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When multiple equilibria exist, the desired traffic equilibrium, may not be reached through a day-to-day dynamic adjustment process. Han et al. ["Discrete-Time Day-to-Day Dynamic Congestion Pricing Scheme Considering Multiple Equilibria." Transportation Research Part B: Methodological 104: 1–16.] proposed a day-to-day dynamic pricing scheme charged on all links to ensure the desired traffic equilibrium can be achieved even when multiple equilibria exist. However, due to many practical constraints, the second-best pricing scheme has more practical interests. This study first discussed the issues of existing congestion pricing schemes for second-best case. Then, this study developed a second-best dynamic road pricing scheme that is implemented on a dynamic subset of the road links in the network. Our rigorous theoretical proof and numerical tests prove that the dynamic pricing scheme can drive the traffic state evolution towards the desired second-best traffic user equilibrium state from any initial traffic state. [ABSTRACT FROM AUTHOR]

This study investigates the potential of non-additive path-based pricing for congestion management in urban transportation networks. We propose a novel path-based reward credit scheme to provide commuter incentives with the goal of reducing traffic congestion. We consider that a known proportion of commuters subscribe to this reward credit scheme and may earn credits when traveling in the network. We introduce a bilevel optimization formulation to determine optimal non-additive, path-based reward credits under traffic equilibrium conditions. In this formulation, the follower problem is a parameterized user equilibrium traffic assignment problem with two classes of users and non-additive path costs. We develop a single-level reformulation based on its first-order optimality conditions and derive theoretical properties of the reward credit scheme. Customized branch-and-bound algorithms are designed to solve the problem. We also introduce a heuristic approach that repeatedly solves parameterized follower problems to enhance scalability. We report numerical results that demonstrate the computational efficiency of the proposed methods over a benchmarking approach. We conduct a comprehensive evaluation of this path-based reward credit scheme compared with a link-based subsidy pricing scheme. We find that, on average, under a limited budget and a user participation level of at least 40%, the proposed path-based incentive mechanism yields larger reductions in traffic congestion over link-based approaches. • We design a path-based, reward credit scheme for congestion management. • We formulate this incentive mechanism as a bilevel optimization problem. • The follower represents a parameterized multiclass traffic assignment problem. • We develop branch-and-bound algorithms to solve this bilevel optimization problem. • The proposed path-based pricing approach outperforms its link-based counterpart. [ABSTRACT FROM AUTHOR]

• A new method based on delay function to compensate for the secondary gradient road traffic is proposed. • A Beckmann minimization objective function with the conditional constraint model is established. • The algorithm is validated by the simulation experiment on the real road network. Congestion charging is considered an effective way to solve traffic congestion. In this paper, the main idea of solving road traffic congestion is to pay for some roads that are prone to congestion, and to compensate for other underutilized roads, this paper proposes a new method based on delay function to compensate for the secondary gradient road traffic compensation. Firstly, a nonlinear programming model of toll/subsidy for road set is given, which is based on Beckmann minimization objective function, and then the conditional constraint of model is established by using Kuhn-Sears and Lagrange multipliers. Secondly, based on heuristic algorithm, the pricing compensation strategy of road traffic is established, the delay function analysis model is established by using marginal cost, then the model is optimized based on the secondary gradient method, finally, the validity of the algorithm is validated by the simulation experiment on the real road network. [ABSTRACT FROM AUTHOR]

This paper considered the congestion pricing to be the effective way to solve the traffic congestion, the main idea of road traffic congestion was to charge for some easy to cause road congestion, and appropriated compensation for other underutilized roads. It presented a subgradient heuristic traffic delay compensation strategy based on function. Firstly, it used a nonlinear programming model in the road toll/subsidies, Beckmann was the main realization based on minimizing the objective function, and used the Kuhn Hills-Lagrange multiplier model to construct the constraint condition. Secondly, the algorithm used the pricing compensation strategy to establish the road traffic model based on heuristic algorithm, and also used the marginal cost model to establish the delay function analysis model. Finally, the simulation experiments on real road networks show that the proposed algorithm has better performance in terms of travel time, traffic flow, convergence and so on, and the effectiveness of the proposed algorithm is verified. [ABSTRACT FROM AUTHOR]

Efficient parking management strategies are vital in central business districts of cities where parking is limited and congestion is intense. Hourly parking pricing is a common parking management strategy where vehicles pay based on their parking duration (dwell time). In this paper, we derive comparative static effects for a small network to show that road pricing and hourly parking pricing are structurally different in how they influence the traffic equilibrium with elastic demand. Whereas road pricing strictly reduces demand, hourly parking pricing can reduce or induce demand depending on the parking dwell time elasticity (to the hourly parking price). When dwell time is elastic, demand always increases with parking price. However, when dwell time is inelastic, demand may increase or decrease with the parking price. Hence, hourly parking pricing can actually cause higher congestion and decay social welfare if imposed imprudently. For larger networks, we present a Variational Inequality model that characterizes the emergent equilibrium. Numerical experiments on a large network validate our analytical findings from a smaller and stylized case study. Our results also show a lower standard deviation in the parking search time (i.e., time to find a parking spot) when dwell time is highly elastic to the hourly parking price. [ABSTRACT FROM AUTHOR]

