Congestion analysis of unsignalized intersections

Abhishek, Marko Boon, Michel Mandjes, Rudesindo Núñez-Queija

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Abstract

This paper considers an unsignalized intersection used by two traffic streams. A stream of cars is using a primary road, and has priority over the other, low-priority, stream. Cars belonging to the latter stream cross the primary road if the gaps between two subsequent cars on the primary road is larger than their critical headways. Questions that naturally arise are: given the arrival pattern of the cars on the primary road, what is the maximum arrival rate of low-priority cars such that the number of such cars remains stable? In the second place, what can be said about the delay experienced by a typical car at the secondary road? This paper addresses such issues by considering a compact model that sheds light on the dynamics of the considered unsignalized intersection. The model, which is of a queueing-theoretic nature, reveals interesting insights into the impact of the user behavior on the above stability and delay issues. The contribution of this paper is twofold. First, we obtain new results for the aforementioned model with driver impatience. Secondly, we reveal some surprising aspects that have remained unobserved in the existing literature so far, many of which are caused by the fact that the capacity of the minor road cannot be expressed in terms of the \emph{mean} gap size; instead more detailed characteristics of the critical headway distribution play a role.
Original languageEnglish
Article number1802.06858v1
Number of pages6
JournalarXiv.org, e-Print Archive, Mathematics
Volume2018
Publication statusPublished - 5 Feb 2018

Bibliographical note

This paper appeared in the proceedings of the 8th International Conference on Communication Systems and Networks (COMSNETS), 5-10 Jan. 2016. A related but more extended paper which analyses a more general model than the one in the present paper can be also found on arXiv:1802.06732

Keywords

  • math.OC
  • math.PR
  • physics.soc-ph

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