A two phase batch arrival retrial queueing system with Bernoulli vacation schedule

We consider an Mx/G/1 queueing system with two phases of heterogeneous service and Bernoulli vacation schedule which operate under classical retrial policy. In addition, each individual customer is subject to a control admission policy upon the arrival. This model generalized both the classical M/G/1 retrial policy with arrivals in batches and a two phase batch arrival queue with single vacation under Bernoulli vacation schedule. We will carry out an extensive stationary analysis of the system, including existence of the stationary regime, embedded Markov chain, steady state distribution of the server state and number of customer in the retrial group, stochastic decomposition and calculation of the first moments.