[recursive]

I'm not familiar with any of these, but this point stuck out to me.

Two random choice says "Max load of any server is O(log log number_of_servers)."

If work accomplished is proportional to load, then the total work done by the entire system is O(number_of_servers * log log number_of_servers). It seems very suspicious, magical even, that the total work is more than linear with the number of servers. Free energy discovered?

[scottlamb]

> If work accomplished is proportional to load, then the total work done by the entire system is O(number_of_servers * log log number_of_servers). It seems very suspicious, magical even, that the total work is more than linear with the number of servers. Free energy discovered?

No free energy for at least a couple reasons:

* This is O(...) meaning (roughly) "bounded above by", not Theta(...) meaning "bounded above and below by".

* This is max load, not average load. Even if it were theta, it wouldn't follow from the max load on a server being Theta(log log number_of_servers) that the total load is Theta(number_of_servers * log log number_of_servers).

[rp1]

I imagine the reason is that the max load on a single server is O(log log number of servers), but it’s not possible for all the servers to be at max load.

For instance, imagine load balancing via random assignment. The theoretical max load of a server is receiving every request, but if one server receives more requests, then the other servers receive less.