Let me show it then. I simulated my method for a little over a million nodes, with a median of 16 neighbors (originally 8, but I pruned nodes with fewer than 5 peers and it pushed up the median), initialized with SafeTime between 0 and 99 inclusive, and then updated to be consistent with my algorithm (to contain their peers’ median + 1). After this, I simulated a large number of random messages.
On average, each node sent or received one message every second from all of its neighbors. (If messages would be more or less frequent, scale the results accordingly.) These are not messages for SafeTime but messages that are part of the regular traffic on the network. SafeTime just piggybacks on them as 8 additional bytes somewhere in the packet.
The results: After just one second of simulation time, half the nodes were within 2 steps of the maximum SafeTime and 95% within 6 steps, and this is where they stayed for the rest of the simulation. It took about 2 more seconds for the minimum (of over 1 million nodes) to settle between 30-40 steps within the maximum, where it stayed. I found the counter is increasing 21 steps each second (occasionally 22), and that means 50% of the nodes are within 0.1s of the maximum, 95% are within 0.3s, and even the worst 5% were just between 0.3s and 2.0s behind. Network latency was not simulated so the real values are expected to be somewhat higher, but this does not alter the conclusion:
Contrary to your worries, my method moves towards synchronicity even on a large and extremely sparsely connected network, though each node sees only a tiny part of the whole (no, I did not misunderstood that about the network).
As for whether it’s “economical”:
- SafeTime needs a few (8?) bytes in each message
- nodes need to store the latest value of SafeTime received from their peers: 8 bytes for a dozen or so peers
- nodes need to calculate the new value after receiving or before sending a message: calculating the median of about a dozen numbers, then adding 1
Let me ask you, does this sound like a tough coding task or something that would waste a lot of bandwidth?