Iím trying to compare one system against another and form some type of expression to compare the cost to update a server.

System One can update a server in log (N) overlay hops (the overlay can be visualized as a circle) where N is the number of nodes in the system. However because these overlay devices are pick arbitrarily one ďoverlay hopĒ on the circle could result in multiple physical hops in the underlying network. This means it would basically cost the same to update your server whether youíre close or far from it. Thus the expression Iím using can be seen below where the second number represents the distance between two randomly chosen points in a square, sourced from here: http://mathworld.wolfram.com/SquareLinePicking.html

Log(N) * 0.521405433.

Now System two works in a similar way. The difference is that the overlay hops are not randomly chosen. A Cantor SFC is used in an attempt to improve the way overlay nodes are chosen so that nodes that are physically close in the network are also somewhat close on the overlay circle. Therefore if you are close to your server, there should be less physical hops to update it.

Can someone please help me to form an expression for this, based on a Cantor SFC?