Functions of OSI and TCP/IP Layers Q.40

0. A group of 15 routers are interconnected in a centralized complete binary tree with a router at each tree node. Router i communicates with router j by sending a message to the root of the tree. The root then sends the message back down to router j. The mean number of hops per message, assuming all possible router pairs are equally likely is

Answer
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Option : C
Explanation : As per question, we have to count average hops per message.
Steps used:
1) Message goes up from sender to root.
2) Message comes down from root to destination
1) Average hops message goes to root – ((3 * 8) + (2 * 4) + (1 * 2) + (0 * 1))/15 = 2.267 // 3 * 8 means represents 3 hops & 8 routers for Bottom most level & So on.
2) Similarly average hops when message comes down -
((3 * 8) + (2 * 4) + (1 * 2) + (0 * 1))/15 = 2.267
So, Total Hops = 2.267 + 2.267 = 4.53.

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