Analysis of the time-varying pricing of a bottleneck with elastic demand using optimal control theory

Yang, Hai; Huang, Hai-Jun

doi:10.1016/s0191-2615(97)00005-2

Cited by 136 publications

(43 citation statements)

References 13 publications

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“…In an earlier time, to solve the no-toll commuting equilibrium, Small and Chu (2003) assumed that a commuter's travel time depends on traffic density at his or her arrival time. This assumption is also adopted in some other studies, e.g., Mahmassani and Herman (1984), Yang and Huang (1997) . Later, Geroliminis and Levinson (2009) extended Small and Chu (2003) by considering user heterogeneity in desired arrival time, and incorporating various pricing strategies to eliminate congestion.…”

Section: Introductionmentioning

confidence: 99%

Modeling the morning commute for urban networks with cruising-for-parking: An MFD approach

Liu¹,

Geroliminis²

2016

Transportation Research Part B: Methodological

103

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a b s t r a c tThis study focuses on the morning commute problem with explicit consideration of cruising-for-parking, and its adverse impacts on traffic congestion. The cruising-for-parking is modeled through a dynamic aggregated traffic model for networks: the Macroscopic Fundamental Diagram (MFD). Firstly, we formulate the commuting equilibrium in a congested downtown network where travelers have to cruise for curbside parking spaces. The cruising-for-parking would yield longer trip distance and smaller network outflow, and thus can induce severe congestion and lengthen the morning peak. We then develop a dynamic model of pricing for the network to reduce total social cost, which includes cruising time cost, moving time cost (moving or in-transit time, which is the duration during which vehicles move close to the destination but do not cruise for parking yet), and schedule delay cost. We show that under specific assumptions, at the system optimum, the downtown network should be operating at the maximum production of its MFD. However, the cruising effect is not fully eliminated. We also show that the time-dependent toll to support the system optimum has a different shape than the classical fine toll in Vickrey's bottleneck model. In the end, analytical results are illustrated and verified with numerical experiments.

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Section: Introductionmentioning

confidence: 99%

Modeling the morning commute for urban networks with cruising-for-parking: An MFD approach

Liu¹,

Geroliminis²

2016

Transportation Research Part B: Methodological

103

View full text Add to dashboard Cite

show abstract

“…Most of the existing literature, however, is based on deterministic settings, with either a fixed capacity and demand (Vickrey 1969;Arnott et al 1990b;Lindsey 2004;Huang and Lam 2002), or a pre-defined elastic demand function (Arnott et al 1993;Yang and Huang 1997). In reality, not only does travel time increase with traffic volume, but there is also a wide range of randomness in the micro behavior of traffic and traffic conditions.…”

Section: Introductionmentioning

confidence: 99%

Congestion Behavior and Tolls in a Bottleneck Model with Stochastic Capacity

Xiao

Huang

Liu

2015

Transportation Science

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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.

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“…The concept of congestion pricing [2,3] was put forward on the basis of marginal cost pricing principle of economics. The major congestion pricing models are the static models (Walters [4], Dafermos and Sparrow [5], Dafermos [6], Yang and Huang [7]) and the dynamic models (Wie and Tobin [8], Yang and Hai-Jun [9], Arnott et al [10]). Some scholars (Walters [4], Yang and Huang [7], Yildirim and Hearn [11]) proposed each link of the network should be charged according to the theory of marginal cost pricing.…”

Section: Introductionmentioning

confidence: 99%

Research on Urban Road Congestion Pricing Strategy Considering Carbon Dioxide Emissions

et al. 2015

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Congestion pricing strategy has been recognized as an effective countermeasure in the practical field of urban traffic congestion mitigation. In this paper, a bi-level programming model considering carbon dioxide emission is proposed to mitigate traffic congestion and reduce carbon dioxide emissions. The objective function of the upper level model is to minimize the sum of travel costs and the carbon dioxide emissions costs. The lower level is a multi-modal transportation network equilibrium model. To solve the model, the method of successive averages (MSA) and the shuffled frog leaping algorithm (SFLA) are introduced. The proposed method and algorithm are tested through the numerical example. The results show that the proposed congestion pricing strategy can mitigate traffic congestion and reduce carbon emissions effectively.

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Analysis of the time-varying pricing of a bottleneck with elastic demand using optimal control theory

Cited by 136 publications

References 13 publications

Modeling the morning commute for urban networks with cruising-for-parking: An MFD approach

Modeling the morning commute for urban networks with cruising-for-parking: An MFD approach

Congestion Behavior and Tolls in a Bottleneck Model with Stochastic Capacity

Research on Urban Road Congestion Pricing Strategy Considering Carbon Dioxide Emissions

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