Homogeneous finite-source retrial queues with server subject to breakdowns and repairs.

*(English)*Zbl 1090.90036Summary: This paper deals with a single server retrial queue with a finite number of homogeneous sources of calls and a single nonreliable server, which means that the server is subject to random breakdowns depending on whether it is busy or idle. The failure of the server may block or unblock the systems’ operations and the service of the interrupted request may be resumed or the call can be transmitted to the orbit. All random variables involved in the model constructions are supposed to be exponentially distributed and independent of each other.

The novelty of the investigation is the variability of this nonreliability of the server which makes the system rather complicated. The MOSEL tool was used to formulate and solve the problem and the main performance and reliability measures were derived and graphically displayed. Several numerical calculations were performed to show the effect of the nonreliability of the server on the mean response times of the calls.

The novelty of the investigation is the variability of this nonreliability of the server which makes the system rather complicated. The MOSEL tool was used to formulate and solve the problem and the main performance and reliability measures were derived and graphically displayed. Several numerical calculations were performed to show the effect of the nonreliability of the server on the mean response times of the calls.

##### MSC:

90B22 | Queues and service in operations research |

90B25 | Reliability, availability, maintenance, inspection in operations research |

##### Keywords:

retrial queuing systems; nonreliable server; performance tools; performance and reliability measures##### Software:

MOSEL
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\textit{B. Almási} et al., Math. Comput. Modelling 42, No. 5--6, 673--682 (2005; Zbl 1090.90036)

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