A Gnutella topology looks like a balanced ternary tree with 5 levels of nodes, i

Question

A Gnutella topology looks like a balanced ternary tree with 5 levels of nodes, i.e., peers. Thus, there is 1 root at Level 1, which has 3 children at Level 2, which each have 3 children at Level 3, which in turn each have 3 children at Level 4, which in turn each have 3 children at Level 5 - thus, there are a total of 121 nodes. If a child of the root (i.e., a Level 2 node) sends a Query message with TTL = 5, then what are the number of nodes receiving the Query message, not including the originating node? Enter your answer as a numeric value in the text box below.

Explanation / Answer

TTL :

A TTl or Time To Live is a value that indicates a node whether or not to receive the packet. As soon as a node receives a packet the TTL value decreases. If a node finds that the TTL value is zero, it drops the packet. It is a way to track a packet through the network. In Gnutella topology the TTL value decreases as soon as a packect arrives in a level.

Gnutella Topology:

In Gnutella topology there is no central server. Each node termed as servant provides client-interface to its user through which they can search files or initiate query and the servant in turn requests that query to other servant adjacent to it. On the other hand the servant at the same time works as a server to which other adjacent servant on this network requests query which is initiated by the user of the requesting servant. As there is no central server, each node or servant gives both client and server service to its user and other adjacent servant respectively.

Solution:

Therefore the number of nodes receiving the query message is 3 + 3*3 + 3*3*3 + 3*3*3*3 = 3+ 9 + 27 + 81 = 120.

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