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Unformatted text preview: at the steadystate equations,
since anything out of a state should some up to anything coming in, i.e. the “ﬂow conservation" idea.] 6. Special case: M/M/1 Queue
An important special case of BD process is the case where transition rates are state independent and
are ﬁxed, one for birth another for death, i.e., =
j = :
j For this example, due to Poisson property (we will visit shortly), the interarrival time is exponentially distributed with mean 1= and the service time is exponentially distributed with mean 1=. Also, known
as the average arrival rate. Remember, we are still talking about Markov chains. This is a special case and
is identiﬁed as the M/M/1 queue (known as Kendall’s notation) where ﬁrst M is for the arrival, the second
M is for the service time and the third entry is to denote we have one server. The statetransition diagram
can be shown as below:
λ
0 1
µ CS 522, v 0.94, d.medhi, W’99 λ λ 3 2
µ •• • µ 11 For this special case, we g...
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 Fall '08
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 Computer Networks

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