Analysis of bulk queue with unreliable service station, second optional repair, N-policy multiple vacation, loss and immediate feedback in production system

In this paper an unreliable server bulk service queue with second optional repair, multiple vacation under N-policy, customer's feedback and impatience are considered. After finishing a service, the server avails a multiple vacation under N-policy only when the queue length is less than 'a'. Server vacation models are very much useful for a queueing system in which server needs to utilise his idle time for a different purpose. The server is subject to breakdown during the service and requires second optional repair for restoration. After repair completion, the server will start its remaining service to the batch of customers whose service was interrupted. Further, it is assumed that the arriving units may balk (loss) from the system when the server is on vacation and immediate feedback service was provided to the dissatisfied customers. The queue size distribution at a random and departure epoch has been derived using the supplementary variable technique. Finally, the stability condition, some performance measures, particular cases and numerical results of the proposed model are obtained.