Yep, that's it exactly. In Bitcoin, you can pay more for your transaction to encourage miners to include your transaction in preference over others when the network is busy and miners can't fit all the transactions into their blocks (if they include your transaction in their block, they get your transaction's fee).
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Now I understand the cumbersome maths behind btc block trx you wrote above. The handsome the fee, the quicker it gets validated in the block.
Between thanks for putting a superb effort in breaking down the nitty gritty of what needs to be understood and worked upon in the system.
I look forward to your next post/part. Can't wait to read it.