Analysis on preemptive priority retrial queue with two types of customers, balking, optional re-service, single vacation and service interruption

TLDR: By using the supplementary variable technique, the steady-state probability generating functions for the system/orbit size are obtained and some important system performance measures and the stochastic decomposition are discussed.

Abstract: This paper concerned with performance analysis of single server preemptive priority retrial queue with a single vacation where two types of customers are considered and they are called priority customers and ordinary customers. The ordinary customers arrive in batch into the system. The priority customers do not form any queue. After the completion of regular service, the customers may demand re-service for the previous service without joining the orbit or may leave the system. As soon as the system is empty, the server goes for vacation and the regular busy server can be subjected to breakdown. By using the supplementary variable technique, we obtain the steady-state probability generating functions for the system/orbit size. Some important system performance measures and the stochastic decomposition are discussed. Finally, numerical examples are presented to visualize the effect of parameters on system performance measures.