Retrial Queue with Balking, Synchronous Working Vacation Interruption, and Non-preemptive Priority

Abstract

This paper deals with a multi-server priority retrial queue with vacation interruption, where the servers are not completely out of service during the vacation period. The system serves two customers classes, denoted P₁ and P₂ . In the discussed system, there is no waiting space for class P₁ customers. Upon a class P₁ customer arrival epoch and all servers are occupied, the customer departs the system. On the other hand, upon a class P₂ customer arrival epoch and all servers are busy, he may balk the system or join the orbit. Whenever there are no customers in the system at the moment of service completion, all servers will be on vacation at the same time. After the vacation ends, the servers are reactivated only if at least q customers are found on the orbit; otherwise, the servers continue with another vacation. The vacation will be interrupted if there are more than or equal to q customers in orbit after the low-rate service is completed. For this system, the effect of system parameters on system characteristics is numerically illustrated. Finally, the optimization analysis is investigated to determine the optimal vacation rate and the optimal number of special servers to maximize profit.