This paper analytically examines the ride-pooling market equilibrium under a single or multiple ride-pooling service(s) considering different pooling sizes (number of riders sharing the same vehicle) and endogenous congestion effect of the ride-pooling fleet, and investigates the optimal operation decisions of the service operator(s) regarding the pricing, fleet size, and pooling size in different administrative and market regimes. We firstly examine the scenario with a single ride-pooling service platform given a specific vehicle type for either profit-maximization or social welfare-maximization (different administrative regimes), and then extend the model to the scenario with two differentiated ride-pooling services (given different vehicle types), where the platforms may either compete or cooperate (different market regimes). We have the following major findings. First, the pooling size should be optimized to accommodate the congestion effect and thus simultaneously increase operator's profit and social welfare. The optimal pooling size balances the marginal pickup time, crowding cost and waiting time cost, and the optimal value is different in different market regimes. Second, the ride-pooling service operator will internalize the congestion effect of providing more vehicles to serve customers, which yields a larger ratio of waiting customers to vacant vehicles (larger demand–supply ratio). Under two differentiated ride-pooling services, in addition to the direct congestion effect of providing more vehicles, its effect on the other operator's decision will also be internalized by the service operator in concern. Our results also suggest that the competition between platforms tends to reduce the waiting customers-vacant vehicles ratio (demand–supply ratio), while the cooperation between or integration of two operators might yield a large ratio. Third, when the endogenous congestion effect of fleet size is zero, the operator's profit at social optimum will always be negative when the matching function exhibits increasing return to scale and the marginal operation cost is less than the average operation cost, which means that the social welfare seeking operator has to be subsidized. When the endogenous congestion effect of the fleet size is positive, the ride-pooling service operator may earn a positive profit at social optimum under certain conditions. This study enhances the understanding in relation to users' reactions to differentiated ride-pooling services, how such services interact with congestion, and how such services can be optimized in different market regimes. • Ride-pooling market equilibrium with flexible pooling size in the presence of congestion effect. • Optimization of pooling size, fleet size, and fare of ride-pooling service. • Differentiated ride-pooling services under competition/cooperation/integration market regimes. • Complex interactions among customer traveling behaviors, service operation decisions and road traffic congestion. [ABSTRACT FROM AUTHOR]

In this paper, we consider repeated routing games with piecewise-constant congestion taxing in which a central planner sets and announces the congestion taxes for fixed windows of time in advance. Specifically, congestion taxes are calculated using marginal congestion pricing based on the flow of the vehicles on each road prior to the beginning of the taxing window (and, hence, there is a time-varying delay in setting the congestion taxes). We motivate the piecewise-constant taxing policy by that users or drivers may dislike fast-changing prices and that they also prefer prior knowledge of the prices. We prove for this model that the multiplicative update rule and the discretized replicator dynamics converge to a socially optimal flow when using vanishing step sizes. Considering that the algorithm cannot adapt itself to a changing environment when using vanishing step sizes, we propose adopting constant step sizes in this case. Then, however, we can only prove the convergence of the dynamics to a neighborhood of the socially optimal flow (with the size of the neighbourhood being of the order of the selected step size). The results are illustrated on a nonlinear version of Pigou’s famous routing game. [ABSTRACT FROM AUTHOR]

This paper presents a solution methodology that can be used to determine the optimal solution for the combined congestion pricing and capacity expansion problems. A bilevel genetic algorithm (GA)-based optimization solution methodology is proposed to determine the optimal toll location, toll rate, percentage capacity expansion, and location for the expansion simultaneously. The upper-level subprogram minimizes the total system travel cost given certain budget and toll constraints. The lower-level subprogram is a user equilibrium problem where all users try to find the route that minimizes their own travel cost (or time). The budget constraint is handled using a penalty parameter. The demand is assumed to be fixed and given a priori. The proposed GA model is applied to Sioux Falls network, which has 76 links and 24 origin-destination (OD)-pairs, assuming homogeneous users. The optimal solution is thus identified. Sensitivity analyses are conducted for the budget and penalty parameter. The proposed methodology will be a very useful tool for transportation network planners for allocation of budgets and prioritization of links for improvements and congestion pricing. [ABSTRACT FROM AUTHOR]

For the two traffic management strategies of information providing and congestion pricing, this paper studied a union pricing strategy. Firstly, it constructed the decision space of the government and the traffic information supplier, calculated the information market penetration. Then, based on the assumption of elastic demand, it presented an equilibrium model which included two travelers (with/without information), and got the travelers' decision space. It also presented a union pricing model based on the game theory at the same time. Last, it used a testing network to analyze the model. The results show that the level of social benefits influence the information and the congestion pricing more significantly. It also find some results of the model which are in accordance with the practical experience. All of these show the reasonable of the model. [ABSTRACT FROM AUTHOR]

