Modified vacation policy for M/G/1 retrial queue with balking and feedback

This paper studies a general retrial queue with balking and Bernoulli feedback, where the server operates a modified vacation policy. If the server is busy or on vacation, an arriving customer either enters an orbit with probability b, or balks (does not enter) with probability 1 − b. Otherwise the service of the arriving customer commences immediately. At any service completion epoch, the test customer may either enter the orbit for another service with probability p or leave the system with probability 1 − p. If the orbit is empty, the server takes at most J vacations until at least one customer is recorded in the orbit when the server returns from a vacation. This retrial system has potential applications in e-mail system and WWW server. By applying the supplementary variable technique, some important performance measures are derived. The effect of various retrial/vacation time distributions and different values of J on the system performance measures is also investigated. The analyses and results presented in this paper may be useful for network system designers and software system engineers.