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ORIE 361/523 – Homework 9
Instructor: Mark E. Lewis
due April 16, 2008 (drop box)
1. Potential customers arrive at a a singleserver station (which works at rate
μ
) in accordance
with a Poisson process with rate
λ
. However, if a customer ﬁnds n people already in the
station, then he will enter the system with probability 1
/
(
n
+1). Find the limiting distribution
of the number of customers in the system.
2. Customers arrive at a twoserver station according to a Poisson process with rate
λ
. Upon
arriving, they join a single queue. Whenever a server completes a service, the person ﬁrst in
line enters service. The service times of server
i
are exponential with rate
μ
i
,i
= 1
,
2
,
where
μ
1
+
μ
2
> λ.
An arrival ﬁnding both servers free is equally likely to go to either one. Deﬁne
an appropriate CTMC for this model and ﬁnd the limiting probabilities.
3. A total of N customers move about among r servers in the following manner. When a customer
is served by i, he then goes to server j,
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This note was uploaded on 03/01/2010 for the course ORIE 361 taught by Professor Lewis,m. during the Spring '07 term at Cornell University (Engineering School).
 Spring '07
 LEWIS,M.

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