Quasi-birth–death process

In queueing models, 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 rather than a Markov process.

References

• G. Latouche, V. Ramaswami (1999) Introduction to Matrix Analytic Methods in Stochastic Modelling, 1st edition. ASA-SIAM Series on Statistics and Applied Probability, SIAM. ISBN 0898714257 (Chapter 1: Quasi-Birth-and-Death Processes;)
• Motyer, A. J.; Taylor, P. G. (2006). "Decay rates for quasi-birth-and-death processes with countably many phases and tridiagonal block generators". Advances in Applied Probability 38 (2): 522. doi:10.1239/aap/1151337083.  edit
• Latouche, G. (2011). "Level-Independent Quasi-Birth-and-Death Processes". Wiley Encyclopedia of Operations Research and Management Science. doi:10.1002/9780470400531.eorms0461. ISBN 9780470400531.  edit