Generalization of the selfish parking problem
DOI:
https://doi.org/10.21638/spbu01.2022.307Abstract
The work is devoted to the study of a new model of random filling of a segment of large length with intervals of smaller length. Two new formulations of the problem are considered. In the first case, a model is considered in which unit intervals are placed on the segment in such a way that with each next placement of the interval next to the left or right, there should be a free space of length not less than a pre-fixed value. The second model is such that intervals of length 2 are randomly placed and no two intervals should be adjacent. In both cases, the behavior of the average number of located intervals depending on the length of the filled segment is investigated.Keywords:
random filling, parking problem, asymptotic behavior
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References
Литература
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References
1. R´enyi A. On a one-dimensional problem concerning space-filling. Publ. of the Math. Inst. of Hungarian Acad. of Sciences 3, 109-127 (1958).
2. Ananjevskii S.M., Kryukov N.A. The problem of selfish parking. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 5 (63), iss. 4, 549-555 (2018). https://doi.org/10.21638/11701/spbu01.2018.402 (In Russian) [Eng. transl.: Vestnik St Petersb. Univ. Math. 51, 322-326 (2018). https://doi.org/10.3103/S1063454118040039].
3. Ananjevskii S.M., Kryukov N.A. On asymptotic normality in one generalization of the Renyi problem. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 6 (64), iss. 3, 353-362 (2019). https://doi.org/10.21638/11701/spbu01.2019.301 (In Russian) [Eng. transl.: Vestnik St Petersb. Univ. Math. 52, 227-233 (2019). https://doi.org/10.1134/S1063454119030026].
4. Clay M.P., Simanyi N.J. R´enyi’s parking problem revisited. Mathematical theory. 29 Dec. 2014. ArXiv:1406.1781v1 [math.PR].
5. Gerin L. The Page-R´enyi parking process. 28 Nov. 2014. ArXiv:1411.8002v1[math.PR].
6. Ananjevskii S.M. Generalizations of the parking problem. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 3 (61), iss. 4, 525-532 (2016). https://doi.org/10.21638/11701/spbu01.2016.401 (In Russian) [Eng. transl.: Vestnik St Petersb. Univ. Math. 49, 299-304 (2016). https://doi.org/10.3103/S1063454116040026].
7. Ananjevskii S.M. The “parking” problem for segments of different length. Zapiski Nauchnykh Seminarov POMI 228, 16-23 (1996). (In Russian) [Eng. transl.: Journal of Mathematical Sciences 93, 259-264 (1999). https://doi.org/10.1007/BF02364808].
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Published
2022-10-10
How to Cite
Ananjevskii, S. M., & Chen, A. P. (2022). Generalization of the selfish parking problem. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 9(3), 464–473. https://doi.org/10.21638/spbu01.2022.307
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Mathematics
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Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.
