Final Exam, Spring Semester, 2009
–
Data Networks
Professor: Sunghyun Choi
20080611 (Thu), 10:30am12:30pm
1.
(10 pts, 5 pts each) Indicate the correct answer to each of the following topics, and briefly explain
why
.
(a)
The maximum achievable throughputs of slotted ALOHA, unslotted ALOHA, splitting algorithm,
CSMA slotted ALOHA, and CSMA/CD can be ordered as follows: unslotted ALOHA < slotted
ALOHA < splitting algorithm < CSMA slotted ALOHA < CSMA/CD.
A.
True
B.
False
Ans. False since the maximum throughputs of CSMA slotted ALOHA and CSMA/CD heavily
depend on the propagation and detection delay beta. For example, for large beta, CSMA/CD
can perform worse than CSMA slotted ALOHA.
(b)
Consider an M/M/1, M/M/m, or M/M/
∞
system with arrival rate
λ
and service rate
μ
.
Suppose that the system starts in steadystate. Then, according to Burke
’
s theorem, the
departure process is Poisson with rate
μ
.
A.
True
B.
False
Ans. False since the departure rate is
λ
, NOT
μ
.
2.
(10 pts) Consider a closed Jackson network where the service time at each queue is independent
of the number of customers at the queue. Suppose that for a given number of customers, the
utilization factor of one of the queues, say queue 1, is strictly larger than the utilization factors of
the other queues. Show that as the number of customers increases, the proportion of time that a
customer spends in queue 1 approaches unity.
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 Spring '09
 ChoiSunghyun
 Poisson Distribution, Probability theory, pts, Queueing theory, reservation, CSMA

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