Can I speed up my transactions based on the fee I am willing to spend? Or perhaps by some other means?
Is there a way to choose between slow, medium, and fast (like on other blockchains) or is there any other way to affect transaction speed?
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Sign up to join this communityShort answer: no. Setting higher fees on your transaction increase the odds to have it processed but does not guarantee that yours will be.
Long answer:
Non-surge mode:
The base fees on the network are 100 stroops even if you put a higher max fee on your transaction. When the network can add all queued transactions to the ledger, the charged fees will be 100 stroops.
Surge mode:
If the ledger has more transactions in queue than what it can accept (currently 1000 operations). (The limit is counted in operations but the ledger add the transaction as a whole). This is the surge mode, at this point the ledger will build transaction set that maximise the number of operation and the charged fees (and a random number?).
You can find more details in CAP-0005