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CDA6530: Performance Models of Computers and Networks
Chapter 7: Basic Queuing Networks
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Open Queuing Network
Jobs arrive from external sources,
circulate, and eventually depart
3
Closed Queuing Network
Fixed population of
K
jobs circulate
continuously and never leave
Previous machinerepairman problem
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FeedForward QNs
Consider two queue tandem system
Q: how to model?
System is a continuoustime Markov chain (CTMC)
State (N
1
(t), N
2
(t)), assume to be stable
π
(i,j) =P(N
1
=i, N
2
=j)
Draw the state transition diagram
But what is the arrival process to the second queue?
5
Poisson in
⇒
Poisson out
Burke’s Theorem:
Departure process of
M/M/
1
queue is Poisson with rate
λ
independent of
arrival process.
Poisson process addition, thinning
Two
independent
Poisson arrival processes adding
together is still a Poisson (
λ
=
λ
1
+
λ
2
)
For a Poisson arrival process, if each customer lefts
with prob. p, the remaining arrival process is still a
Poisson (
λ
=
λ
1
·
p)
Why?
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State transition diagram: (N
1
, N
2
), N
i
=0,1,2,
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This note was uploaded on 01/14/2012 for the course CDA 6530 taught by Professor Zou during the Fall '11 term at University of Central Florida.
 Fall '11
 Zou

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