I'm running core 0.11.2 for around 8 hours each day. I've got 8 outbound nodes and no inbound nodes. bandwidth is around 30Kb/s most times. Recently I've noticed that ping rates during synchronisation for about half of the nodes can be in excess of 500,000ms. Once I have synchronised, then all rates seem to drop below 400ms, and are often in double digits. Is this just a coincidence ( it's just an impression, I haven't kept any stats), or do some nodes try to discourage contact from nodes that are synchronising?
Maybe it is just that a high volume of received traffic distorts the ping checking.
Did you really mean 500,000ms? e.g. 500 seconds? If so, that would seem something else is going on.