Consider a $128 \times 10^3$ bits/second satellite communication link with one way propagation delay of 150 milliseconds. Selective retransmission (repeat) protocol is used on this link to send data with a frame size of 1 kilobyte. Neglect the transmission time of acknowledgement. The minimum number of bits required for the sequence number field to achieve 100% utilization is _______.

To achieve $100\%$ link utilization, the sender window size $W_s$ must be sufficient to keep transmitting throughout the round-trip time ($RTT$).

Given:

• Bandwidth, $B = 128 \times 10^3\text{ bits/s} = 128000\text{ bps}$

• Propagation delay, $T_p = 150\text{ ms} = 0.150\text{ s}$

• Frame size, $L = 1\text{ KB} = 1024\text{ bytes} = 1024 \times 8 = 8192\text{ bits}$ *(Taking $1\text{ KB} = 1000\text{ B} = 8000\text{ bits}$ also yields the same final integer result)*

• Transmission time of an ACK, $T_a \approx 0$

Step 1: Calculate the frame transmission time ($T_t$)

Step 2: Calculate the parameter $a$

Step 3: Determine the required sender window size ($W_s$)

Since the window size must be an integer:

Step 4: Determine the minimum number of sequence numbers for Selective Repeat In the Selective Repeat protocol, the receiver window size is equal to the sender window size ($W_r = W_s = 6$). The minimum number of distinct sequence numbers required is:

Step 5: Calculate the number of sequence number bits ($k$)

Thus, the minimum number of bits required for the sequence number field is 4.