Abstract: We consider a public and congested airport served by airlines that may have market power, and two types of travelers with different relative values of time. We find that in the absence of passenger-type-based price discrimination by airlines, it can be useful to increase the airport charge so as to protect passengers with a great relative time value from excessive congestion caused by passengers with a low relative time value. As a result, the socially efficient airport charge can be substantially higher than what we learned from the recent literature on congestion pricing with non-atomistic airlines. [Copyright &y& Elsevier]

Abstract: This study investigates Pareto-improving congestion pricing and revenue refunding schemes in general transportation networks, which make every road user better off as compared with the situation without congestion pricing. We consider user heterogeneity in value of time (VOT) by adopting a multiclass user model with fixed origin–destination (OD) demands. We first prove that an OD and class-based Pareto-improving refunding scheme exists if and only if the total system monetary travel disutility is reduced. In view of the practical difficulty in identifying individual user’s VOT, we further investigate class-anonymous refunding schemes that give the same amount of refund to all user classes traveling between the same OD pair regardless of their VOTs. We establish a sufficient condition for the existence of such OD-specific but class-anonymous Pareto-improving refunding schemes, which needs information only on the average toll paid and average travel time for trips between each OD pair. [Copyright &y& Elsevier]

Abstract: This paper considers the problem of dynamic congestion pricing that determines optimal time-varying tolls for a pre-specified subset of arcs with bottleneck on a congested general traffic network. A two-person nonzero-sum dynamic Stackelberg game model is formulated with the assumption that the underlying information structure is open loop. Characteristics of the Stackelberg equilibrium solution are analyzed. The Hooke–Jeeves algorithm that obviates an evaluation of the gradient vector of the objective function is presented with a numerical example. The paper concludes with its future extensions. [Copyright &y& Elsevier]

• This study models the ridesharing program in a doubly dynamical system. • This study adopts a trip-based MFD approach to model within-day traffic dynamics. • This study finds that the emerging ridesharing program may not necessarily reduce traffic congestion. • This study develops and compares different pricing strategies to improve system performance. This study models a multi-modal network with ridesharing services. The developed model reproduces the scenario where travelers with their own cars may choose to be a solo-driver, a ridesharing driver, a ridesharing rider, or a public transit passenger while travelers without their own cars can only choose to be either a ridesharing rider or a public transit passenger. The developed model can capture the (clock) time-dependent choices of travelers and the evolution of traffic conditions, i.e., the within-day traffic dynamics. In particular, the within-day traffic dynamics in a city region is modeled through an aggregate traffic representation, i.e., the Macroscopic Fundamental Diagram (MFD). This paper further develops a doubly dynamical system that examines how the within-day time-dependent travelers' choices and traffic conditions will evolve from day to day, i.e., the day-to-day dynamics. Based on the doubly dynamical framework, this paper proposes two different congestion pricing schemes that aim to reduce network congestion and improve traffic efficiency. One scheme is to price all vehicles including both solo-driving and ridesharing vehicles (for ridesharing trips, the price is shared by the driver and rider), while the other scheme prices the solo-driving vehicles only in order to encourage ridesharing. The pricing levels (under each scheme) can be determined either through an adaptive adjustment mechanism from period to period driven by observed traffic conditions, or through solving a bi-level optimization problem. Numerical studies are conducted to illustrate the models and effectiveness of the pricing schemes. The results indicate that the emerging ridesharing platform may not necessarily reduce traffic congestion, but the proposed congestion pricing schemes can effectively reduce congestion and improve system performance. While pricing solo-driving vehicles only may encourage ridesharing, it can be less effective in reducing the overall congestion when compared to pricing both solo-driving and ridesharing vehicles. [ABSTRACT FROM AUTHOR]

Worsening highway congestion is a challenge to megaregional competitiveness; changing regional geographies and development location decisions, among other factors, demand that public policy responses go beyond traditional demand-management approaches. Congestion-pricing has been suggested as a remedy. In this paper, the writers analyze the outcomes of multiple congestion-pricing approaches for the capital megaregion that spans the following five metropolitan planning organization regions: (1) Washington (District of Columbia, Maryland, and Virginia), (2) Baltimore (Maryland), (3) Wilmington (Delaware), (4) Fredericksburg (Virginia), and (5) Frederick (Maryland), in addition to counties in the adjoining states of New Jersey, Pennsylvania, and West Virginia in the United States. Using a megaregional travel-demand model, the writers incorporate different values-of-time (VOTs) for travelers under different conditions. However, unlike past approaches, the writers' VOT estimates go beyond income categories and include trip purposes across a number of scenarios. The writers demonstrate that adding the trip purpose to congestion-price determination provides added insight both at the megaregional level and for individual subregions. The results of this paper show how highway users respond differently and (in some cases) in unexpected ways to congestion charges when trips in accordance with income and purpose are assigned a unique VOT. The findings reported in this paper provide engineers, planners, and policymakers with a new analytical approach to measuring traveler elasticity to tolls while demonstrating the complexity involved with road-pricing mechanisms. The writers conclude with implications for adopting this approach and ideas for implementing them in a complex institutional setup. [ABSTRACT FROM AUTHOR]