Vestnik KRAUNC. Fiz.-Mat. Nauki. 2022. vol. 40. no. 3. pp. 101–110. ISSN 2079-6641
A complete system of conditions for uncongested traffic of vehicles in front of a traffic light at a symmetrical two-lane intersection
V. Ch. Kudaev, A. K. Buzdov
Institute of Informatics and Regional Management Problems of the KBNTS RAS, Kabardino-Balkar Republic, Nalchik, Russia.
E-mail: email@example.com, firstname.lastname@example.org
The problem of optimizing the transport system of cities has not yet been solved. One of the urgent practical problems is the problem of the operation mode of traffic light at the city intersections. The present article is based on the theoretically proven by M. Lighthill and J. Whitham and now widely known condition of non-accumulation of vehicles in front of an intersection traffic light operating in two modes (red light on, green light on) along each of the intersection routes. Although more than 70 years have passed since the Lighthill-Whitham condition was proved, this condition is not used in practice, and is treated as a purely theoretical result. However, the Lighthill-Whitham condition may quite simply get a practical interpretation and average values of the traffic flow would be obtained, based on measurements of the intersection lanes’ traffic. Based on the Lighthill-Whitham condition, the paper proves the general condition (necessary and sufficient) to avoid the congestion of vehicles in front of a traffic light at an intersection as a whole and a sufficient condition for blocking an intersection, which makes it possible to identify symmetrical two-lane intersections along each of the highways in the city, that are close to blocking. An optimal solution to the problem of a traffic light is presented
based on a commutation relation that sets the limiting times for the green traffic light to be on along each of the intersection routes. It was a symmetrical two-lane intersection that was considered in the work, for the reason that such intersections make up a larger part of urban intersections.
Key words: symmetrical intersection, traffic light problem, non-congestion of vehicles conditions.
Original article submitted: 05.10.2022
Revision submitted: 29.10.2022
For citation. Kudaev V. Ch., Buzdov A. K. A complete system of conditions for uncongested traffic of vehicles in front of a traffic light at a symmetrical two-lane intersection. Vestnik KRAUNC. Fiz.-mat. nauki. 2022, 40: 3, 101-110. DOI: 10.26117/2079-6641-2022-40-3-101-110
Competing interests. The authors declare that there are no conflicts of interest regarding authorship and publication.
Contribution and Responsibility. All authors contributed to this article. Authors are solely responsible for providing the final version of the article in print. The final version of the manuscript was approved by all authors.
The content is published under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/deed.ru)
© Kudaev V. Ch., Buzdov A. K., 2022
- Gasnikova A. V. Vvedenie v matematicheskoe modelirovanie transportnykh potokov. Moscow, MFTI, 2010, 417,(In Russian).
- Lighthill M. J., Whitham G. B. On kinematic waves: II Theory of traffic flow on long crowded roads, Proc. R. Soc. London. Ser. A., 1955, 229, 281–345.
- Uizem Dzh. Lineynye i nelineynye volny. Moscow, Mir, 1977 (In Russian).
- Richards P.I. Shock Waves on the Highway. Oper. Res., 1956, 4, 42–51.
- Shets S.P., Spravtseva E. V., Kalmykov A. A. Primenenie imitatsionnogo modelirovaniya pri sovershenstvovanii organizatsii dorozhnogo dvizheniya na perekrestke goroda Bryanska, Vestnik Bryanskogo gosudarstvennogo tekhnicheskogo universiteta, 2017, 56:3, 67–72 (In Russian).
- Dolgushin D.Yu., Myznikov T. A. Imitatsionnoye modelirovaniye avtotransportnykh potokov dlya otsenki al’ternativnykh skhem organizatsii dorozhnogo dvizheniya v gorodskikh usloviyakh, Vestnik SibADI, 2(20), 2011, 47-52 (In Russian).
- Novikov A. N., Eremin S. V., Shevtsova A. G. Osnovnye printsipy rascheta programmy svetofornogo regulirovaniya na osnove upravlyaemykh setey i potoka nasyshcheniya, Vestnik SibADI, 2019, 16:6, 680–691 (In Russian).
- Novikov I. A., Shevtsova A.G., Kravchenko A. A., Burlutskaya A. G. Razrabotka metodiki adaptatsii modeli reguliruemogo peresecheniya, Vestnik SibADI, 2020, 17:6, 726–735 (In Russian).
- Glukharev K.K., Kalinin I.N. K optimizatsii potoka na perekrestke, Trudy 53-y nauchnoy konferentsii MFTI «Sovremennyye problemy fundamental’nykh i prikladnykh nauk Chast’ III. Aerofizika i kosmicheskiye issledovaniya, 2010, 2, 72–74 (In Russian).
- Kalinin I. N., Glukharev K. K., Interchange integral characteristics study via microscopic traffic flowmodels, Computer Research and Modeling, 2014, 6:4, 523-534 (In Russian).
Kudaev Valery Cherimovich – Ph.D. (Phys. & Math.), Head of the Department of the Institute of Informatics and Regional Management Problems of the KBNTS RAS, Kabardino-Balkar Republic, Nalchik, Russia, ORCID 0000-0002-8313-4199.
Buzdov Aslan Karalbievich – Ph.D. (Phys. & Math.), Senior Researcher, Institute of Informatics and Problems of Regional Management, KBNTS RAS, Kabardino-Balkarian Republic, Nalchik, Russia, ORCID 0000-0001-9097-3348.