Packet transmission on the Internet uses a communications protocol known as ARQ
ID: 3069600 • Letter: P
Question
Packet transmission on the Internet uses a communications protocol known as ARQ (Automatic Repeat reQuest) in which the receiver (automatically) asks the transmitter to repeat a packet that has been received in error. If the packet is received in error again, another re-transmission is requested, and the packet transmitted again. This process continues until the packet finally is received correctly. Suppose that a packet is received correctly with probability 0.9. Let X denote the total number of times that a packet is transmitted. (a) What values does X take on, and what is the pmf of X? (b) What is the expected value of X? Hint: it may be helpful to review Problem lc of the Extra Problem Set HW1x. (c) In practice, repeats are requested a fixed number of times, say (K-1) times, and if the packet is received incorrectly all K times, it is considered to be lost, and no further re-transmissions are requested. The throughput of the channel is T, which has value 1/X if the packet is received correctly after XX K transmissions, while if all K packet transmissions are received incorrectly, then T has value 0. Find Pípacket loss), and use LOTUS to find the average throughput E[T]Explanation / Answer
a) Here X takes values 0, 1,2,3,... and PMF of X is given by,
P(X=x)=pq^x x=0,1,2,3,..., 0<p<1 & p+q=1
= 0 otherwise.
Here p=probability of success=0.9
Hence P(X=x)=0.9*0.1^x
b) Expected value is q/p=0.1/0.9=0.1111111
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