A study on M/G/1 retrial G - queue with two phases of service, immediate feedback and working vacations

Abstract

In this paper, we discuss about the steady state behaviour of M/G/1 retrial queueing system with two phases of services and immediate feedbacks under working vacation policy where the regular busy server is affected due to the arrival of negative customers. Upon arrival if the customer finds the server busy, breakdown or on working vacation it enters an orbit; otherwise the customer enters into the service area immediately. After service completion, the customer is allowed to make finite number of immediate feedback. The feedback service also consists of two phases. At the service completion epoch of a positive customer, if the orbit is empty the server goes for a working vacation. The server works at a lower service rate during working vacation (WV) period. Using the supplementary variable technique, we found out the steady state probability generating function for the system and in orbit. System performance measures and reliability measures are discussed. Finally, some numerical examples are presented to validate the analyticalresults.