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What is the mempool?
It’s a datastructure or list of all the unconfirmed transactions waiting to be picked by the miners to be added to the blockchain.
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What happens if the miners can’t keep up with the rate of the new transaction?
The miners will prioratize transactions with the higher fees, so all the other transactions will stay in the mempool until they’re eventually picked. The higher the fee, the greater and faster is the chance of being included in the next block.
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How does a growing mempool effect transaction fees?
The fees are payed per Byte, which means the larger the transaction is in size (binary representation), the higher the fees.
To explain:
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A transaction of 1000 Btc with 1 Input and 1 Output will be cheaper than the same transaction with 10 Inputs and 10 Outputs
This happens because each block has limited size, so the more Inputs/Outputs there are in a transaction, the more space (Byte) will it waste and the miners won’t be able to add other transactions with better fees. This in return generates an increase of unconfirm transactions in the mempool, which leads to increased fees as well.