Title: The discrete analysis of relay-races

Authors: Evgenii V. Larkin; Aleksandr N. Privalov

Addresses: Tula State University, pr-kt Lenina, 92, Tula, Tula region, 300012, Russia ' Tula State Lev Tolstoy Pedagogical University, pr-kt Lenina, 125, Tula, Tula region, 300026, Russia

Abstract: It is shown that relay-races as a form of concurrency, are widespread in such fields of human activity, as industry, defence, economics, politics, etc. The analytical description of J stages relay-races, in which participate M teams, is considered. The model based on the semi-Markov process theory allows investigating a process evolution in detail but is of little use for computer calculation of forfeit, which the winner team receives from loser teams. To adapt analytical description to computer calculations, the method based on sampling of continual time densities of passing stages is proposed. Due to the method, initial semi-Markov process is converted to semi-Markov process with degenerative distributions, and the task of forfeit calculation is reduced to the task of rigid schedules effectiveness analysis, in which schedules are selected stochastically from the densities samples. Formulae for the stochastic summation of forfeits, is obtained. The results may be used for optimal planning the activity of participant teams when passing the distance.

Keywords: relay-race; semi-Markov process; time density sampling; rigid schedule; distributed forfeit; stochastic summation.

DOI: 10.1504/IJISE.2020.106854

International Journal of Industrial and Systems Engineering, 2020 Vol.35 No.1, pp.100 - 113

Received: 30 Jul 2018
Accepted: 14 Oct 2018
Published online: 23 Apr 2020 *

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