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A useful class of Markov processes when analyzing queueing systems are birthdeath processes. The only possible state transitions in this kind of processes are from i to i1 or from i to i+1. The transition intensity from state i to i+1 is designated
for
and the transition intensity from state i to state i1 is designated
for .
Figure 4:
Model graph for a Birthdeath process

The state space of the birthdeath process is
.
The intensity matrix will be of tridiagonal type since there are only two ways of leaving a state. Hence, we have the intensity matrix
As mentioned earlier, certain types of queuing systems are suitably modeled by birthdeath processes. The numbers
and
are interpreted as the arrival rate of the queue and service rate of the server, respectively.
Anders Andersson
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