Batch arrival retrial queue with delay time and additional multi-optional repair

This paper deals with MX/G/1 retrial queue with unreliable server and multi-optional repair. It is assumed that the server is subject to active breakdowns and the repair of the failed server starts after a random amount of time. Restoration of the failed server is done with two phases, first essential and second multi optional. After completion of the repair the server continues the interrupted service and it is not allowed to accept new customers until the interrupted customer leaves the system. The retrial, service, delay and repair times are arbitrarily distributed. The model is analysed using the supplementary variable technique and the probability generating function of system size at random epoch and stochastic decomposition are obtained. Performance measures and reliability indices to predict the behaviour of the system are derived.