Analysis of a retrial queueing system with priority service and modified multiple vacations

This paper studies an M/G/1 retrial queueing system with modified multiple vacations, in which a new external arrival may expel the customer being served out of the system and directly starts to be served or join the retrial orbit. Once the server finds the orbit is empty at the end of a service, it will immediately take a random length vacation. If the orbit is still empty when a vacation is finished, the server takes another same vacation. This pattern continues until the orbit is not empty when a vacation is completed or the server has already taken M vacations. By constructing an embedded Markov chain, we provide the sufficient and necessary condition of system stability. The distributions of the orbit size and the system size in steady-state are derived through the supplementary variable method. Then, some system performance measures and the Laplace-Stieltjes transform of sojourn time distribution are obtained. Besides, we perform the cost analysis of the system. Finally, several numerical illustrations are given to investigate the effects of system parameters on the essential system characteristics.