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Abstract In this paper, we examine a single-server queuing model where units join the queue according to a Poisson arrival process. The server encounters two distinct customer types. The first type is the positive customer, who promptly joins the service if a server is free. Otherwise, they enter an imaginary queue called a retrial orbit and make subsequent service attempts after a certain period. The second customer type is the negative customer, whose arrival not only results in a server failure but also entails the removal of the customer currently being serviced. Following a failure, the server undergoes immediate essential repairs, with an option for additional optional repairs upon completion. Upon concluding the service of a positive customer, the server may opt for a vacation with a probability denoted by 'θ'. Further we have applied server orbital search policy to reduce the idle time of server after completion of service or repair or vacation. We employ the supplementary variable technique to comprehensively analyze the model and derive explicit expressions for performance measures. To provide practical insights, we conduct a numerical illustration to investigate the sensitivity of various parameters on performance indices. MSC: 60K25 68M20 90B22
Binay Kumar (Tue,) studied this question.