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Vestnik YuUrGU. Ser. Mat. Model. Progr., 2015, Volume 8, Issue 2, Pages 43–54 (Mi vyuru262)  

This article is cited in 3 scientific papers (total in 3 papers)

Mathematical Modelling

Simulation of concurrent games

A. N. Ivutin, E. V. Larkin

Tula State University, Tula, Russian Federation

Abstract: Concurrent games, in which participants run some distance in real physical time, are investigated. Petri–Markov models of paired and multiple competitions are formed. For paired competition formula for density function of time of waiting by winner the moment of completion of distance by loser is obtained. A concept of distributed forfeit, which amount is defined as a share of sum, which the winner gets from the loser in current moment of time is introduced. With use of concepts of distributed forfeit and waiting time the formula for common forfeit, which winner gets from loser, is obtained. The result, received for a paired competition, was spread out onto multiple concurrent games. Evaluation of common wins and loses in multiple concurrent game is presented as a recursive procedure, in which participants complete the distance one after another, and winners, who had finished the distance get forfeits from participants, who still did not finish it. The formula for evaluation of common winning in concurrent game with given composition of participants is obtained. The result is illustrated with numerical example.

Keywords: competition; concurrent game; Petri–Markov net; distance; distributed forfeit; waiting time; common winning; paired competition, multiple competition.

DOI: https://doi.org/10.14529/mmp150204

Full text: PDF file (460 kB)
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Bibliographic databases:

UDC: 519.83
MSC: 93A30
Received: 11.02.2015
Language:

Citation: A. N. Ivutin, E. V. Larkin, “Simulation of concurrent games”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 8:2 (2015), 43–54

Citation in format AMSBIB
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\by A.~N.~Ivutin, E.~V.~Larkin
\paper Simulation of concurrent games
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2015
\vol 8
\issue 2
\pages 43--54
\mathnet{http://mi.mathnet.ru/vyuru262}
\crossref{https://doi.org/10.14529/mmp150204}
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\elib{http://elibrary.ru/item.asp?id=23442152}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. V. Larkin, D. V. Gorbachev, A. N. Privalov, “O priblizhenii potoka sobytii k puassonovskomu”, Chebyshevskii sb., 18:2 (2017), 222–234  mathnet  crossref  elib
    2. E. V. Larkin, A. N. Privalov, “Alternative routs of games with rigid schedule”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 10:3 (2018), 30–40  mathnet  crossref  elib
    3. E. V. Larkin, A. V. Bogomolov, A. N. Privalov, N. N. Dobrovolsky, “Discrete model of paired relay-race”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 11:3 (2018), 72–84  mathnet  crossref  elib
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