Quote:

The factor of 3/2 for each term is explained as follows. Let the lowest-order sibling squares containing the destination and the server be order-k squares X and Y, respectively. The update packet is first forwarded in a straight line towards Y while inside X. Once crossing the boundary between X and Y, it is forwarded in a sequence of steps in traversing up the hierarchy starting from an order-1 square and reaching the order-(k - 1) square containing the server. Since the sequence of steps are directionless and the expected distances

they travel are recursively doubled, they incur an approximate factor of 2 overhead compared to the direct distance between the starting point and finishing point inside square Y. The factor of 2 overhead while traversing inside Y and the straight line path inside X together contribute to the factor of 3/2 for each term in the above average hop count formula for update packets.

If anyone can grasp what is meant by this and why it should be included in the equation I would really appreciate the help.