Stochastic congestion and pricing model with endogenous departure time selection and heterogeneous travelers.

This paper proposes a stochastic congestion and pricing model that combines a bottleneck model with stochastic queuing to study roadway congestion and pricing. Employing this model, two pricing schemes are developed: one is omniscient pricing for which the transportation administrative agency is assumed to be aware of each and every traveler's cost structure (i.e., their detailed valuation of journey cost as well as early and late penalties), and the other is observable pricing, for which only queuing delay is considered. Travelers are characterized by their late-acceptance level and the effects of various compositions of late-averse, late-tolerant and late-neutral travelers on congestion patterns with and without pricing are discussed.� Numerical simulation indicates that omniscient pricing scheme is most effective in suppressing peak hour congestion and distributing demands over longer time horizon. Also, congestion pricing is found to be more effective when travelers have diversified cost structures than identical cost structures, and congestion is better reduced with heterogeneous traveler composition than with single composition. This is consistent with earlier studies in the literature. In addition, the simulation results indicate that omniscient pricing in general reduces Expected Total Social CostAgent-based Model, Game Theory, Congestion, Queueing, Traffic Flow, Congestion Pricing, Road Pricing, Value Pricing

Cordon pricing consistent with the physics of overcrowding

This paper describes the modeling of recurring congestion in a network. It is shown that the standard economic models of marginal cost cannot describe precisely traffic congestion in networks during time-dependent conditions. Following a macroscopic traffic approach, we describe the equilibrium solution for a congested network in the no-toll case. A dynamic model of cordon-based congestion pricing (such as for the morning commute) for networks is developed consistent with the physics of traffic.Ê The paper combines VickreyÕs theory with a macroscopic traffic model, which is readily observable with existing monitoring technologies. The paper also examines some policy implications of the cordon-based pricing to treat equity and reliability issues, i.e. in what mobility level a city should choose to operate. An application of the model in a downtown area shows that these schemes can improve mobility and relieve congestion in cities.Cordon Pricing, Congestion Pricing, Road Pricing, Value Pricing, Social Equity

Efficiency Comparison of Various Parking Charge Schemes Considering Daily Travel Cost in a Linear City

In this paper, we introduce a new duration dependent parking fee regime based on the travel cost for an entire day, rather than a single commute trip. Commuters are assumed to reside at one end of a linear city and work in a business center at the other end. A two-stage differential method is used to derive user equilibrium travel patterns for both morning and evening rush hour commutes. Both individual travel cost and system travel cost are derived as functions of travel demand. We then compare the efficiency of the duration dependent parking fee regime with that of three previously proposed pricing regimes in the context of elastic travel demand. Results show that a pricing regime with both time-varying road tolls and location dependent parking fees is most efficient, followed by a regime with time-varying road tolls alone. Depending on the parking fee rate, a uniform duration-based parking fee regime may or may not be more efficient than a no-pricing regime. Under the duration dependent parking fee regime, an optimal parking fee rate can be obtained by minimizing system cost or maximizing social surplus, which gives rise to a system-wide performance no worse than that in the no-pricing regime

Queue replacement principle for corridor problems with heterogeneous commuters

This study investigates the theoretical properties of a departure time choice problem considering commuters' heterogeneity with respect to the value of schedule delay in corridor networks. Specifically, we develop an analytical method to solve the dynamic system optimal (DSO) and dynamic user equilibrium (DUE) problems. To derive the DSO solution, we first demonstrate the bottleneck-based decomposition property, i.e., the DSO problem can be decomposed into multiple single bottleneck problems. Subsequently, we obtain the analytical solution by applying the theory of optimal transport to each decomposed problem and derive optimal congestion prices to achieve the DSO state. To derive the DUE solution, we prove the queue replacement principle (QRP) that the time-varying optimal congestion prices are equal to the queueing delay in the DUE state at every bottleneck. This principle enables us to derive a closed-form DUE solution based on the DSO solution. Moreover, as an application of the QRP, we prove that the equilibrium solution under various policies (e.g., on-ramp metering, on-ramp pricing, and its partial implementation) can be obtained analytically. Finally, we compare these equilibria with the DSO state.Comment: 36 pages, 15 figure

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

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

The evening commute with cars and transit: Duality results and user equilibrium for the combined morning and evening peaks

Abstract This paper extends The paper then considers both the morning and evening peaks together for a single mode bottleneck (all cars) with identical travelers that share the same wished times. For a schedule penalty function of the morning departure and evening arrival times that is positive definite and has certain properties, a user equilibrium is shown to exist in which commuters travel in the same order in both peaks. The result is used to illustrate the user equilibrium for two cases: (i) commuters have decoupled schedule preferences in the morning and evening, and (ii) commuters must work a fixed shift length but have flexibility when to start. Finally, a special case is considered with cars and transit: commuters have the same wished order in the morning and evening peaks. Commuters must use the same mode in both directions, and the complete user equilibrium solution reveals the number of commuters using cars and transit and the period in the middle of each rush when transit is used