CPE 650 – Network Modeling and Analysis (1/2554)
Homework III (Due July 20, 2011)
1. A group of two computers are connected to the Internet and are shared by 10 workers in an o
ﬃ
ce of
cubicles. The workers attempt to use the computers at a rate of
λ
per hour per worker during the busy
hour. Each computer session is distributed with a mean holding time of
1
/μ
. For the Markov chain
deﬁned by the number of busy computers at time
t
, answer the following:
(a) Determine the transition rate matrix
Q
and draw the corresponding state transition diagram.
(b) Determine the steady state probability distribution.
(c) Plot the steadystate probabilities for the case of
λ
= 0.1 and
μ
= 1.
2. Consider a system with
M
clients served by a single server with service time exponentially distributed
with mean
1
/μ
. Once the client is serviced, it waits for an exponentially distributed amount of time with
mean
1
/λ
before sending another request to the server.
(a) Model the number in the server by a CTMC. Determine the transition rate diagram and the steady
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This document was uploaded on 07/18/2011.
 Spring '11

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