Cloud messaging costs scale linearly with message count. For \(n\) devices publishing at rate \(r\) messages/minute:
\[C_{\text{monthly}} = n \cdot r \cdot 1440 \frac{\text{min}}{\text{day}} \cdot 30 \frac{\text{days}}{\text{month}} \cdot \frac{\$1}{10^6 \text{ msgs}}\]
For this fleet with \(n = 10,000\) devices at \(r = 1\) msg/min: \[C_{\text{MQTT}} = 10,000 \times 1 \times 1,440 \times 30 \times \frac{\$1}{10^6} = \$432/\text{month}\]
HTTP requires connection overhead: each message becomes request + response (2 messages): \[C_{\text{HTTP}} = 10,000 \times 1 \times 1,440 \times 30 \times 2 \times \frac{\$1}{10^6} = \$864/\text{month}\]
Plus ALB processing fees (~$200/month), total HTTP cost = $1,064/month vs MQTT’s $432/month.
The cost ratio \(C_{\text{HTTP}}/C_{\text{MQTT}} = 1,064/432 = 2.46\times\) shows persistent connections reduce cloud costs by 60%.