Simulation of Concurrent Games

Ivutin, Alexey; Larkin, Eugene

doi:10.14529/mmp150204

Cited by 15 publications

(9 citation statements)

References 5 publications

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“…The distribution density of time taken by the l group of semi-Markov processes to reach the aggregated absorbing state is calculated with the correspondence [11][12][13] where w l p -the probability that the l group of semiMarkov processes will be the last one out of L-parallel processes to reach the aggregated absorbing state:…”

Section: Ml-parallel Semi-markovmentioning

confidence: 99%

«Concurrency» in M-L-Parallel Semi-Markov Process

Larkin

Ivutin

2017

MATEC Web Conf.

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Abstract. This article investigates the functioning of a swarm of robots, each of which receives instructions from the external human operator and autonomously executes them. An abstract model of functioning of a robot, a group of robots and multiple groups of robots was obtained using the notion of semi-Markov process. The concepts of aggregated initial and aggregated absorbing states were introduced. Correspondences for calculation of time parameters of concurrency were obtained.

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Section: Ml-parallel Semi-markovmentioning

confidence: 99%

«Concurrency» in M-L-Parallel Semi-Markov Process

Larkin

Ivutin

2017

MATEC Web Conf.

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“…During evolution the ordinary semi-Markov processes, described by (1), compete between them [2,5]. Let us consider the common case, when processes under competition are described with densities θ 1 (t), .…”

Section: Common Formulae For Evolution Parametersmentioning

confidence: 99%

“…If from competing processes of θ α (t) and θ β (t), θ β (t) wins the process, it waits until θ α (t) will be completed, which may be evaluated as [2,5] …”

Section: Common Formulae For Evolution Parametersmentioning

confidence: 99%

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Simulation of Relay-Races

Larkin¹,

Kotov²,

Ivutin³

et al. 2016

Bulletin of the SUSU. MMP

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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 semiMarkov 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 dierence of stages of participants compete in pairs is introduced. Dependence for evaluation of total forfeit for every participant is obtained.

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