Multiple gap-filling is an extension of gap-filling where an FBA model is generated by simultaneously computing minimal completions of the reactions in the reaction network, the metabolites for the biomass reaction, the nutrients and the secretions.
When the minimal transmission completion time of the relaxed optimization problem in (13) is achieved, the two sources have equal transmission completion time and all of their available power is utilized.
The minimal transmission completion time of RoNo thus can be obtained by maximizing the transmission rate using water-filling algorithm in each slot.
When the minimal transmission completion time of the relaxed optimization problem in (29) is achieved, the NC traffic and the UC traffic are allocated all available resources such that the two types of traffic experience equal transmission completion time.
So we can state that, although we explore the resource allocation schemes towards minimal transmission completion time, our proposed schemes also can be used to achieve maximal average transmission rate with proportional fairness for two-way relay OFDM transmission systems.
Theorem 2 indicates that to obtain the minimal transmission completion time in the relay phase, the two types of traffic should be allocated proportionally in their transmission rates, satisfying that RNC II):R UC II)=MNC MUC, which this gives us an insight to design the suboptimal resource allocation schemes for relay phase.
The objective to seeking the minimal transmission completion time DI, DII, and DTot in the problem of (11), (12), and (2) is equivalent to finding the maximal average transmission rate with proportional fairness for the source phase transmission, the relay phase transmission, and the end-to-end two-way transmission in a two-way relay OFDM system.
Theorem 1 claims such an important fact in the view of network planning: to obtain the minimal transmission completion time in the source phase, the two sources should proportionally allocate their transmission rates, satisfying that RA(I):R B(I =MA MB.
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