Maximum entropy approach for an unreliable MX/G/1 queueing system with Bernoulli vacation, restricted admission and delayed phase repair under N-policy

The present article deals with a bulk arrival queueing model with an unreliable server and modified Bernoulli vacation under N‐policy. The repairman who restores the server requires a setup time before starting his job. The repair to the failed server is provided in K‐phases where first phase of repair is essential and remaining (K‐1) phases are optional. The service time, vacation time, setup time and repair time of each phase are assumed to be independent and general distributed. The queue size distribution and other performance indices are obtained by employing the generating function and supplementary variable techniques. Further, the principle of maximum entropy is used to derive the approximate formulae for the waiting time of the customers. We perform the sensitivity analysis in order to observe the effects of different system parameters on various performance indices.