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**A repairable queueing model with two-phase service, start-up times and retrial customers.**
*(English)*
Zbl 1178.90090

Summary: A repairable queueing model with a two-phase service in succession, provided by a single server, is investigated. Customers arrive in a single ordinary queue and after the completion of the first phase service, either proceed to the second phase or join a retrial box from where they retry, after a random amount of time and independently of the other customers in orbit, to find a position for service in the second phase. Moreover, the server is subject to breakdowns and repairs in both phases, while a start-up time is needed in order to start serving a retrial customer. When the server, upon a service or a repair completion finds no customers waiting to be served, he departs for a single vacation of an arbitrarily distributed length. The arrival process is assumed to be Poisson and all service and repair times are arbitrarily distributed. For such a system the stability conditions and steady state analysis are investigated. Numerical results are finally obtained and used to investigate system performance.

### MSC:

90B22 | Queues and service in operations research |

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

### Keywords:

Poisson arrivals; two-phase service; retrial queue; breakdowns; repairs; start-up time; vacation
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\textit{I. Dimitriou} and \textit{C. Langaris}, Comput. Oper. Res. 37, No. 7, 1181--1190 (2010; Zbl 1178.90090)

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