Congestion behavior and tolls in a bottleneck model with stochastic capacity

In this paper we investigate a bottleneck model in which the capacity of the bottleneck is assumed stochastic and follows a uniform distribution. The commuters’ departure time choice is assumed to follow the user equilibrium principle according to mean trip cost. The analytical solution of the proposed model is derived. Both the analytical and numerical results show that the capacity variability would indeed change the commuters’ travel behavior by increasing the mean trip cost and lengthening the peak period. We then design congestion pricing schemes within the framework of the new stochastic bottleneck model, for both a time-varying toll and a single-step coarse toll, and prove that the proposed piecewise time-varying toll can effectively cut down, and even eliminate, the queues behind the bottleneck. We also find that the single-step coarse toll could either advance or postpone the earliest departure time. Furthermore, the numerical results show that the proposed pricing schemes can indeed improve the efficiency of the stochastic bottleneck through decreasing the system’s total travel cost

"Pricing the major hub airports"

Implementing congestion pricing at twenty-seven major US airports would reduce delays by thirteen passenger-years and one thousand aircraft-hours every day, saving three to five million dollars. Chicago and Atlanta would save about one thousand dollars per aircraft. Airport revenues would increase about eleven million dollars daily. A bottleneck model with stochastic queues estimates substantial welfare gains whether or not airlines internalize self-imposed delays. Erroneously imposing fees from the non-internalizing specification on internalizing airlines, however, would be a costly mistake. The model calculates equilibrium traffic rates, queuing delays, layover times, connection times, and congestion fee schedules by minute of the day.airport congestion pricing, stochastic queuing, bottleneck model.

Stochastic bottleneck capacity, merging traffic and morning commute

This paper investigates the impact of stochastic capacity at the downstream bottleneck after a merge and the impact of merging behavior on the morning commuters' departure-time patterns. The classic bottleneck theory is extended to include a uniformly distributed capacity and the commuters' equilibrium departure patterns are derived for two different merging rules. The results show that uncertainty in the bottleneck capacity increases the commuters' mean trip cost and lengthens the peak period, and that the system total cost is lower under give-way merging than under a fixed-rate merging. Capacity paradoxes with dynamic user responses are found under both merging rules

Road Pricing for Congestion Management and Infrastructure Financing

Road pricing has two distinct objectives, to alleviate the congestion problem, and to generate revenue for transportation infrastructure financing. Accordingly, road pricing studies can be roughly classified into two branches with overlapping, one on congestion pricing and the other on toll roads. This dissertation contributes to both branches of road pricing studies. Three topics are discussed. The first two are related with congestion pricing and the third one is related with infrastructure financing. The first topic is that we study the optimal single-step coarse toll design problem for the bottleneck model where the toll level and toll window length have maximum acceptable upper bounds and the unconstrained optimal solution exceeds the upper bounds. We consider proportional user heterogeneity where users’ values of time and schedule delay vary in fixed proportions. Three classic coarse tolling models are studied, the ADL, Laih and braking models. In the ADL model, toll non-payers form a mass arrival at the bottleneck following the last toll payer. In the Laih model, there is a separated waiting facility for toll non-payers to wait until the toll ends. In the braking model, toll non-payers can choose to defer their arrival at the bottleneck to avoid paying the toll. We find that, in the ADL and the Laih models, the optimal solution chooses the maximum acceptable toll level and toll window length. The ADL model further requires the tolling period to be started as late as possible to eliminate the queue at the toll ending moment. In the braking model, if the upper bound of the toll window length is too small, no toll should be charged. Otherwise the optimal solution chooses the maximum acceptable toll window length and may choose a toll price less than the maximum acceptable level. The second topic is that we develop a new coarse tolling model to address the coarse tolling problem during morning peak hour. An “overtaking model” is proposed by considering that toll payers could overtake those braking commuters (toll non-payers) to pay toll to pass the bottleneck. This would allow commuters to brake and in the meanwhile can make the bottleneck fully utilized during the tolling period, i.e., eliminate the somewhat unrealistic unused tolling period in the braking model. The overtaking model systematically combines the Laih model and the braking model together, capturing both of their properties. Specifically, the overtaking model reduces to the Laih model when the unit overtaking cost approaches zero, and reduces to the braking model when the unit overtaking cost is too high. An unconstrained optimal tolling scheme is developed, and we find out that, unlike the ADL and the Laih models, in the overtaking model, the tolling scheme causing capacity waste could be better than tolling scheme without capacity waste. It is found that, the optimal tolling scheme is affected by the unit overtaking cost. One critical unit overtaking cost is defined. For a small unit overtaking cost, the optimal tolling scheme is similar to that of the Laih model, i.e., featured by no queue exists at the toll starting and ending moments and no capacity waste exists; for a large unit overtaking cost, the optimal tolling scheme is to set the toll high enough to prevent users from overtaking and thereby make the model reduce to the braking model. In the latter case, although the unused tolling period (as in the braking model) can be fully utilized through lowering the toll to make commuters overtake, the system cost will be increased by doing so. The third topic is that we investigate the profit maximizing behavior of a private firm which operates a toll road competing against a free alternative in presence of cars and trucks. Trucks differ from cars in value of time (VOT), congestion externality, pavement damage, and link travel time function. We consider mixed travel behaviors of cars and trucks in that trucks choose routes deterministically, while cars follow stochastic user equilibrium in route choice. We derive the equilibrium flow pattern under any combination of car-toll and truck-toll, and identify an integrated equilibrium range within which each road is used by both cars and trucks. We find that, depending on the per-truck pavement damage cost, the firm may take a car-strategy, a truck-strategy, or a car-truck mixed strategy. The perception error of car users, the VOTs and traffic demands of cars and trucks are critical in shaping the firm’s strategy

Atomistic Congestion Tolls at Concentrated Airports? Seeking a Unified View in the Internalization Debate

The goal of this paper is to bring some unity to the theoretical side of the debate on internalization of airport congestion by showing that all the literature’s theoretical results can be derived within one simple and unified framework. The analysis starts by replicating the results of Brueckner (2002), who showed that, because airlines behaving in Cournot fashion internalize congestion, they should be charged low congestion tolls. The analysis then validates the findings of Daniel (1995), who argued that larger atomistic tolls are required in a model where a Stackelberg leader interacts with competitive fringe airlines. However, it is shown that this result only holds approximately when the carriers’ outputs are imperfect substitutes.