Performance analysis of an M<SUP align='right'>x/G/1 feedback retrial queue with non-persistent customers and multiple vacations with N-policy

This paper is concerned with the analysis of an Mx/G/1 feedback retrial queue with non-persistent customers and multiple vacations with N-policy. If an arriving batch of customers finds the server idle, one of the arriving customers starts its service immediately and the rest joins a retrial group. Otherwise, if an arriving batch of customers on arrival finds the server busy, becomes impatient and leaves the system with probability (1 - α) and with probability α, they enter into the orbit. At a service completion epoch, if the number of customers in the orbit is zero, the server does a secondary job (vacation) repeatedly until the retrial group size reaches N. At the secondary job completion epoch, if the orbit size is at least N, then the server remains in the system to render service for customers from main pool or from retrial group. At a service completion epoch, the leaving customer may either request for another service with probability f or leave the system forever with probability d (where f + d = 1).