CS/EE 147
HW 3: Practice with CTMCs
Guru: Raga
Assigned: 4/13/10
Due: 4/28/10, Raga’s mailbox, 1pm
We encourage you to discuss these problems with others, but you need to write up the actual solutions alone.
At the top of your homework sheet, list all the people with whom you discussed. Crediting help from other
classmates will not take away any credit from you. Start early and come to office hours with your questions!
1
Warmup: Practice with Poisson processes [15 points]
(a) Consider a stream of packets arriving according to a Poisson process with rate
λ
per second. Suppose
each packet is of type “Green” with probability 5% and of type “Yellow” with probability 95%. Given
that 100 Green packets arrived during the previous second, (i) what is the expected number of Yellow
packets which arrived during the previous second? and (ii) what is the probability that 2000 Yellow
packets arrived during the previous second?
(b) Red packets arrive according to a Poisson Process with rate
λ
1
= 30
packets/sec. Black packets arrive
according to a Poisson Process with rate
λ
2
= 10
packets/sec. Assume the streams are statistically
multiplexed into one stream. Suppose we are told that 60 packets arrived during the second. What’s the
probability that exactly 40 of those were red? You can verify your answer by reasoning out this problem
in 2 different ways.
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 Fall '09
 Poisson Distribution, Probability theory, Poisson process, FCFS, CTMCs

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