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Base Station (BS) sleeping operation is one of the effective ways to save energy, but it may lead to longer delay to the customers. In order to evaluate the tradeoffs between energy consumption and customer delay, the authors model the BS sleep mode operation as an N-policy M/G/1 queue with setup and closedown times, where the BS enters sleep mode if no customers arrive during the close-down time after the queue becomes empty and it starts to setup when it sees N customer arrivals during its sleep period. Several closed-form formulas are derived to demonstrate the tradeoffs between energy consumption and mean delay by changing the close-down time and N.
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