Abstract
The author concerned the reliability evaluation as well as queueing analysis of \(M_1 ,{{M_2 } \mathord{\left/ {\vphantom {{M_2 } {G_1 }}} \right. \kern-\nulldelimiterspace} {G_1 }},{{G_2 } \mathord{\left/ {\vphantom {{G_2 } 1}} \right. \kern-\nulldelimiterspace} 1}\)
retrial queues with two different types of primary customers arriving according to independent Poisson flows. In the case of blocking, the first type of customers can be queued whereas the second type of customers must leave the service area but return after some random period of time to try their luck again. The author assumes that the server is unreliable and it has a service-type dependent, exponentially distributed life time as well as a service-type dependent, generally distributed repair time. The necessary and sufficient condition for the system to be stable is investigated. Using a supplementary variable method, the author obtains a steady-state solution for queueing measures, and the transient as well as the steady-state solutions for reliability measures of interest.
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*This research is sponsored by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, Education Ministry and the National Natural Science Foundation of China under Grant Nos 10526004 and 60504016.
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WANG, J. On the single server retrial queue with priority subscribers and server breakdowns. J Syst Sci Complex 21, 304–315 (2008). https://doi.org/10.1007/s11424-008-9114-x
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DOI: https://doi.org/10.1007/s11424-008-9114-x