TWO-QUEUE AND TWO-SERVER MODEL WITH A HYSTERETIC CONTROL SERVICE POLICY

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 (F1; F2) and a set of two reverse thresholds (R1; R2) 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. The arrival process for each queue is Poisson, and the service times are exponentially distributed with di erent 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.

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