I am currently changing a computer networking system so that instead of sending out a message to every node that owns a piece of data x, it chooses the most appropriate node from which to take the information.

So basically if 7 nodes in the system have a data item, instead of 7 nodes replying, only 1 (the best one) replies. Clearly this will reduce the network overhead

I would like to quantify the improvement and think the big O notation might be appropriate for this? (Please correct me if I'm wrong)...

If I were to take a guess at it would I be improving the performance by O(n-1) where n is the number of nodes??

Really appreciate any advice anyone can give me.
Many thanks