A two-queue and two-server model with a threshold-based control service policy

This paper investigates a queueing system consisting of two-parallel queues and two servers. The service policy is a threshold-based control one such that two thresholds v (⩾0) and N (⩾v) called control level are set up in one of the two queues, say, the second queue. At each epoch of service completion, the server decides which queue is to be served next according to the control level the number of customers in the second queue reaches. For both queues, the arrival processes are Poisson, and the service times are exponentially distributed with different means. We derive the generating functions of the stationary joint queue-length distribution, and then obtain the mean queue length and the mean waiting time for each queue.