Markov Chain and Stationary Distribution
MC has been a valuable tool for analyzing the performance of complex stochastic systems since it was introduced by the Russian mathematician A. A. Markov (1856–1922) in the early 1900s. More and more system analyses have been carried out by using MC, including the analysis on CA and CF. In this chapter, we will briefly review the essential ingredients of MC that are necessary for the performance analysis presented in this book. A more comprehensive introduction of MC and its applications can be found in Nelson (2013, Probability, stochastic processes, and queueing theory: the mathematics of computer performance modeling).
- 1.Nelson R (2013) Probability, stochastic processes, and queueing theory: the mathematics of computer performance modeling. Springer Science & Business Media, New YorkGoogle Scholar
- 2.Anderson WJ (2012) Continuous-time Markov chains: an applications-oriented approach. Springer Science & Business Media, New YorkGoogle Scholar
- 3.Peng B (2004) Convergence, rank reduction and bounds for the stationary analysis of Markov chains. PhD dissertation, North Carolina State UniversityGoogle Scholar