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Between UE level and SBS level, let s i indicate the ID of SBS connected to UE i, and b i indicate the number of UEs connected to SBS i. s i = k indicates that UE i connects to SBS k and we denote {H}_{ji}^{SBS- UE}=left{begin{array}{c}1,kern1.25em mathrm{if} j=k 0,kern1em mathrm{if} jne kend{array}right.
The ( U_{mathcal{P}}_i^k ) is the unit price for the kth resource unit in the SBS i and ( cleft(U_{mathcal{P}}_i^k(i),{xi}_j^k(i right) ) is the cost function of SBS i.
In this case, the value function (v(SBS i )) of the SBS i becomes ( vleft({mathrm{SBS}}_iright)=-U_{mathcal{P}}_i^ktimes left({mathcal{A}}_i^k-{partial}_i^kright) ).
At the end of each time period, the re-distributed kth resource amount for the SBS i (( {Pi}_i^k )(t)) is obtained periodically as follows.
Conversely, if ( {partial}_i^k>{mathcal{A}}_i^k ), the deficient resource amount ( left({partial}_i^k-{mathcal{A}}_i^kright) ) is needed in the SBS i.
Indeed, I still try not to become too distant from the world of real scientific discovery, and since starting at SBS, I have contributed in very minor ways to ongoing research projects and have written an undergraduate textbook about ecology.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com