Question

In the lecture, we provided an outline of the derivation of the efficiency of Slotted Aloha. In this problem, we'll complete the derivation.

Which of the following statements is correct regarding the efficiency of Slotted Aloha?
a) The efficiency is maximized when there is no collision in the system.
b) The efficiency is calculated by dividing the number of successful transmissions by the total number of slots.
c) The efficiency formula involves the exponential term
, where
G is the traffic intensity.
d) Increasing the number of slots per frame increases the efficiency proportionally.

Answer 1

The efficiency of Slotted Aloha is calculated using the formula e^-G, where G is the traffic intensity.

Step-by-step explanation:

The correct statement regarding the efficiency of Slotted Aloha is option c) The efficiency formula involves the exponential term e-G, where G is the traffic intensity.

To derive the efficiency formula for Slotted Aloha, we first need to define the traffic intensity G, which represents the fraction of slots in which a transmission is attempted. The efficiency is then calculated as the probability that a slot is successful, which is equal to the probability that there is only one active transmission in a slot.

1. We start by considering the probability that there is no transmission in a slot, which can be given as (1 - G). This means that the probability of at least one transmission attempt in a slot is equal to 1 - (1 - G) = G.
2. Next, we consider the probability that there is only one active transmission in a slot. This can be calculated as G * (1 - G)^(n-1), where n is the number of slots per frame.
3. The overall efficiency is the product of the probability of a slot having no transmission and the probability of a slot having only one active transmission, which is e-G * G * (1 - G)^(n-1).

Therefore, the efficiency formula for Slotted Aloha involves the exponential term e-G, where G is the traffic intensity.