If I understand it correctly: The higher txn fee ups the chances of your txn being in the next block (it's up to the miner that wins the block which txns are i

If I understand it correctly: The higher txn fee ups the chances of your txn being in the next block (it's up to the miner that wins the block which txns are included - some set a minimum fee). Once your txn is placed in a block, it is included in the future blocks too. A confirmation is generated by each block your txn is in, and a block is generated every ten minutes, so for 6 confirmations, you still need an hour. Running a dedicated miner wouldn't help since you'd have to be the one to win the next block to be able to process your txns.