In this paper, the problem of setting traffic light cycles at crossroads and intersections is considered in order to reduce traffic congestion by minimizing total vehicle waiting time. A method to determine the family ℘ of all discrete cycle phasing systems with the minimum number of phases is presented. The aim is to detect the most appropriate phasing sequence for traffic control corresponding to a current traffic situation from among all the components of ℘. The method is applied at a complex multi-cross intersection. The problem, dealing with traffic movements and the conflicting relations that arise, is stated within the framework of graph theory. There are several methods for setting traffic signal cycles at traffic light intersections. In this paper and in the context of graph theory, we develop a method which aims to determine the family of all discrete phases of phase systems with the smallest number of phases. The aim is to select from the elements of the the appropriate phase system that corresponds to the current traffic situation.
| Published in | American Journal of Applied Mathematics (Volume 9, Issue 3) |
| DOI | 10.11648/j.ajam.20210903.12 |
| Page(s) | 70-74 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2021. Published by Science Publishing Group |
Traffic Signal Cycles, Graph Coloring, Pedestrian Crosswalk
| [1] | Alexiou D., (2018), Generating the family of all traffic signal light cycles coordinated with pedestrian crosswalks, Optimization Letter. |
| [2] | Alexiou D., Katsavounis S. (2013), Determining the Minimum Number of Ware-houses and their Space-Size for Storing Compatible Items, Optimization Theory, Decision Making, and Operations Research Applications, Springer Proceedings in Mathematics & Statistics 189-198. |
| [3] | Bollobas B. (1998), Modern Graph Theory. Springer-Verlag. |
| [4] | Bondy J. A. (2008), Graph Theory. Springer. |
| [5] | Beineke L. (2004), Robin Wilson and Peter Cameron. Graph theory, Group Theory. Topics in Algebraic Graph Theory Cambridge Univ. Press. |
| [6] | Christofides N. (1975), Graph Theory, an Algorithmic Approach (Academic Press). |
| [7] | Claude B. (1998), Theorie des Graphes et ses Applications, Dunod (Paris). |
| [8] | Neubüser J. An elementary introduction to coset table methods in computational group theory. |
| [9] | Novikov P. S. (1955), On the algorithmic insolvability of the word problem in group theory. Trudy Mat. Inst. Steklov 44, p. 1-143. |
| [10] | Papageorgiou M, Diakaki C., Dinopoulou V., Kotsialos A., and Wang Y (2003)., Review of road traffic control strategies, Proceedings ofthe IEEE, Vol. 91, Issue: 12. |
| [11] | Traffic Signal Operation, Transport Management Center, RTA-TC-106 (2010), http://www.rms.nsw.gov.au/doingbusinesswithus/downloads/technicalmanuals/trafficsignalspecifications/rtatc106b.pdf. |
| [12] | Mathew, T., Krishna R.: Traffic signal design-I, Chap. 41, NPTEL (2006). |
| [13] | B. Bollobas: Modern Graph Theory, Springer-Verlag, 1 edition (1998). |
| [14] | Raychaudhuri, A.: Optimal multiple interval assignments in frequency assignment and traffic phasing. Discrete Appl. Math. 40 (3), 319–332 (1992). |
| [15] | Opsut, R. J., Roberts, F. S.: I-Colorings. I-Phasings and I-intersection assignments for graphs, and their applications. Networks 13, 327–345 (1983b). |
APA Style
Dimitra Alexiou, Leonidas Bakouros. (2021). The Problem of Setting Traffic Signal Cycles at Crossroads. American Journal of Applied Mathematics, 9(3), 70-74. https://doi.org/10.11648/j.ajam.20210903.12
ACS Style
Dimitra Alexiou; Leonidas Bakouros. The Problem of Setting Traffic Signal Cycles at Crossroads. Am. J. Appl. Math. 2021, 9(3), 70-74. doi: 10.11648/j.ajam.20210903.12
AMA Style
Dimitra Alexiou, Leonidas Bakouros. The Problem of Setting Traffic Signal Cycles at Crossroads. Am J Appl Math. 2021;9(3):70-74. doi: 10.11648/j.ajam.20210903.12
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Download@article{10.11648/j.ajam.20210903.12,
author = {Dimitra Alexiou and Leonidas Bakouros},
title = {The Problem of Setting Traffic Signal Cycles at Crossroads},
journal = {American Journal of Applied Mathematics},
volume = {9},
number = {3},
pages = {70-74},
doi = {10.11648/j.ajam.20210903.12},
url = {https://doi.org/10.11648/j.ajam.20210903.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20210903.12},
abstract = {In this paper, the problem of setting traffic light cycles at crossroads and intersections is considered in order to reduce traffic congestion by minimizing total vehicle waiting time. A method to determine the family ℘ of all discrete cycle phasing systems with the minimum number of phases is presented. The aim is to detect the most appropriate phasing sequence for traffic control corresponding to a current traffic situation from among all the components of ℘. The method is applied at a complex multi-cross intersection. The problem, dealing with traffic movements and the conflicting relations that arise, is stated within the framework of graph theory. There are several methods for setting traffic signal cycles at traffic light intersections. In this paper and in the context of graph theory, we develop a method which aims to determine the family of all discrete phases of phase systems with the smallest number of phases. The aim is to select from the elements of the the appropriate phase system that corresponds to the current traffic situation.},
year = {2021}
}
TY - JOUR T1 - The Problem of Setting Traffic Signal Cycles at Crossroads AU - Dimitra Alexiou AU - Leonidas Bakouros Y1 - 2021/06/07 PY - 2021 N1 - https://doi.org/10.11648/j.ajam.20210903.12 DO - 10.11648/j.ajam.20210903.12 T2 - American Journal of Applied Mathematics JF - American Journal of Applied Mathematics JO - American Journal of Applied Mathematics SP - 70 EP - 74 PB - Science Publishing Group SN - 2330-006X UR - https://doi.org/10.11648/j.ajam.20210903.12 AB - In this paper, the problem of setting traffic light cycles at crossroads and intersections is considered in order to reduce traffic congestion by minimizing total vehicle waiting time. A method to determine the family ℘ of all discrete cycle phasing systems with the minimum number of phases is presented. The aim is to detect the most appropriate phasing sequence for traffic control corresponding to a current traffic situation from among all the components of ℘. The method is applied at a complex multi-cross intersection. The problem, dealing with traffic movements and the conflicting relations that arise, is stated within the framework of graph theory. There are several methods for setting traffic signal cycles at traffic light intersections. In this paper and in the context of graph theory, we develop a method which aims to determine the family of all discrete phases of phase systems with the smallest number of phases. The aim is to select from the elements of the the appropriate phase system that corresponds to the current traffic situation. VL - 9 IS - 3 ER -
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