×

zbMATH — the first resource for mathematics

Congestion analysis of unsignalized intersections: the impact of impatience and Markov platooning. (English) Zbl 1403.90223
Summary: This paper considers an unsignalized intersection used by two traffic streams. The first stream of cars is using a primary road, and has priority over the other stream. Cars belonging to the latter stream cross the primary road if the gaps between two subsequent cars on the primary road are larger than their critical headways. A question that naturally arises relates to the capacity of the secondary road: given the arrival pattern of cars on the primary road, what is the maximum arrival rate of low-priority cars that can be sustained? This paper addresses this issue 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 capacity. The contributions of this paper are threefold. First, we introduce a new way to analyze the capacity of the minor road. By representing the unsignalized intersection by an appropriately chosen Markovian model, the capacity can be expressed in terms of the solution of an elementary system of linear equations. The setup chosen is so flexible that it allows us to include a new form of bunching on the main road that allows for dependence between successive gaps, which we refer to as Markov platooning; this is the second contribution. The tractability of this model facilitates studying the impact that driver impatience and various platoon formations on the main road have on the capacity of the minor road. Finally in numerical experiments, we observe various surprising features of the aforementioned model.

MSC:
90B20 Traffic problems in operations research
90B22 Queues and service in operations research
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Abhishek; Boon, M. A.A.; Mandjes, M.; Núñez Queija, R., Congestion analysis of unsignalized intersections, Proceedings of the intelligent transportation systems workshop, COMSNETS 2016, 1-6, (2016)
[2] Abou-Henaidy, M.; Teply, S.; Hund, J. H., Gap acceptance investigations in Canada, (Akçelik, R., Proceedings of the second international symposium on highway capacity, 1, (1994)), 1-19
[3] Catchpole, E. A.; Plank, A. W., The capacity of a priority intersection, Transportation Research-B, 20B, 6, 441-456, (1986)
[4] Cheng, T. E.C.; Allam, S., A review of stochastic modelling of delay and capacity at unsignalized priority intersections, EJOR, 60, 3, 247-259, (1992) · Zbl 0825.90402
[5] Drew, D. R.; Buhr, J. H.; Whitson, R. H., The determination of merging capacity and its applications to freeway design and control, Report 430-4, (1967), Texas Transportation Institute
[6] Drew, D. R.; LaMotte, L. R.; Buhr, J. H.; Wattleworth, J., Gap acceptance in the freeway merging process, Report 430-2, (1967), Texas Transportation Institute
[7] Gaur, A.; Mirchandani, P., Method for real-time recognition of vehicle platoons, Transportation Research Record, 1748, 8-17, (2001)
[8] Guo, R. J.; Lin, B. L., Gap acceptance at priority-controlled intersections, Journal of Transportation Engineering, 137, 4, 269-276, (2011)
[9] Guo, R.-J.; Wang, X.-J.; Wang, W.-X., Estimation of critical gap based on Raff’s definition, Computational Intelligence and Neuroscience, 2014, (2014), Article ID 236072, 7 pages
[10] Heidemann, D.; Wegmann, H., Queueing at unsignalized intersections, Transportation Research-B, 31, 3, 239-263, (1997)
[11] Horn, R. A.; Johnson, C. R., Matrix analysis, (1986), Cambridge University Press: Cambridge University Press New York, NY, USA
[12] Jia, D.; Lu, K.; Wang, J.; Zhang, X.; Shen, X., A survey on platoon-based vehicular cyber-physical systems, IEEE Communications Surveys & Tutorials, 18, 1, 263-284, (2016)
[13] Li, B., Stochastic modeling for vehicle platoons (I): Dynamic grouping behavior and online platoon recognition, Transportation Research Part B, 95, 364-377, (2017)
[14] Mayne, A. J., Some further results in the theory of pedestrians and road traffic, Biometrika, 41, 3/4, 375-389, (1954) · Zbl 0059.12201
[15] Takagi, H., Queueing analysis: A foundation of performance evaluation, Vacation and priority systems, Part 1, 1, (1991), North-Holland: North-Holland Amsterdam
[16] Tanner, J. C., The delay to pedestrians crossing a road, Biometrika, 38, 3/4, 383-392, (1951) · Zbl 0043.34004
[17] Tanner, J. C., A theoretical analysis of delays at an uncontrolled intersection, Biometrika, 49, 1/2, 163-170, (1962) · Zbl 0213.45602
[18] Wegmann, H., Intersections without traffic signals II, (Brilon, W., A general capacity formula for unsignalized intersections, (1991), Springer-Verlag), 177-191
[19] Wei, D.; Kumfer, W.; Wu, D.; Liu, H., Traffic queuing at unsignalized cross-walks with probabilistic priority, Transportation Letters, 10, 3, 129-143, (2018)
[20] Weiss, G. H.; Maradudin, A. A., Some problems in traffic delay, Operations Research, 10, 1, 74-104, (1962) · Zbl 0113.12603
[21] Wu, N., A universal procedure for capacity determination at unsignalized (priority-controlled) intersections, Transportation Research Part B, 35, 593-623, (2001)
[22] Wu, N., Equilibrium of probabilities for estimating distribution function of critical gaps at unsignalized intersections, Transportation Research Record, 2286, 49-55, (2012)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.