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A datagram network allows routers to drop packets whenever they need to. The probability of a router discarding a packet is p. Consider the case of a source host connected to the source router, which is connected to the destination router, and then to the destination host. If either of the routers discards a packet, the source host eventually times out and tries again. If both host-router and router-router lines are counted as hops, what is the mean number of hops a packet makes per transmission?

1. $p^2-3p+3$
2. $p^2+3$
3. $3p+3$
4. $p+3$
edited | 180 views
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Ans b?
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Can you send solutions?
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First let me know whether it is correct or not
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Correct answer is given to be A
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+1 vote
Each  packet  may make 1, 2 or 3 hops. For 1 hop,  the  first  router  drops it and the  probability  is p.  For 2 hops,  it goes  through first router but not the second and the probability is $(1-p)p$.  For 3 hops,  it goes through both routers and the  probability is $(1-p)(1-p)$.
Mean hops  per transmission is given by

$1*p + 2*(1-p)p + 3*(1-p)(1-p)$ which simplifies to $p^2 - 3p +3$

A is the correct option!
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