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UCLA Electrical Engineering Department
EE132B
HW Set #3
Professor Izhak Rubin
Problem 1
Consider a broadcasting bus sys
tem. 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 token for a random period of time. Let H
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This note was uploaded on 11/11/2010 for the course EE 132B taught by Professor Izhakrubin during the Fall '09 term at UCLA.
 Fall '09
 IzhakRubin
 Electrical Engineering

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