GSPN analysis of retrial systems with servers breakdowns and repairs.

*(English)*Zbl 1156.68319Summary: Multiserver retrial systems arise in telecommunication and computer networks areas. It is of basic importance to study performance and reliability of retrial systems with unreliable servers, because of limited ability of repairs and heavy influence of the breakdowns on the performance of the system. However, so far the repairable retrial systems are analyzed only by queueing theory and almost works assumed that service station consists of one single server. In this paper, we give a detailed analysis of finite-source retrial systems with multiple servers subject to random breakdowns and repairs using generalized stochastic petri nets model. We show how this high level model allows us to cope with the complexity of such retrial systems involving the unreliability of the servers, under the different breakdowns disciplines. The main steady-state performance and reliability indices are derived and several numerical calculations were performed to show the effect of servers number, retrial, failure and repair rates on the performability measures of the system.

##### MSC:

68M20 | Performance evaluation, queueing, and scheduling in the context of computer systems |

##### Keywords:

Retrial systems; Finite source; Multiple symmetric servers; Breakdowns and repairs; Generalized stochastic Petri nets; Performance and reliability analysis
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\textit{N. Gharbi} and \textit{M. Ioualalen}, Appl. Math. Comput. 174, No. 2, 1151--1168 (2006; Zbl 1156.68319)

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