Geodesic
Discrete model of paired relay-race
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 11 (2018) no. 3, pp. 72-84

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The case of the active and passive team relay-race, in which an active team operates in accordance with rigid schedule and a passive team overcome the stage of its distance at randomly selected alternative routs during occasional time intervals is considered. Due to high complexity of classical relay-race analysis, method of simulation, based on representation of time intervals densities of passing stages routs with discrete distributions is proposed. It is shown, that after transformation of time intervals densities into discrete distributions the problem of a relay race analysis reduces to the task of analysis of two-team system with rigid schedules. The method of sampling of densities composition with estimation a sampling error, and recursive procedure of rigid schedule relay-race analysis with calculation of forfeit are worked out. It is shown, that forfeit depends on the difference of stages, teams overcome at current time and a strategy, which active team realizes during relay-race.
Keywords: relay race; semi-Markov process; distance; stage; route; sampling; schedule; distributed forfeit. 
@article{VYURU_2018_11_3_a5,
     author = {E. V. Larkin and A. V. Bogomolov and A. N. Privalov and N. N. Dobrovolsky},
     title = {Discrete model of paired relay-race},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {72--84},
     publisher = {mathdoc},
     volume = {11},
     number = {3},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2018_11_3_a5/}
}
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E. V. Larkin; A. V. Bogomolov; A. N. Privalov; N. N. Dobrovolsky. Discrete model of paired relay-race. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 11 (2018) no. 3, pp. 72-84. http://geodesic.mathdoc.fr/item/VYURU_2018_11_3_a5/