Bulk arrival multi-stage retrial queue with vacation (original) (raw)

Bulk arrival retrial queueing model with M stages of service and Bernoulli vacation is considered. Customers arrive in batches according to Poisson process. Server provides M stages of heterogeneous service in succession to each customer. After receiving service from one stage, the customer may either move to next stage or depart the system. If the customer leaves the system, the server takes Bernoulli vacation. The vacation time, service time and retrial time are assumed to be generally distributed. Using generating function technique, the steady state distributions of the server state and the number of customers in the orbit are obtained along with important performance measures. Stochastic decomposition law is verified. The effects of various parameters on the system performance are analysed numerically.