This is a puzzle about measuring network latency that I created. I believe the solution is that it's impossible, but friends disagree. I'm looking for convincing explanations either way. (Though it is posed as a puzzle I think it fits on this web site because of its applicability to the design and experience of communication protocols such as in online games, not to mention NTP.)
Suppose two robots are in two rooms, connected by a network with differing one-way latencies as shown in the graphic below. When robot A sends a message to robot B it takes 3 seconds for it to arrive, but when robot B sends a message to robot A it takes 1 second to arrive. The latencies never vary.
The robots are identical and do not have a shared clock, though they can measure the passage of time (e.g. they have stop watches). They do not know which of them is robot A (whose messages are delayed 3s) and which is robot B (whose messages are delayed by 1s).
A protocol to discover the round trip time is 'when receiving TICK send TOCK, start watch, send TICK, await TOCK, stop watch, record time difference (4s)'.
Is there a protocol to determine the one way trip delays? Can the robots discover which of them has the longer message sending delay?