Suppose that we have two computers interconnected by a 30 km-long optical fiber pair…

Suppose that we have two computers interconnected by a 30 km-long optical fiber pair (full-duplex) that transfers data at the rate of Rb = 100 Mbit/s (the same data rate is achieved over the forward and feedback channels). Due to the long fiber length, the bit-error rate Pbit is quite high, that is, Pbit = 10−4. In addition, bit errors are i.i.d., data packets are L = 4500 bits long (including a CRC field of LCRC = 32 bits and a header field of LHDR = 160 bits) and the size of acknowledgments is 496 bits (including CRC and header fields). GBN-ARQ is used for error control at the link layer. Assume that light within this fiber propagates at a rate of 3 · 105 km/sec and that the processing time at the nodes is zero.

a) What is the probability that a packet and the corresponding acknowledgment are received correctly (referred to as “packet success rate” ps)?

b) What window size should be used for GBN-ARQ?

c) What is the realized transmission efficiency ηGBN−ARQ (the data bits that are successfully sent over the channel per second)?