ALOHA - Throughput and probabilities I have a few questions regarding slotted-ALOHA. Assume a network have 25 users and transmission request probability = 0.25.

1) What is the throughput and what is the probability that a user will successfully transmit a frame after three unsuccessful attempts? I have managed to calculate the throughput as 0.00627. But the major problem is the probability to succeed after 3 attempts. Should I use these two formulas?

$$ n_a = \sum_{n=0}^\infty n(1-p_a)^n p_a $$

$$ n_a = \frac{1-p_a}{p_a} $$

2) What is the average number of unsuccessful attempts before a user can transmit a frame in the above problem?

Can somebody assist me?

Best regards
I assumed that you have calculated the probability of successful transmit (which is about 1e-4 or something)

$$
P[trials =  3] = P[Fail] ^3 * P[Succ]
$$
$$
Average = E[X] = 1/P[Succ]
$$

Please revise or study (if you haven't) the geometric distribution