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.