M/EK/1 Queueing System with Vacation, Two types of Repair facilities and Server Timeout

Abstract

 In this paper, we detailed a queueing model with Two types of Repair facilities (TRF) and server timeout. Each customer in the system is to be served in k independent and identically distributed exponential phases. The server does the service for the waiting customer exhaustively. After service is completed, the server waits for the fixed time ‘c’ for the customer arrive called server Time-out, otherwise go for vacation. During Time-out, server commence service if one customer arrive else it goes for vacation. If the system fails, repair process will be initiated instantly. Here failure server is expedited with two Two types of Repair facilities (TRF) “where Type –I service facility is used with a probability of 1-q to resume the interrupted service when the server fails during a service and customer stays in service facility to get the balance service whereas Type-II service facility is done with a probability q when the server fails before the staring of service to a new customer who joins the head of the queue”. Explicit expressions are derived for various constants of queueing system and also illustrated numerical results.