A bottleneck with randomly distorted arrival times

Daphne van Leeuwen, Liron Ravner, Sara Ghazanfari, Rudesindo Núñez Queija

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Abstract

We investigate the impact of random deviations in planned arrival times on user equilibrium in an extension of Vickrey's celebrated bottleneck model. The model is motivated by the fact that in real life, users can not exactly plan the time at which they depart from home, nor the delay they experience before they join the congestion bottleneck under investigation. We show that the arrival density advocated by the Nash equilibrium in Vickrey's model, is not a user equilibrium in the model with random uncertainty. We then investigate the existence of a user equilibrium for the latter and show that in general such an equilibrium can neither be a pure Nash equilibrium, nor a mixed equilibrium with a continuous density. Our results imply that when random distortions influence user decisions, the dynamics of standard bottleneck models are inadequate to describe such more complex situations. We illustrate with numerical analysis how the mechanics of a bottleneck with delayed arrivals are unstable for any continuous arrival strategy, thus shedding more light on the non-existence result.

Original languageEnglish
Title of host publicationProceedings of the 12th EAI International Conference on Performance Evaluation Methodologies and Tools, VALUETOOLS 2019
Place of PublicationNew York
PublisherAssociation for Computing Machinery, Inc
Pages55-62
Number of pages8
ISBN (Electronic)978-1-4503-6596-3
DOIs
Publication statusPublished - 12 Mar 2019
Event12th EAI International Conference on Performance Evaluation Methodologies and Tools, VALUETOOLS 2019 - Palma de Mallorca, Spain
Duration: 12 Mar 201915 Mar 2019

Conference

Conference12th EAI International Conference on Performance Evaluation Methodologies and Tools, VALUETOOLS 2019
CountrySpain
CityPalma de Mallorca
Period12/03/1915/03/19

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Keywords

  • Mixed equilibrium
  • Pure equilibrium
  • Random arrival
  • Traffic congestion
  • Travel time uncertainty
  • Vickrey model

Cite this

van Leeuwen, D., Ravner, L., Ghazanfari, S., & Queija, R. N. (2019). A bottleneck with randomly distorted arrival times. In Proceedings of the 12th EAI International Conference on Performance Evaluation Methodologies and Tools, VALUETOOLS 2019 (pp. 55-62). New York: Association for Computing Machinery, Inc. https://doi.org/10.1145/3306309.3306319