Prepared for submission to [Operations] [Research]. The idle time ratio of a queueing system (i.e., the ratio of idle to total time summed over all channels) is a measure of the efficiency of the system. In trying to improve the operations of a queueing system, the question naturally arises as to the possibility of decreasing the idle time by simply choosing a state-dependent arrival discipline. This paper presents a negative answer to this question for a simple queue. 5 pp. Ref.
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