A working vacation queue with priority customers and vacation interruptions

In this paper, we analyse a working vacation queueing model with priority customers where the customer service times follow phase-type distributions. The server serves the customers at a lower rate during a working vacation period than in a non-vacation one. After serving a customer in working vacation, if the server finds any customer waiting in queue, the vacation is interrupted and the server switches its service rate from working vacation to the non-vacation service rate. The length of busy period, busy cycle and the distributions of queue length as well as of waiting times are derived for two types of priority customers. The response times are also analysed. With the help of numerical experiments the effects of system parameters on its performance is demonstrated.