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20092ee132B_1_hw3sol

# 20092ee132B_1_hw3sol - U CLA Electrical Engineering...

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UCLA Electrical Engineering Department EE132B HW Set Solution #3 Professor Izhak Rubin Solution to Problem 1 { } ( 29 { } ( 29 { } 1 (1) If no collision occurs, it takes seconds to transmit a message. (2) The channel is idle when all the stations are idle. Thus, we have: min , 1,2,... min , 1,2,... i i N i i M R T T i N P T t P T i N t P T t = = = = = = I ( 29 ( 29 1 1 1 1 exp 1 exp (3) No collision occurs if all stations except station i are idle during the message transmission time. Note that the message tr i N i i N t i N i i N i i P T t e t P T t t λ λ λ = - = = = = Π = Π = - = - - ( 29 ( 29 { } ( 29 {1,..., }\{ } {1,..., }\{ } {1,..., }\{ } ansmission time is sec. Thus, no collision all the other stations are idle for more than sec. / / exp / j j N i j j N i j j N i M R P P M R P T M R P T M R M R λ = = = Π = - I

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Solution to Problem 2 ( 29 ( 29 ( 29 ( 29 ( 29 13 13 1 2 13 1 2 1 2 2 2 0 1 2 2 (1) Let denote the time elapsed from the instant station 1 receives the token to the instant station 3 receives the token, i.e.
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