This paper investigates a queueing system consisting of two-parallel queues and two servers. The service policy is a hysteretic control one such that a set of two forward thresholds (F_1, F_2) and a set of two reverse thresholds (R_1, R_2) are set up in one of two queues, say, the second queue, and 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.
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