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We present a single server with two heterogeneous service stages having different general (arbitrary) distribution, subject to random breakdowns and Bernoulli scheduled server vacation. The customers arrive in batches and the server provides service one by one. The second stage service must be provided after completing the first stage service by the server. On completion of the first phase of the service with FCFS schedule, the second phase starts. With probability p the customer feedback to the tail of original queue for repeating the service until the service be successful. With probability 1 - p = q the customer departs the system if service be successful. Upon the completion of the second stage service, the server will go for vacation with probability

iosr journal of mathematics

Batch Arrival, Single Server with Two Stage Heterogeneous Service, Bernoulli Schedule Server Vacation Feed Back, Random Break Down and Delayed Repair Time