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Markov Chain and Stationary Distribution

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Channel Aggregation and Fragmentation for Traffic Flows

Part of the book series: SpringerBriefs in Electrical and Computer Engineering ((BRIEFSELECTRIC))

Abstract

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).

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Notes

  1. 1.

    Without specifying the distribution of the sojourn time, the process becomes Semi-Markov process [1], and its future evolution depends on the current state of the process and on the length of the time for which the process has been in that state.

  2. 2.

    Here we consider the time order as 0 → t → h and thus the forward equations apply. Similarly, when we consider 0 → h → t, we can have the backward equations.

References

  1. Nelson R (2013) Probability, stochastic processes, and queueing theory: the mathematics of computer performance modeling. Springer Science & Business Media, New York

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  2. Anderson WJ (2012) Continuous-time Markov chains: an applications-oriented approach. Springer Science & Business Media, New York

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  3. Peng B (2004) Convergence, rank reduction and bounds for the stationary analysis of Markov chains. PhD dissertation, North Carolina State University

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Author information

Authors and Affiliations

  1. The Department of Information and Communication Technology, University of Agder, Grimstad, Norway

    Lei Jiao

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  1. Lei Jiao
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Jiao, L. (2020). Markov Chain and Stationary Distribution. In: Channel Aggregation and Fragmentation for Traffic Flows. SpringerBriefs in Electrical and Computer Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-33080-4_2

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  • DOI: https://doi.org/10.1007/978-3-030-33080-4_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-33079-8

  • Online ISBN: 978-3-030-33080-4

  • eBook Packages: EngineeringEngineering (R0)

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