Wardrop Equilibrium for Networks with the BPR Latency Function

Lien, Jaimie W.; Mazalov, Vladimir V.; Melnik, Anna V.; Zheng, Jie

doi:10.1007/978-3-319-44914-2_4

Cited by 15 publications

(11 citation statements)

References 13 publications

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“…11 It is worth noting that the presence of oblivious commuters influences the flow, prices and firms' profits of both routes, as exhibited by the parameter α in the cutoff value expressions of Inequality (7). 10 To see whyα ∈…”

Section: 2mentioning

confidence: 99%

Pricing equilibrium of transportation systems with behavioral commuters

Lien¹,

Мазалов²,

Zheng³

2020

Journal of Dynamics &Amp; Games

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We study Wardrop equilibrium in a transportation system with profit-maximizing firms and heterogeneous commuters. Standard commuters minimize the sum of monetary costs and equilibrium travel time in their route choice, while "oblivious" commuters choose the route with minimal idle time. Three possible scenarios can arise in equilibrium: A pooling scenario where all commuters make the same transport choice; A separating scenario where different types of commuters make different transport choices; A partial pooling scenario where some standard commuters make the same transport choice as the oblivious commuters. We characterize the equilibrium existence condition, derive equilibrium flows, prices and firms' profits in each scenario, and conduct comparative analyses on parameters representing route conditions and heterogeneity of commuters, respectively. The framework nests the standard model in which all commuters are standard as a special case, and also allows for the case in which all commuters are oblivious as the other extreme. Our study shows how the presence of behavioral commuters under different route conditions affects equilibrium behavior of commuters and firms, as well a the equilibrium outcome of the transportation system.

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Section: 2mentioning

confidence: 99%

Pricing equilibrium of transportation systems with behavioral commuters

Lien¹,

Мазалов²,

Zheng³

2020

Journal of Dynamics &Amp; Games

Self Cite

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“…Denote by u(p, t) the costs of passengers who used a service with a ticket price p and a trip time t. In papers [4,15], the costs were expressed as the ticket price plus the expected trip time, and the customers were assumed to choose the cheapest service. In this case, the incoming Poisson flow of intensity λ st is decomposed into n subflows…”

Section: Two-stage Gamementioning

confidence: 99%

“…ese results were obtained for the Wardrop model, where the consumers minimize the expected trip time. For a generalized case in which the costs include the trip time and price of service, in paper [15] it was demonstrated that the price of anarchy can be infinite. e influence of oblivious users on the price of anarchy was analyzed in [5].…”

Section: Introductionmentioning

confidence: 99%

Optimal Parameters of Service in a Public Transportation Market with Pricing

Gao

Mazalov

Xue

2020

Journal of Advanced Transportation

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The problem of choosing the optimal parameters of service by carriers in public transport passenger flows is considered. This problem is modeled as a two-stage game. At the first stage, the players (carriers) select the parameters of their service (the number and schedule of vehicles, etc.). At the second stage, the players announce the prices of service and the consumers choose an appropriate service. The Wardrop equilibrium is applied to the competition model with rational consumers preferring the carriers with minimum cost, where the cost of service includes the price and also the expected trip time. The equilibrium in the pricing game is found and the optimal parameters of service as a solution to a noncooperative game are determined. Some results of computer simulations are presented.

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“…Volume-delay functions are typically employed in utility estimation (e.g., time cost) for static or semidynamic traffic assignments, and informing route choices for agent-based modeling (Suh et al, 1990;Çolak et al, 2016). The differentiable form and convex nature of volume-delay functions make them an ideal candidate for optimization-based traffic assignment, such as the assignment that satisfies Wardrop's equilibrium (Lien et al, 2016). Despite their extensive use in research and practice, the volume-delay functions have several limitations.…”

Section: Literature Reviewmentioning

confidence: 99%

Context-specific volume–delay curves by combining crowd-sourced traffic data with automated traffic counters: A case study for London

Casey

Zhao

Kumar

et al. 2020

DCE

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Traffic congestion across the world has reached chronic levels. Despite many technological disruptions, one of the most fundamental and widely used functions within traffic modeling, the volume–delay function has seen little in the way of change since it was developed in the 1960s. Traditionally macroscopic methods have been employed to relate traffic volume to vehicular journey time. The general nature of these functions enables their ease of use and gives widespread applicability. However, they lack the ability to consider individual road characteristics (i.e., geometry, presence of traffic furniture, road quality, and surrounding environment). This research investigates the feasibility to reconstruct the model using two different data sources, namely the traffic speed from Google Maps’ Directions Application Programming Interface (API) and traffic volume data from automated traffic counters (ATC). Google’s traffic speed data are crowd-sourced from the smartphone Global Positioning System (GPS) of road users, able to reflect real-time, context-specific traffic condition of a road. On the other hand, the ATCs enable the harvesting of the vehicle volume data over equally fine temporal resolutions (hourly or less). By combining them for different road types in London, new context-specific volume–delay functions can be generated. This method shows promise in selected locations with the generation of robust functions. In other locations, it highlights the need to better understand other influencing factors, such as the presence of on-road parking or weather events.

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Wardrop Equilibrium for Networks with the BPR Latency Function

Cited by 15 publications

References 13 publications

Pricing equilibrium of transportation systems with behavioral commuters

Pricing equilibrium of transportation systems with behavioral commuters

Optimal Parameters of Service in a Public Transportation Market with Pricing

Context-specific volume–delay curves by combining crowd-sourced traffic data with automated traffic counters: A case study for London

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