20092ee132B_1_hw3

20092ee132B_1_hw3 - U CLA Electrical Engineering Department...

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UCLA Electrical Engineering Department EE132B HW Set #3 Professor Izhak Rubin Problem 1 Consider a broadcasting bus system. Attaching to the bus are N stations, and they share the channel under pure ALOHA scheme. Suppose that the transmission rate is R (bits/sec), and the message size is M bits. Neglect the effect of propagation delay. 1) How long does it take to transmit a single message? 2) Let T i denote the idle time for station i. Suppose that T i is exponentially distributed with parameter λ i , and {T i , i=1. 2, …, N } is a set of independent random variables. Let T denote the idle time for the broadcast channel. Note that the channel is idle when every station is idle. What is the distribution function for T? (P(T t)=?) 3) Suppose that the channel is idle and station i initiates a message transmission at time 0. What is the collision probability for this message transmission? Problem 2 Consider a slotted token ring system with N stations. The token travels in the counter clockwise direction. In this polling system, a busy station will capture the token and hold it for the duration of its frame transmission. It then releases the token and makes it available for capture by the neighboring station along the ring network. Assume for our analysis that each station holds the
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20092ee132B_1_hw3 - U CLA Electrical Engineering Department...

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