Analysis of an M/G/1 retrial queue with Bernoulli vacation, two types of service and starting failure

The proposed queueing model discusses a single server retrial queueing system subject to a Bernoulli vacation, two types of service and starting failure. The single server provides two types of service in which the customer either chooses type 1 service or type 2 services. We assume that the server may subject to starting failure. After each service completion the server will take a Bernoulli vacation. For such queueing model the necessary and sufficient condition for steady state has been derived. The model has been solved through use of supplementary variable technique. To validate the proposed model some performance measures, special cases and numerical illustrations have been discussed.