A SINGLE SERVER BULK INPUT QUEUE WITH RANDOM FAILURES AND TWO PHASE REPAIRS WITH DELAY

Abstract

We study a batch arrival single server queueing system, where the server (service channel) provides one by one general service to customers. It is assumed that the service channel goes through random failures from time to time. As the result of a breakdown, the service of a customer in service is suspended, the service channel waits for the repairs to start and this waiting time termed as ‘delay time’ is assumed to be general. Further, the repair process involves two phases of repairs with different general repair time distributions. We derive the queue size distribution as well as mean number of customers in the system at a random epoch under the steady state conditions. In addition, we discuss some particular cases and derive some known results known earlier