132B_1_Recitation3_Network_Examples

132B_1_Recitation3_Network_Examples - EE132B - Recitation 3...

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EE132B - Recitation 3 Network Examples Prof. Izhak Rubin rubin@ee.ucla.edu Electrical Engineering Department UCLA 1
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Example 1 We have 4 stations communicating in a pure ALOHA scheme. T 1 is the idle time for station 1, T 2 is the idle time for station 2, T 3 is the idle time for station 3, and T 4 is the idle time for station 4. T 1 , T 2 , T 3 and T 4 are random variables. When each station broadcasts, it sends a message of 1000 bits. The channel transmission rate is 5 Kbps. Station 2 Station 3 Station 1 Station 4 Broadcast channel Station 1 T 1 message 2
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Example 1 - 2 Question 1 – For each station, the idle time T i is exponentially distributed with parameter λ i . T 1 , T 2 , T 3 and T 4 are all independent random variables. Let λ 1 = 1 [1/sec], λ 2 = ½ [1/sec], λ 3 = λ 4 = 0.1 [1/sec]. – What is the probability density function for T 2 ? Question 2 – What is P(T 2 <= t) ? 2 2 2 2 0.5 22 ( ) 0.5 tt T f t e e   2 2 0.5 0.5 2 2 2 0 0 ( ) ( ) | 1 t t T P T t f t dt e e     3
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Example 1 - 3 Question 3 What is P(T 2 > t)? Question 4 P(T 1 <= t) = P(T 3 <= t) = P(T 4 <= t) = Question 5 If a station transmits a message and no collision occurs, how long does it take to transmit a message?
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132B_1_Recitation3_Network_Examples - EE132B - Recitation 3...

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