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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 Spring '09
 IzhakRubin
 Electrical Engineering, Probability theory, Multiplexing, Slot 1, propagation delay, Clockwise

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