Data transmission in networks takes place in the form of packets. Each packet th
ID: 3202105 • Letter: D
Question
Data transmission in networks takes place in the form of packets. Each packet that is transmitted is stored in memory and kept there until an acknowledgement is received back at the transmitting end indicating that the packet was recovered and no retransmission is necessary. Then the packet is removed from memory. In heavy traffic and noisy conditions, the probability of packet recovery decreases and the number of retransmissions per packet increases. Each packet transmission and reception is considered to be statistically independent of that of all other packets. If the probability of packet correct recovery is p = 0.44, determine, a) the probability that it will take exactly four transmission for a packet to be finally recovered; b) the probability that it will take four or more transmissions for a packet to be finally recovered; c) What value p would be required for there to be a probability of 0.95 that packets are recovered after no more than three transmissions. An analytical solution for this part may not be possible so investigate other solution methods.Explanation / Answer
here as probabilty of recovery =0.44
therefore probabilty of not recovery =(1-0.44) =0.56
a) probabilty that it will take exactly 4 transmission for a packet to be finally recovered =P(first 3 attmet failed and data recovered in fth attempt)
=0.563*0.44 =0.0773
b) probabilty that it takes 4 or more transmission for data to be recoverd =P(it will not recover in first 3 attempts)
=0.563 =0.1756
c)probabilty that packet recovered in first 3 trails =P(it recoverd in first trail+first trail failed and got recovered in 2nd trail+first 2 trails failed and got recoverd in 3 rd trail)
=p+(1-p)p+p(1-p)2 =p(1+1-p+1+p2-2p) =p(3-3p+p2) =3p-3p2+p3
as this should be equal to or greater then 0.95
hence 3p-3p2+p3 >=0.95
solving above equation
p=0.6316
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