Geodesic
Simulation of relay-races
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 9 (2016) no. 4, pp. 117-128

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It is shown that multistage concurrent games, or relay-races, are widely used in practice. It is proposed to model relay-races in the state space, in which discrete co-ordinates are the mathematical analogue of stages, which participants pass in the current time, and basic principle of modelling of residence of participant in space states is the $M$-parallel semi-Markov process. With use of the proposed formalisms formulae for evaluation of stochastic and time characteristics of relay-races evolution are obtained. For arbitrary realization of switching trajectory the recurrent procedure of evolution with evaluation of stochastic and time characteristics of realization under investigation is worked out. Conception of distributed forfeit, which depends on difference of stages of participants compete in pairs is introduced. Dependence for evaluation of total forfeit for every participant is obtained.
Keywords: relay-race; concurrent game; $M$-parallel semi-Markov process; distance; stage; state space; evolution; distributed forfeit; trajectory realization; recurrent procedure. 
@article{VYURU_2016_9_4_a10,
     author = {E. V. Larkin and V. V. Kotov and A. N. Ivutin and A. N. Privalov},
     title = {Simulation of relay-races},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {117--128},
     publisher = {mathdoc},
     volume = {9},
     number = {4},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2016_9_4_a10/}
}
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E. V. Larkin; V. V. Kotov; A. N. Ivutin; A. N. Privalov. Simulation of relay-races. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 9 (2016) no. 4, pp. 117-128. http://geodesic.mathdoc.fr/item/VYURU_2016_9_4_a10/