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 language | English |
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Title of host publication | Proceedings of the 12th EAI International Conference on Performance Evaluation Methodologies and Tools, VALUETOOLS 2019 |
Publisher | Association for Computing Machinery |
Pages | 55-62 |
Number of pages | 8 |
ISBN (Electronic) | 9781450365963 |
DOIs | |
State | Published - 12 Mar 2019 |
Externally published | Yes |
Event | 12th EAI International Conference on Performance Evaluation Methodologies and Tools, VALUETOOLS 2019 - Palma de Mallorca, Spain Duration: 13 Mar 2019 → 15 Mar 2019 |
Publication series
Name | ACM International Conference Proceeding Series |
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Conference
Conference | 12th EAI International Conference on Performance Evaluation Methodologies and Tools, VALUETOOLS 2019 |
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Country/Territory | Spain |
City | Palma de Mallorca |
Period | 13/03/19 → 15/03/19 |
Bibliographical note
Publisher Copyright:© 2019 Association for Computing Machinery.
Keywords
- Mixed equilibrium
- Pure equilibrium
- Random arrival
- Traffic congestion
- Travel time uncertainty
- Vickrey model
ASJC Scopus subject areas
- Software
- Human-Computer Interaction
- Computer Vision and Pattern Recognition
- Computer Networks and Communications