# In the previous problem, we found that the probability of a station (in a G-station network) successfully

## Question:

In the previous problem, we found that the probability of a station (in a G-station network) successfully sending a frame in a vulnerable time is P = e^{−2G} for a pure Aloha and P = e^{−G} for a slotted Aloha network. In this problem, we want to find the throughput of these networks, which is the probability that any station (out of G stations) can successfully send a frame during the vulnerable time.

a. Find the throughput of a pure Aloha network.

b. Find the throughput of a slotted Aloha network.

**Previous Problem**

To formulate the performance of a multiple-access network, we need a mathematical model. When the number of stations in a network is very large, the Poisson distribution, p[x] = (e^{−λ} × λ^{x})/(x!), is used. In this formula, p[x] is the probability of generating x number of frames in a period of time and λ is the average number of generated frames during the same period of time.

## Step by Step Answer:

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