Cost considerations for centralized NAT with Transit Gateway

Intro of what to accomplish

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Figure 1: Setup Overview of EC2-based VPN endpoint for Site-to-Site VPN with AWS

\[Price_{NGW}=( 720 hr / month \cdot Num_{VPC} \cdot Cost_{NGW-Attachment} ) + (traffic \cdot Cost_{NGW-Traffic})\] \[Price_{TGW+NGW}= ( 720 hr / month \cdot Num_{VPC} \cdot Cost_{TGW-Attachment} ) + \\ ( 720 hr / month \cdot Num_{AZ} \cdot Cost_{NGW-Attachment} ) + \\ (traffic \cdot ( Cost_{TGW-Traffic} + Cost_{NGW-Traffic}))\] \[Price_{TGW+NGW} \leq Price_{NGW}\] \[( 720 hr / month \cdot Num_{VPC} \cdot Cost_{TGW-Attachment} ) + \\ ( 720 hr / month \cdot Num_{AZ} \cdot Cost_{NGW-Attachment} ) + \\ (traffic \cdot ( Cost_{TGW-Traffic} + Cost_{NGW-Traffic})) \\ \leq ( 720 hr / month \cdot Num_{VPC} \cdot Cost_{NGW-Attachment} ) + (traffic \cdot Cost_{NGW-Traffic})\] \[traffic \cdot Cost_{TGW-Traffic} + traffic \cdot Cost_{NGW-Traffic} - traffic \cdot Cost_{NGW-Traffic} \\ \leq ( 720 hr / month \cdot Num_{VPC} \cdot Cost_{NGW-Attachment} ) - \\ ( 720 hr / month \cdot Num_{VPC} \cdot Cost_{TGW-Attachment} ) - \\ ( 720 hr / month \cdot Num_{AZ} \cdot Cost_{NGW-Attachment} )\] \[traffic \cdot Cost_{TGW-Traffic} \\ \leq 720 hr / month \cdot (( Num_{VPC} \cdot Num_{AZ} \cdot Cost_{NGW-Attachment} ) \\ - ( Num_{VPC} \cdot Cost_{TGW-Attachment} ) - ( Num_{AZ} \cdot Cost_{NGW-Attachment} ))\] \[traffic \leq \frac{720 hr / month}{Cost_{TGW-Traffic}} \cdot \\ (( Num_{VPC} \cdot Num_{AZ} \cdot Cost_{NGW-Attachment} ) - \\ ( Num_{VPC} \cdot Cost_{TGW-Attachment} ) - ( Num_{AZ} \cdot Cost_{NGW-Attachment} ))\]