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where K is the maximum backoff stage.
They depend on the initial backoff window, retransmission limit, and maximum backoff stage.
The minimum contention window size is W and the maximum backoff stage is m.
Again, (Z_{m_{z}}) represents the "maximum backoff stage" of the ZigBee node.
From this definition, (W_{m_{w}}) denotes the "maximum backoff stage" of the WLAN node.
the probabilities of fail transmission due to no channel to use after reaching the maximum backoff stage at the maximum retransmission stage.
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This takes about 7.2 ms, including data, ack and the maximum backoff duration of first backoff stage, and it wastes channel time for both ZigBee and Wi-Fi networks.
At the maximum number of backoff stages m, the maximum contention window size CW max = CW m = 2 m * CW min. Fig. 1 Markov chain model for the 802.11e backoff process.
Finally, the forth equation accounts for the fact that if the number of retries reaches the maximum value Lretry, the backoff stage will be reset to 0 no matter the consequent transmission is successful or failed.
Table 1 Analytical parameters Parameter Value (ms) Channel occupied by successful transmission T s 9.6 Channel occupied by a collision T c 0.417 Duration of first packet d 0.288 Duration of CTS d cts 0.24 Idle channel σ c 0.02 Maximum retry limit m 6 Backoff stage at which window size is max m ′ 5 Minimum window size W 0 16.
is the maximum number of backoff stages.
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