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lec6 - UCI University of California Irvine EECS 161...

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EECS 161 - Introduction to Computer Networking Scott Jordan Local Area Networks / ALOHA UCI University of California, Irvine Coin Tossing: Suppose you toss a coin N times, and each toss is independent of previous tosses. Sup- pose the probability that a single toss is Heads is p . (1) Denote the number of Heads in N tosses by X . Then X is a random variable with a Binomial distribution, namely (2) Denote the number of tosses until you get Heads for the first time by Y . Then Y is a random variable with a Geometric distribution, namely P X x = ( ) N x p x 1 p ( ) N x = P Y y = ( ) 1 p ( ) y 1 p =

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EECS 161 - Introduction to Computer Networking Scott Jordan Local Area Networks / ALOHA UCI University of California, Irvine Throughput of slotted ALOHA? (Walrand fig. 4.18) S = rate of successful transmissions = throughput (packets per time slot) G = rate of total transmissions (packets per time slot)
EECS 161 - Introduction to Computer Networking Scott Jordan Local Area Networks / ALOHA UCI University of California, Irvine Throughput of slotted ALOHA? (Walrand fig. 4.18) S = rate of successful transmissions = throughput (packets per time slot) G = rate of total transmissions (packets per time slot) p = P(transmission is successful) S = pG

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EECS 161 - Introduction to Computer Networking Scott Jordan Local Area Networks / ALOHA UCI University of California, Irvine Throughput of slotted ALOHA? (Walrand fig. 4.18) S = rate of successful transmissions = throughput (packets per time slot) G = rate of total transmissions (packets per time slot) p = P(transmission is successful) S = pG p = ?
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