Unreliable server retrial <i>G</i>-queue with bulk arrival, optional additional service and delayed repair

Abstract

The retrial bulk arrival queue with unreliable server and negative customers is considered. On arrival of the group of customers, one of the customers gets the service immediately if the server is idle and other customers join the retrial orbit. There is a provision to opt additional service after completion of the essential service of the customers. The server may fail due to arrival of negative customers during any stage of the service. After completion of the service, the customer may again join the queue as a feedback customer to get another regular/optional service or depart from the system. The non-persistent (impatient) phenomenon also occurs because of the delayed in repair/repair time of the failed server. By using the supplementary variable approach, various measures of queueing and reliability characteristics are analysed. To facilitate the comparative study of the performance metrics of the system, the maximum entropy principle is used. The numerical results for various performance indices and optimal cost are obtained.