I broadcasted a low fee (11sat/vbyte) transaction last week, just at the time when they fees went up.
I knew that the fee was low and that the transaction would take a few days to confirm (according to https://twitter.com/CoreFeeHelper , it would take around 3 days) but it's been a week and my transaction is still in the mempool. Sometimes my wallet (electrum) shows it with a blue "unbroadcasted" icon and I have to rebroadcast it again. I also sometimes use "free" tx accelerator services which basically rebroadcast the transaction everywhere.

My question is what is the algorithm that a miner picks a transaction from the mempool to include it to a block?
Is it a greedy algorithm which just picks the ones with highest fees? Is the "age" of a transaction in the mempool also a factor? Or is it just a combination of fee and a random choice?