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.