulation improves system-wise performance while locally prevents queue spillovers, de-facto reds, and gridlocks. A meta-heuristic algorithm is developed that incorporates microscopic traffic flow models and system optimal traffic assignment in genetic algorithms. This solution technique efficiently optimizes signal timing parameters, at the same time solves system optimal traffic assignment, and accounts for oversaturated conditions and different driver's behaviors. This study also proposes a framework to calculate an upper bound on the value of the objective function by solving the problem while several constraints (i.e., network loading and traffic assignment) are relaxed. An empirical case study for a portion of downtown Springfield, Illinois has been conducted under four demand patterns. Findings indicate that our solution approach can solve the problem effectively. Several managerial insights have also been drawn. [ABSTRACT FROM PUBLISHER]

This paper provides an approach to solve the system optimal dynamic traffic assignment problem for networks with multiple O–D pairs. The path-based cell transmission model is embedded as the underlying dynamic network loading procedure to propagate traffic. We propose a novel method to fully capture the effect of flow perturbation on total system cost and accurately compute path marginal cost for each path. This path marginal cost pattern is used in the projection algorithm to equilibrate the departure rate pattern and solve the system optimal dynamic traffic assignment. We observe that the results from projection algorithm are more reliable than those from method of successive average algorithm (MSA). Several numerical experiments are tested to illustrate the benefits of the proposed model. [ABSTRACT FROM AUTHOR]

Traffic management during an evacuation and the decision of where to locate the shelters are of critical importance to the performance of an evacuation plan. From the evacuation management authority’s point of view, the desirable goal is to minimize the total evacuation time by computing a system optimum (SO). However, evacuees may not be willing to take long routes enforced on them by a SO solution; but they may consent to taking routes with lengths not longer than the shortest path to the nearest shelter site by more than a tolerable factor. We develop a model that optimally locates shelters and assigns evacuees to the nearest shelter sites by assigning them to shortest paths, shortest and nearest with a given degree of tolerance, so that the total evacuation time is minimized. As the travel time on a road segment is often modeled as a nonlinear function of the flow on the segment, the resulting model is a nonlinear mixed integer programming model. We develop a solution method that can handle practical size problems using second order cone programming techniques. Using our model, we investigate the importance of the number and locations of shelter sites and the trade-off between efficiency and fairness. [ABSTRACT FROM AUTHOR]

Several transportation problems, such as implementation of truck-only lanes, require understanding the interaction of heterogeneous dynamic traffic flows in order to provide accurate solutions. System-optimal dynamic traffic assignment can be modeled using a network loading procedure based on the cell transmission model, that is, the hydrodynamic wave model, and solved by linear programming. However, this framework cannot handle the asymmetric integration between the flow of trucks and cars. This article presents a novel formulation for network loading in system-optimal dynamic traffic assignment considering car–truck interactions. By using an embedded cell transmission model, this formulation incorporates a set of assumptions related to the kinematic characteristics of the flow of cars, trucks, and their interactions that can be solved using linear programming. We present numerical results supporting our modeling assumptions. Likewise, the observed emergent behavior captures the car–truck interactions accurately and indicates that minimum system-optimal travel time is obtained by encouraging cars to use highways with shorter distances. [ABSTRACT FROM AUTHOR]

Highlights: [•] A cell based non-holding back linear programming formulation. [•] Introducing penalty scheme to all the cells in the network. [•] Rigorously proves the properties of the formulation. [•] The formulation can be extended to network with multiple ODs. [•] Various tests have been conducted to verify the formulation’s properties. [ABSTRACT FROM AUTHOR]

Proper traffic control and guidance are imperative to reduce fatalities and property damage. When resources are scarce during emergency evacuation for any natural or artificial disasters, it is crucial to identify the most critical traffic control locations or intersections to deploy temporary control devices or to arrange manual traffic guidance so that the best system performance can be achieved. To answer the urgent theoretical and practical deployment problems, this study has proposed mixed integer nonlinear programming (MINLP) models for both static and dynamic situations. The proposed models aim to find the most crucial intersections, the optimal traffic control strategies for those intersections, and the best destination choices for evacuees to minimize the total system cost. The proposed models assume that evacuees will follow their past travel experience to safe zones unless they encounter the critical intersections. At those fully controlled critical intersections, evacuees will completely comply with the evacuation guidance to help achieve the minimum total system cost. The proposed MINLP models have also been expanded to include cell-based modules to capture the dynamic nature of evacuation flows, which is essential for real-time operation. Numerical tests on a large network with multiple origins and destinations have shown that the proposed models perform reasonably well. [ABSTRACT FROM AUTHOR]

