Question: Consider a GBN-ARQ operating between two terminals A and B. Let β be the expected number of PDUs transmitted from A to B between the completion of the transmission (from A) of a given PDU and the instant where the feedback message for this PDU is entirely received at A. Let p be the probability that a PDU is erroneously received at B, assuming an iid PDU error process. Assume that a correct feedback is received for each PDU (ideal feedback channel) and that, whenever a negative acknowledgment is received for PDU i, terminal A goes back transmitting PDUs i, i + 1, i + 2,... .
a) Let γ be the expected number of PDUs transmitted from A to B for each PDU successfully received at B. Show that γ = 1 + p(β + γ).
b) Defining the normalized throughput as S = 1/γ, find S as a function of β and p.