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 × λx)/(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. Using the Poisson distribution:
a. Find the probability that a pure Aloha network generates x number of frames during the vulnerable time. The vulnerable time for this network is two times the frame transmission time (Tfr).
b. Find the probability that a slotted Aloha network generates x number of frames during the vulnerable time. The vulnerable time for this network is equal to the frame transmission time (Tfr).
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