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<p>Created page with &quot; == Abstract == xtabstractWe investigate the impact of random deviations in planned arrival times on user equilibrium in an extension of Vickrey’s celebrated bottleneck mod...&quot;</p> <p><b>New page</b></p><div><br /> == Abstract ==<br /> <br /> xtabstractWe 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.<br /> <br /> <br /> == Original document ==<br /> <br /> The different versions of the original document can be found in:<br /> <br /> * [https://dare.uva.nl/personal/pure/en/publications/a-bottleneck-with-randomly-distorted-arrival-times(32f44cd7-c638-4d20-835a-015992bf95e4).html https://dare.uva.nl/personal/pure/en/publications/a-bottleneck-with-randomly-distorted-arrival-times(32f44cd7-c638-4d20-835a-015992bf95e4).html]<br /> <br /> * [https://ir.cwi.nl/pub/29527 https://ir.cwi.nl/pub/29527]<br /> <br /> * [https://ir.cwi.nl/pub/29527/29527.pdf https://ir.cwi.nl/pub/29527/29527.pdf]<br /> <br /> * [https://research.tue.nl/nl/publications/a-bottleneck-with-randomly-distorted-arrival-times(451e79b6-4cc8-499b-8c3b-f8ea890f4f0d).html https://research.tue.nl/nl/publications/a-bottleneck-with-randomly-distorted-arrival-times(451e79b6-4cc8-499b-8c3b-f8ea890f4f0d).html]<br /> <br /> * [https://research.vu.nl/en/publications/578b0122-92fe-40ae-bcab-50d8518bbc4c https://research.vu.nl/en/publications/578b0122-92fe-40ae-bcab-50d8518bbc4c]<br /> <br /> * [http://dl.acm.org/ft_gateway.cfm?id=3306319&amp;ftid=2041100&amp;dwn=1 http://dl.acm.org/ft_gateway.cfm?id=3306319&amp;ftid=2041100&amp;dwn=1],<br /> : [http://dx.doi.org/10.1145/3306309.3306319 http://dx.doi.org/10.1145/3306309.3306319] under the license http://www.acm.org/publications/policies/copyright_policy#Background<br /> <br /> * [http://www.scopus.com/inward/record.url?scp=85062819010&amp;partnerID=8YFLogxK http://www.scopus.com/inward/record.url?scp=85062819010&amp;partnerID=8YFLogxK],<br /> : [http://dx.doi.org/10.1145/3306309.3306319 http://dx.doi.org/10.1145/3306309.3306319]<br /> <br /> * [https://ir.cwi.nl/pub/29527 https://ir.cwi.nl/pub/29527],<br /> : [http://dx.doi.org/10.1145/3306309.3306319 http://dx.doi.org/10.1145/3306309.3306319]<br /> <br /> * [https://research.vu.nl/en/publications/a-bottleneck-with-randomly-distorted-arrival-times https://research.vu.nl/en/publications/a-bottleneck-with-randomly-distorted-arrival-times],<br /> : [https://www.narcis.nl/publication/RecordID/oai%3Acwi.nl%3A29527 https://www.narcis.nl/publication/RecordID/oai%3Acwi.nl%3A29527],<br /> : [https://research.tue.nl/en/publications/a-bottleneck-with-randomly-distorted-arrival-times https://research.tue.nl/en/publications/a-bottleneck-with-randomly-distorted-arrival-times],<br /> : [https://ir.cwi.nl/pub/29527 https://ir.cwi.nl/pub/29527],<br /> : [https://dl.acm.org/citation.cfm?id=3306319 https://dl.acm.org/citation.cfm?id=3306319],<br /> : [https://ir.cwi.nl/pub/29527/29527.pdf https://ir.cwi.nl/pub/29527/29527.pdf],<br /> : [https://dblp.uni-trier.de/db/conf/valuetools/valuetools2019.html#LeeuwenGRN19 https://dblp.uni-trier.de/db/conf/valuetools/valuetools2019.html#LeeuwenGRN19],<br /> : [https://academic.microsoft.com/#/detail/2917009873 https://academic.microsoft.com/#/detail/2917009873]</div>

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