Bulk arrival multi-stage retrial queue with vacation

TLDR: Bulk arrival retrial queueing model with M stages of service and Bernoulli vacation with steady state distributions of the server state and the number of customers in the orbit is discussed in this chapter.

Abstract: Bulk arrival retrial queueing model with M stages of service and Bernoulli vacation is discussed in this chapter. Customers arrive in batches according to Poisson process. Server provides M stages of heterogenous 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. The stability condition of the system is derived. 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. The model is further analysed to construct the membership function of the mean orbit size with fuzzy parameters.