Abstract
This article analyses a bulk arrival retrial queueing system with a single server and two-stage service coupled with a backup server. Client arrivals occur in batches following a compound Poisson process. If the server is idle, one of the clients from the batch receives the first-stage service immediately, and the rest join the orbit. Otherwise, the entire arriving batch joins the orbit. Once the first stage of service is completed, the client moves to the second stage of the service facility. Unsatisfied clients after receiving two stages of service may become feedback clients. After every two-stage service completion, the server may take a vacation of random length. The server has the option to extend its vacation. Breakdowns of the main server can occur at any point during the busy state, and the server has the option to choose its repair type with probabilities. During the vacation and repair period of the main server, clients receive service from a standby (backup) server. Performance measures are derived, stochastic decomposition laws are also verified and special cases are analysed. Numerical results are presented to validate the impact of parameters on the system. Cost analysis and optimization have been carried out for the proposed model.
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