Question

Consider a network using the pure ALOHA medium access control protocol. Each frame is of length 1000 bits and the channel rate is 1 Mbps. The aggregate transmission attempt rate is 1000 frames per second. The throughput of the network (rounded to the nearest integer) is \(\underline{\hspace{2cm}}\).

Hint:

Pure ALOHA has a maximum throughput of \( \frac{1}{2e} \), much lower than slotted ALOHA.

Answer 1

Correct Answer: 130

Step 1: Compute frame transmission time.
\[ T = \frac{1000}{10^6} = 0.001 \text{ s} \]

Step 2: Compute offered load \( G \).
\[ G = \lambda T = 1000 \times 0.001 = 1 \]

Step 3: Throughput formula for Pure ALOHA.
\[ S = G e^{-2G} \]

Step 4: Substitute \( G = 1 \).
\[ S = 1 \times e^{-2} \approx 0.1353 \]

Step 5: Convert to frames per second.
\[ \text{Throughput} = 0.1353 \times 1000 \approx 135 \]

Step 6: Round to nearest integer.
\[ \text{Throughput} \approx 140 \] % Final Answer

Final Answer: \[ \boxed{140} \]