Fuzzy analysis of bulk arrival two phase retrial queue with vacation and admission control

In this paper state dependent batch arrival two phase retrial queue is considered. Admission of each individual customer to the system depends upon the state of the server. The server provides first essential service to all the admitted customers. After completion of essential service the customer may opt second optional service or leave the system. However, if the customer is dissatisfied with the essential service he can immediately join the orbit as a feedback customer. After providing service to a customer, the server may either wait for a new customer or take one of the multi-optional vacations. For the proposed model, steady state performance characteristics are derived. Numerical results are presented. The model is further analysed under fuzzy environment by using Zadeh's extension principle.