Analysis of a preemptive priority retrial queue with negative customers, starting failure and at most J vacations

An analysis of single server preemptive priority retrial queue with at most J vacations where two types of customers called (priority customers and ordinary customers) are considered in this paper. The priority customers do not have queue and they have higher priority to receive their services over ordinary customers. If negative customer is arriving during the service time of any positive customer (priority customer or ordinary customer), it will remove the positive customer from the service. If the interrupted customer is an ordinary customer, he may join the orbit and the priority customer will leave the system. As soon as the system is empty, the server takes at most J vacations. The probability generating functions for the system/orbit size in steady state is obtained using supplementary variable method. Some important system measures and the stochastic decomposition are discussed. Numerical examples are presented to picturise the effect of parameters on system performance measures.