Quasi-birth-death process
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In queueing model
Queueing model
In queueing theory, a queueing model is used to approximate a real queueing situation or system, so the queueing behaviour can be analysed mathematically...

s, a discipline within the mathematical theory of probability, the quasi-birth–death process describes a generalisation of the birth–death process. As with the birth-death process it moves up and down, but unlike the birth-death process is a semi-Markov process
Semi-Markov process
A continuous-time stochastic process is called a semi-Markov process or 'Markov renewal process' if the embedded jump chain is a Markov chain, and where the holding times are random variables with any distribution, whose distribution function may depend on the two states between which the move is...

 rather than a Markov process.
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