Correct Answer - Option 2 : 18%
Concept
ALOHA is a medium access control (MAC) protocol for the transmission of data via a shared network channel
Formula:
Throughput of pure ALOHA (F(G)) = G × e-2G
Calculation:
F(G) = G × e-2G
F’(G) = -2G × e-2G + e-2G
To get maximum value
0 = -2G × e-2G + e-2G
0 = e-2G (-2G × 1)
e-2G ≠ 0
(-2G × 1) = 0
∴ G = 1 ÷ 2
η = Maximum throughput of pure ALOHA = \(\frac{1\times e^{-2\frac{1}{2}}}{2}\)
put = G = 1 ÷ 2
η = 1 ÷ 2e = 0.1839 ≈ 0.184
Efficiency in percentage = 0.184 × 100 = 18.4 %
Option 2 is the closest answer
Note:
To find the value of G use the concept of maxima and minima value in application of differentiation
