In a MANET, any node can be selected as a source or a destination. Assuming equal probability of a node being selected as a source or destination, what is the average number of hops the message has to travel in P13.16?
If one of the four center nodes (A, B, C, D) or the corner nodes (E, F, G, H) is
selected as the source, then the average number of hops can be calculated as
follows:
Distance 1 2 3 4 5 6 7 8 9 10 11 12 13 14
(A, B, C, D) 4 8 12 14 12 8 4 1
(E, F, G, H) 2 3 4 5 6 7 8 7 6 5 4 3 2 1
AV EHOPs(A,B,C,D)=(4*1 + 8*2 + 13*3 + 14*4 + 12*5 + 8*6 + 4*7 + 1*8
)/63= 259 /63= 4:11
AV EHOPs(E,F, G,H) =458/63= 7.26
As the source node is assumed to be selected arbitrarily, with equal probability,
the overall average distance in terms of number of hops will be between 4.11 and
7.26. As an appropriation, that value can be said to be average of the two bounds
and is equal to 5.685.
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