NDLI: System Analysis of Semi-Markov Processes

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System Analysis of Semi-Markov Processes

Content Provider	IEEE Xplore Digital Library
Author	Howard, Ronald A.
Copyright Year	1963
Description	Flow graph analysis has proved a valuable approach to the study of probabilistic systems. This paper extends the analytic procedures to semi-Markov processes, Markov processes whose transition times can also be arbitrary random variables. First we present the basic theory of the semi-Markov process. We derive expressions for the interval transition probabilities, the probabilities that the system will be in each state after the passage of a time interval of length t, and find the limit of these probabilities when t is large. Then we develop the flow graph interpretation of these relations. We consider the special cases of counting transitions, transient processes, and first passage times. We investigate the effect on interval transition probabilities of starting the process in different ways, including choosing a time at random to begin observation of the process. We find that results are often most conveniently expressed by the matrix flow graph for the process.
Starting Page	114
Ending Page	124
Page Count	11
File Size	2055672
File Format	PDF
ISSN	05361559
Volume Number	8
Issue Number	2
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1964-04-01
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Flow graphs Markov processes Random variables Density functional theory Signal processing Statistics Equations Probability distribution
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering Aerospace Engineering

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