Abstract: This paper Analyzes a new tradable credit scheme (TCS) for managing commuters’ travel choices, which seeks to persuade commuters to spread evenly within the rush hour and between primary and alternative routes so that excessive traffic congestion can be alleviated. The scheme defines a peak time window and charges those who use the primary route within that window in the form of mobility credits. Those who avoid the peak-time window, by either traveling outside the peak time window or switching to the alternative route, may be rewarded credits. A market is created such that those who need to pay credits can purchase them from those who acquire them from their rewarding travel choices. A general analytical framework is proposed for a system of two parallel routes. The framework (1) considers a variety of assumptions about commuters’ behavior in response to the discontinuous credit charge introduced at the boundary of the peak-time window, (2) allows modeling congestion effects (or demand elasticity) on the alternative route, and (3) enables both the design of system optimal TCS and the analysis of the efficiency of any given TCS. Our analyses indicate that the proposed TCS not only achieves up to 33% efficiency gains in the base scenario, but also distributes the benefits among all the commuters directly through the credit trading. The results also suggest that very simple TCS schemes could provide substantial efficiency gains for a wide range of scenarios. Such simplicity and robustness are important to practicability of the proposed scheme. Numerical experiments are conducted to examine the sensitivity of TCS designs to various system parameters. [Copyright &y& Elsevier]

Abstract: Traffic holding-back is considered an undesirable issue in dynamic traffic assignment since the vehicles are artificially held back on links in spite of the availability of downstream capacity. Holding-back occurs naturally in some system optimal dynamic traffic assignment models. In this paper, we focus on the holding back issue in the cell transmission based models and review the current methods of solving holding-back to understand their advantages and drawbacks. Then, we propose improvements to overcome the drawbacks of the current models. Finally, we propose a novel model which completely eliminates holding-back in a system optimal dynamic traffic assignment for traffic networks with multiple O–D pairs. Rigorous numerical results illustrate the benefits of using the proposed models. [Copyright &y& Elsevier]

Traffic congestion is a substantial time cost for many urban commuters. This paper studies the response of subjects in an experimental setting in which subjects choose between a short direct route that becomes increasingly congested as more people travel on it and a more indirect route that does not become congested. More specifically, I investigate how subjects respond to the use of a toll that theory predicts will minimize travel time costs. The experimental results reported in this paper show that this toll comes very close to achieving efficient use of the travel network. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study the pricing strategies in the discrete time single bottleneck model with general heterogeneous commuters. We first prove that in the system optimal assignment, the queue time must be zero for all the departures. Based on this result, the system optimal problem is formulated as a linear program. The solution existence and uniqueness are discussed. Applying linear programming duality, we then prove that the optimal dual variable values provide an optimal toll with which the system optimal solution is also an equilibrium solution. Extensive computational results are reported to demonstrate the insights gained from the formulations in this paper. These results confirm that a system optimal equilibrium can be found using the proposed approach. [Copyright &y& Elsevier]

The cell-transmission model-based single-destination system optimal dynamic traffic assignment problem proposed by Ziliaskopoulos was mostly solved by standard linear programming (LP) methods, e.g., simplex and interior point methods, which produce link-based flows involving vehicle-holding phenomenon. In this paper we present a network flow algorithm for this problem. We show that the problem is equivalent to the earliest arrival flow and then solve the earliest arrival flow on a time-expanded network. In particular, a scaled flow scheme is proposed to deal with the situation in which the ratio of backward wave speed to forward wave speed is less than one. The proposed algorithm produces path-based flows exhibiting realistic nonvehicle-holding properties. Complexity and numerical analyses show that the algorithm runs more efficiently than LP. [ABSTRACT FROM AUTHOR]

One of the main goals in transportation planning is to achieve solutions for two classical problems, the traffic assignment and toll pricing problems. The traffic assignment problem aims to minimize total travel delay among all travelers. Based on data derived from the first problem, the toll pricing problem determines the set of tolls and corresponding tariffs that would collectively benefit all travelers and would lead to a user equilibrium solution. Obtaining high-quality solutions for this framework is a challenge for large networks. In this paper, we propose an approach to solve the two problems jointly, making use of a biased random-key genetic algorithm for the optimization of transportation network performance by strategically allocating tolls on some of the links of the road network. Since a transportation network may have thousands of intersections and hundreds of road segments, our algorithm takes advantage of mechanisms for speeding up shortest-path algorithms. [ABSTRACT FROM AUTHOR]

• A multi-hop control scheme is proposed to route traffic through intermediate checkpoints. • The scheme promises to strike a better balance between efficiency and control intensity. • The problem is formulated and solved as a mathematical program with equilibrium constraints. • The scheme is shown to be effective in reducing congestion at a reasonable cost. We propose a multi-hop control scheme (MHCS) that aims to route traffic through a set of designated intermediate checkpoints (ICs). Because travelers are allowed to freely choose routes for each "hop" that connects real (origin and destination) and ICs, MHCS promises to keep intervention at a more tolerable level, compared to conventional route-based control schemes. The MHCS problem has a natural bi-level structure: the upper level attempts to minimize congestion by adjusting the hopping ratios, which are then used in the lower level problem to route travelers according to user equilibrium conditions. Accordingly, we formulate the problem as a mathematical program with equilibrium constraints (MPEC), establish its solution existence, and propose to solve it using a sensitivity analysis based algorithm. We examine sixteen heuristic rules for choosing ICs. Results based on five hundred experiments suggest that selecting the most used and most congested nodes at system optimum as the ICs delivered the largest travel time savings. Based on this finding, a set of efficient ICs are identified and adopted to test the potential of a full-scale scheme. The results from numerical experiments indicate that these checkpoints are highly effective in reducing traffic congestion at a reasonable cost of control and unfairness. In particular, they outperform, by a large margin, other choices such as most congested nodes at user equilibrium. [ABSTRACT FROM AUTHOR]