Asymptotic analysis of the \(MMPP|M|1\) retrial queue with negative calls under the heavy load condition.

*(Russian. English summary)*Zbl 1455.90040Summary: In the paper, a single-server retrial queueing system with \(MMPP\) arrivals and an exponential law of the service time is studied. Unserviced calls go to an orbit and stay there during random time distributed exponentially, they access to the server according to a random multiple access protocol. In the system, a Poisson process of negative calls arrives, which delete servicing positive calls. The method of the asymptotic analysis under the heavy load condition for the system studying is proposed. It is proved that the asymptotic characteristic function of a number of calls on the orbit has the gamma distribution with the obtained parameters. The value of the system capacity is obtained, so, the condition of the system stationary mode is found. The results of a numerical comparison of the asymptotic distribution and the distribution obtained by simulation are presented. Conclusions about the method applicability area are made.

##### MSC:

90B22 | Queues and service in operations research |

60K25 | Queueing theory (aspects of probability theory) |

60K20 | Applications of Markov renewal processes (reliability, queueing networks, etc.) |

##### Software:

MOSEL##### References:

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