Analysis of $M^{[X_{1}]}, M^{[X_{2}]}/G_{1},G_{2}/1$ retrial queueing system with priority services, orbital search, compulsory short vacation, optional long vacation, working breakdown and repair

Abstract

In this paper, we consider M1,M2/G1,G2/1 retrial queue with priority services, orbital search, compulsory short vacation, optional long vacation, working breakdown and repair under Bernoulli schedule controlled policy. There are two types of customers, namely high priority and low priority arriving in batches. After completion of each high priority service, the server goes for short vacation and after completion of each low priority service, the server can option to take a long vacation. Further, the server subject to breakdown, the system either goes to repair immediately or continue slower rate service for current customer with some probability. The primary customers who find the server is long vacation are allowed to balk. After completion of low priority service (if the server not taking vacation), repair or both types of vacation the server can search for the customers in the orbit or remains idle, if there are no customers in the high priority queue. We use the established norm which is the corresponding steady state results for time dependent probability generating functions are obtained. Along with that, the expected waiting time for the expected number of customers for both high and low priority queues are computed. Numerical results along with the graphical representations are shown elaborately.