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s7T - Cmpen/EE 362 Asst 7 Solution Spring 2009 Problem...

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Cmpen/EE 362 Asst. 7 Solution Spring 2009 Problem 1 .Text Problem 4.5. A large population of ALOHA users manages to generate 50 requests/sec., including both originals and retransmissions. Time is slotted in units of 40 millisec.sec. Answer with respect to a given user that makes a first attempt. Also answer b and c with respect to a given user that has made a number of attempts with collision. a) What is the chance of success on the first attempt? Solution. a) In 40 ms, average of 50*.04 = 2 = G attempts are made. Given one sends, success if no one else sends, or e = .1353 -2 (The unconditional probability that exactly one sends, thus resulting in success, is 2 e = .27067, but this is a different -2 view). b) What is the probability of exactly k collisions, and then a success? Solution. From the point of view of one user, this is someone else sends the first k tries, no one else on the k+1 th: (1-e ) *e = (.8647) @ (0.1353) . -G k -G k c) What is the expected number of transmission attempts needed?
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