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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

(a) hops a packet makes per transmission?
(b) transmissions a packet makes?
(c) hops required per received packet?
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(a) host - router ,then router - router,then router to destination

so,in total 3 hops for a packet.

(b) mean number of transmissions -

it might be possible that there is only 1 transmission i.e packet is nt dropped by any router.

or it might be the case that in first transmission,packet is dropped by a router,so again source will start transmission,hence 'p' this time

in this way 1+ p + p*p  +  p*p*p +........

so,mean number of transmissions are (1/1-p)

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i think for c it is always 3 becouse  hops required  host - router ,then router - router,then router to destination

correct me if iam wrong.

B.)

A) THERE ARE THREE HOPS IN TOATAL

L1   -----------------   1

L2   -----------------   (1-P) * 1

L3   ----------------    (1-P)*(1-P)*1

### C) TOTAL NO. OF HOPS PER RECEIVED PACKETS IS 3 .

edited

mean number of transmissions -

p + (1-p)p +(1-p)p^2..........

so thee above is the probability but not the mean of no of transmissions mean of no of transmissions will be

3+6+9+12+..............................................

3(1+2+3+............................)

3(n(n+1)/2)

asit is mean we need to divide with no of transmissions so it whould be

(3n+3)/2

according to me option A and option C are similar    hops a packet makes per transmission? (which means no of hops   for a succesful transmission )