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Keywords:
regularity measures; optimal location; coordination; transport; common leg; marshalling yard; polygon vertices; scheduling of periodically repeating processes
regularity measures; optimal location; coordination; transport; common leg; marshalling yard; polygon vertices; scheduling of periodically repeating processes
Summary:
The paper deals with the problem how to locate a set of polygon vertices on given circles fulfilling some criteria of "regularity" of individual and composed polygons. Specifying the conditions we can obtain a lot of particular versions of this general problem. Some of them are already solved, the others are not.
Applications of this theory can be found in scheduling of periodically repeating processes, e.g. in coordination of several urban lines on a common leg, in optimization of the rhythm of a marshalling yard etc.
References:
[1] J. Černý M. Hejný: Optimization of the rhythm of a net of urban transport with respect to the total waiting time of passengers for a net of type Y. (Slovak) Doprava 6 (1965), 437-443.
[2] J. Černý M. Hejný: Mathematical solution of optimization of the rhythm of a net of type У. (Slovak) Sborník prací VŠD a VÚD 5, (1967), 5-15.
[3] J. Černý: Problems of systems of regular polygons on a circle and their application in transport. (Slovak) Matematické obzory l, (1972), 51 - 59.
[4] J. Černý: Applied mathematics and transport. (Slovak) Pokroky matematiky, fyziky a astronómie 6 (1974), 316-323. MR 0469252
[5] F. Guldan: Mathematical problems of transport schedules design. (Slovak) (Thesis) Comenius University (1975).
[6] F. Guldan: Maximization of distances of regular polygons on a circle and a generalization of the problem. (Slovak) (Dissertation) Comenius University (1976).
[7] F. Guldan: Maximization of distances of regular polygons on a circle. Aplikace matematiky 25 (1980), 182-195. MR 0568524 | Zbl 0444.90101
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