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Spring 2011 OR3510/5510
Problem Set 10
When this is due:
We are back to the usual, noncrisisprelim schedule. This problem
set is due noon Monday April 25.
Reading: We are just about ﬁnished with Chapter 6 and about to begin renewal theory in
Chapter 7.
(1) In the M/M/s queueing model, let
R
(
t
) be the number of busy servers at time t. If
ρ <
1
show that a limit distribution exists
lim
t
→∞
P
[
R
(
t
) =
k
] =
η
k
,
0
≤
k
≤
s.
Find it.
What is the mean of the limit distribution?
(2)
Rework–Dissatisﬁed customers:
The grill at Harry’s restaurant is modelled as an
M/M/1 queue with a wrinkle. Harry has hired an inexperienced college student to do
the grilling and customers may be dissatisﬁed with the item they receive and may ask to
be served again. (This paradigm corresponds to
rework
in manufacturing settings.) The
college student is only capable of working on one item at a time so dissatisﬁed customers are
served again immediately until they are satisﬁed. Suppose on receiving an order, there is
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This note was uploaded on 09/17/2011 for the course ORIE 3510 taught by Professor Resnik during the Spring '09 term at Cornell University (Engineering School).
 Spring '09
 RESNIK

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