  In this paper, we study the power efficiency and delay performance of the
IEEE 802.3az Energy Efficient Ethernet (EEE) protocol. A new approach is
proposed to analyze the M/G/1 queue with the vacation time that is governed by
the arrival process and the parameter {\tau} and N of the BTR strategy. Our key
idea is to establish the connection between the vacation time and the arrival
process to account for their dependency. We first derive the distribution of
the number of arrivals during a vacation time based on an event tree of the BTR
strategy, from which we obtain the mean vacation time and the power efficiency.
Next, from the condition on the number of arrivals at the end of a vacation
period, we derive a generalized P-K formula of the mean delay for EEE systems,
and prove that the classical P-K formula of the vacation model is only a
special case when the vacation time is independent of the arrival process. Our
analysis demonstrates that the {\tau} policy and N policy of the BTR strategy
are compensating each other. The {\tau} policy ensures the frame delay is
bounded when the traffic load is light, while the N policy ensures the queue
length at the end of vacation is bounded when the traffic load is heavy. These
results, in turn, provide the rules to select appropriate {\tau} and N. Our
analytical results are confirmed by simulations.
