The Corridor Problem with Discrete Multiple Bottlenecks

Akamatsu, Takashi; Wada, Koh; Hayashi, Shunsuke

doi:10.1016/j.trpro.2015.06.025

Cited by 11 publications

(5 citation statements)

References 22 publications

(28 reference statements)

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“…Furthermore, although the bottleneck capacity expansion generates a Pareto In this paper, we consider a city with a single bottleneck. Therefore, we need to examine the robustness of our result by analyzing a model with multiple bottlenecks (Kuwahara, 1990;Akamatsu et al, 2015;Fosgerau and Kim, 2019). In addition, it would be valuable for future research to study toll-revenue redistribution schemes that lead to a Pareto improvement.…”

Section: Resultsmentioning

confidence: 99%

Who gains and who loses from congestion pricing in a monocentric city with a bottleneck?

Takayama

2020

Economics of Transportation

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This study develops a model in which heterogeneous commuters choose their residential locations and departure times from home in a closed monocentric city with a bottleneck located at the entrance to the central business district (CBD). We show that commuters sort themselves both temporally and spatially according to their income, value of time, and flexibility at the equilibria with and without an optimal congestion pricing. These two equilibria exhibit fundamentally different properties, indicating that congestion pricing alters the urban spatial structure. We then consider two cases wherein rich commuters are either flexible or inflexible and demonstrate that (a) rich commuters reside farther from the CBD in the former case and closer to the CBD in the latter case; (b) congestion pricing makes cities denser and more compact in the former, whereas it causes cities to become less dense and to expand spatially in the latter; and (c) in both cases, pricing helps rich commuters but hurts poor commuters. We further reveal that although expanding the capacity of the bottleneck generates a Pareto improvement when commuters do not relocate, it can lead to an unbalanced distribution of benefits among commuters: commuters residing closer to the CBD gain, while those residing farther from the CBD lose. This suggests that expanding capacity financed by the revenue from congestion pricing could be regressive in a city where rich commuters are inflexible.

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Section: Resultsmentioning

confidence: 99%

Who gains and who loses from congestion pricing in a monocentric city with a bottleneck?

Takayama

2020

Economics of Transportation

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“…The ordering property is useful for analytically investigating the properties of equilibrium, as utilised in previous studies (e.g. Kuwahara and Akamatsu, 1993;Akamatsu et al, 2015;Wada et al, 2019). Especially, with this property and the theory of weakly acyclic games, Satsukawa et al (2019) established the convergence and stability of dynamic user equilibrium in a unidirectional network.…”

Section: Proof See Appendix Cmentioning

confidence: 95%

Dynamic system optimal traffic assignment with atomic users: Convergence and stability

Satsukawa¹,

Wada²,

Watling³

2021

Preprint

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In this study, we analyse the convergence and stability of dynamic system optimal (DSO) traffic assignment with fixed departure times. We first formulate the DSO traffic assignment problem as a strategic game wherein atomic users select routes that minimise their marginal social costs, called a 'DSO game'. By utilising the fact that the DSO game is a potential game, we prove that a globally optimal state is stochastically stable under the logit response dynamics, and the better/best response dynamics converges to locally optimal states. Furthermore, as an application of DSO assignment, we examine characteristics of the evolutionary implementation scheme of marginal cost pricing. Through theoretical comparison with a fixed pricing scheme, we found the following properties of the evolutionary implementation scheme: (i) the total travel time decreases smoother to an efficient traffic state as congestion externalities are perfectly internalised; (ii) a traffic state would reach a more efficient state as the globally optimal state is stabilised. Numerical experiments also suggest that these properties make the evolutionary scheme robust in the sense that they prevent a traffic state from going to worse traffic states with high total travel times.

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“…In modeling a traffic assignment problem, we describe traffic variables mainly in a Lagrangian-like coordinate system (Akamatsu et al, 2015(Akamatsu et al, , 2021. In this system, variables are expressed as functions of the arrival time at the destination, and not at the origin or bottleneck.…”

Section: Formulation In a Lagrangian-like Coordinate Systemmentioning

confidence: 99%

Non-existence of queues for system optimal departure patterns in tree networks

Sakai¹,

Satsukawa²,

Akamatsu³

2022

Preprint

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This study proves the non-existence of queues for a dynamic system optimal (DSO) departure pattern in a directed rooted tree network with a single destination. First, considering queueing conditions explicitly, we formulate the DSO problem as mathematical programming with complementarity constraints (MPCC) that minimizes the total system cost which consists of the schedule and queueing delay costs. Next, for an arbitrary feasible solution to the MPCC, we prove the existence of another feasible solution where the departure flow pattern on every link is the same but no queue exists. This means that the queues can be eliminated without changing the total schedule delay cost. Queues are deadweight losses, and thus the non-existence theorem of queues in the DSO solution is established. Moreover, as an application of the non-existence theorem, we show that the MPCC can be transformed into a linear programming (LP) problem by eliminating the queueing conditions.

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The Corridor Problem with Discrete Multiple Bottlenecks

Cited by 11 publications

References 22 publications

Who gains and who loses from congestion pricing in a monocentric city with a bottleneck?

Who gains and who loses from congestion pricing in a monocentric city with a bottleneck?

Dynamic system optimal traffic assignment with atomic users: Convergence and stability

Non-existence of queues for system optimal departure patterns in tree networks

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