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Final Homework (Due Day:
2011/1/17)
1.
Consider the following closed queueing network (Figure 1) with only two
customers; find P(k
1
,k
2
,k
3
) explicitly in terms of
μ
.
Figure 1
2.
Persons arrive at a Xerox machine according to a Poisson process with rate one
per minute. The number of copies to be made by each person is uniformly
distributed between 1 and 10. Each copy requires 3 sec. Persons with no more
than 3 copies to make are given preemptive priority over other persons. Find the
average waiting time in queue for twopriorities persons (denoted by W
1
and W
2
).
3.
Consider an open queueing network of three queues, as shown in Figure 2. The
output of Queue 1 is split by a probability p into two streams; one goes into Queue
2 and the other goes into Queue 3 together with the output of Queue 2. If the
arrival to Queue 1 is a Poisson process with rate l and the service times at all
queues are exponentially distributed with the rates shown in the diagram, find the
mass function of the state probability for the whole network.
Figure 2
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 Fall '10
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