Suppose we are transmitting frames between two nodes using Stop-and-Wait protocol. The frame size is 3000 bits. The transmission rate of the channel is 2000 bps (bits/ second) and the propagation delay between the two nodes is 100 milliseconds. Assume that the processing times at the source and destination are negligible. Also, assume that the size of the acknowledgement packet is negligible. Which ONE of the following most accurately gives the channel utilization for the above scenario in percentage?

The correct option is 88.23.

To find the channel utilization of the Stop-and-Wait protocol, we need to calculate the total time required to transmit one frame and receive its acknowledgment, and then determine the fraction of this total time that is actually spent transmitting the frame.

Let us break down the calculations step-by-step:

Step 1: Calculate the Transmission Delay ($T_t$)
The transmission delay is the time taken to push all the bits of the frame onto the transmission medium.
It is given by the formula:
$T_t=\frac{\mathrm{Frame\; Size\; (L)}}{\mathrm{Transmission\; Rate\; (R)}}$
Given:
Frame size, $L=3000\text{bits}$
Transmission rate, $R=2000\text{bps}$
Substituting these values:
$T_t=\frac{3000}{2000}=1.5\text{seconds}$

Step 2: Identify the Propagation Delay ($T_p$)
The propagation delay is the time taken for the signal to travel from the source to the destination.
Given:
Propagation delay, $T_p=100\text{milliseconds}=0.1\text{seconds}$

Step 3: Calculate the Total Time for One Cycle ($T_{\mathrm{total}}$)
In the Stop-and-Wait protocol, the sender transmits a frame and then waits for the acknowledgment (ACK) from the receiver before sending the next frame.
Since the processing times at the source and destination are negligible, and the size of the ACK packet is also negligible, the total time for one complete cycle is:
$T_{\mathrm{total}}=T_t+2·T_p$
Here, $2·T_p$ accounts for the propagation delay of the frame traveling to the destination and the propagation delay of the ACK traveling back to the source.
Substituting the values:
$T_{\mathrm{total}}=1.5+2·0.1=1.5+0.2=1.7\text{seconds}$

Step 4: Calculate the Channel Utilization ($\eta$)
Channel utilization represents the fraction of time the channel is busy transmitting useful data. It is calculated as:
$\eta =\frac{T_t}{T_{\mathrm{total}}}$
Substituting the values:
$\eta =\frac{1.5}{1.7}\approx 0.88235$
To express this value as a percentage:
$\eta (\%)=0.88235·100\%\approx 88.23\%$

Therefore, the channel utilization is approximately 88.23%.