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