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Therefore it is not necessary to consider the corresponding minimum value constraints on the transmission time in this section.
Recall that in Approximation 1, we only consider the case where none of the nodes achieves its maximal transmit power and thus we can ignore the minimum value constraints on transmission time.
The minimum value constraints on T ab and T ba are due to the transmit power constraints, without which the data rates B ab /T ab and B ba /T ba will be too high to be supported even with the maximal transmit powers.
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The minimum value constraint for T ba, i.e., T ba ≥ Tmin2, is also due to the maximum transmit power constraint like that for T ab in (15), and Tmin2 can be derived similarly as Tmin1.
This turns into a minimum value constraint for the transmit time, which is T a b ≥ B a b / W 2 log 2 1 + ( P max t ) 2 h a r 2 h b r 2 h a r 2 P max t N 0 + h b r 2 P max t N 0 + N 0 2 ≜ T min 1. (15).
For the rate constraint we show the maximum and minimum value of constraint violation.
It is shown that for optimal networks the rate of internal generation of entropy, σ, attains its minimum value compatible with constraints describing: (i) the transformations to be operated on the process streams and (ii) the subsidiary character of shaft power generation to thermal energy recovery as heating power.
We demonstrate via ns2 simulations that ABS successfully stabilizes the buffer size at its minimum value under given constraints, scales to a wide spectrum of flow populations and link capacities, exhibits fast convergence rate and stable dynamics in various network settings, and is robust to load changes and generic Internet traffic (including FTP, HTTP, and non-TCP flows).
The minimum value of this constraint was justified because there is fossil evidence that divergence within all of these clades began > 45 Ma, reviewed in [ 31].
In addition, since the optimal power is known explicitly with (28) under a delay constraint ddr, the minimum value of for a given delay constraint ddr can be obtained by searching the optimal number of receivers.
In addition to AE and subchannel limitations, we also apply the constraint derived from Equation 2 into the power limitation where we choose the minimum value between the two power constraints P i (maximum transmission power limitation) and p c -P(d i ).
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