# 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

• You shouldn't use formulas at all. If you are guessing which formula to use, you are in the mode of thinking of high-school. You should switch to the mode of thinking of academia, in which the goal is to understand what you're doing rather than to guess which formula to plug in values to. – Yuval Filmus Mar 9 '18 at 4:29

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