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Performance analysis of retrial M/G/1 model with optional services, vacation and delayed repair under instant Bernoulli feedback policy
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DOI：10.1016/j.eij.2026.100945.png)
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Abstract
En 中文
In present article, we investigate a retrial queue model, where units arrive individually in a Poisson fashion. A single server provides two types of services: the first is essential, and the second is optional. After receiving the essential service, a unit may choose the ith optional service from among k available options with a probability of pi . The server is prone to unexpected failures and may malfunction at any phase of the necessary or optional services. When a server fails, it is sent for repair promptly if the repair facility is accessible; otherwise, it must wait for the repair to start. After repair, it is assumed that server is as good as new one and resumes the service of unit already in service. The server may take a vacation of random duration once the system becomes idle. Additionally, after finishing both phases of service, an unsatisfied unit may again request for the same service so that it may get desired level of accuracy. The unit may repeat the same service at most l-1 time. We apply the probability generating function and supplementary variable techniques to analyse the model. Various performance indices associated with the present model are evaluated in explicit form. Finally, the cost structure of the performance indices is studied, and a sensitivity analysis of these indices is discussed.
Keywords:
Retrial
Bernoulli feedback
Optional services
Unreliable server
Delayed repair
Single vacation
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68M20
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