• BATCH ARRIVAL OF TWO STAGES WITH STANDBY SERVER DURING GENERAL VACATION TIME & GENERAL REPAIR TIME

Abstract

This Paper study about a batch arrival queueing model with two stages of service, Random breakdowns and Bernoulli schedule server vacations .An additional aspect of stand by server is considered here .After a service completion, the server has the option to leave the system or to continue serving customers by staying in the system. .It is assumed that customers arrive to the system in batches of variable size, but served one by one. After completion of first stage of service, the server must provide the second stage of service to the customers. Vacation time and repair time follows general distribution. Stand by server time follows exponential distribution. We obtain steady state results in explicit and closed form in terms of the probability generating functions for the number of customers in the queue, average number of customers, and the average waiting time in the queue.