If station a intends to transmit M data-frames

Problem 1

Consider an ARQ stop-and-wait communication session between two stations A and

B.

(a) If station a intends to transmit M data-frames, where M>=2, what is the

probability that the number of retransmissions NR(M) is equal to 2? (Hint:

Express the probability in terms of M and p.)

Problem 2

Consider an ARQ stop-and-wait scheme which is similar to the scheme described

in Problem 1 but a distinct feature: suppose that an acknowledgement can be lost

during its transmissions with probability q. If an acknowledgement is lost, station A

will retransmit the data-frame after time-out. Such retransmission process continues

until station A receives an acknowledgement.

(a) If station A intends to transmit a single data frame, what is the average number

of retransmissions required for the successful delivery of data frames? (Hint:

Express the average number of retransmissions in terms of p and q.)

(b) Find the probability that station A retransmits exactly twice. (Hint: express

the probability in terms of p and q. (You do not need to simplify your answer).

NOTES:

NT=number of transmissions needed for correct reception.

NR=number of retransmissions needed for correct reception.

P{(NT=j)} = P^j-1 (1-P) where j >=1.

P{(NR=j) = P^j (1-P) where j>=0

P is probability that a frame is received incorrectly. 1-P is probability that it is received correctly.

E{(NT)} = 1/1-P

E{(NR)} = P/1-P

NT=1+NR

E(NT)=1 + E(NR)

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