Analysis of a two phases batch arrival queueing model with bernoulli vacation schedule

We consider a single server bulk arrival queueing system with two phases of heterogeneous service under Bernoulli schedule vacation, where the customers arrive in batches of the random variable 'X'. Using the imbedded Markov chain technique, we first derive the queue size distribution at a stationary point of time. Next, we obtain a recursive solution of the stationary queue size distribution of this model. Finally, we obtain the Laplace Stieltjes Transform of the waiting time distribution and some related performance measures. The method proposed here is not only easily amenable to computation but can be applied to solve more complicated problems of similar nature.