On the limit behavior of certain quantities in a subcritical storage model

1985 ◽  
Vol 17 (2) ◽  
pp. 443-459 ◽  
Author(s):  
Prem S. Puri ◽  
Eric S. Tollar
Keyword(s):  
Markov Process ◽  
Asymptotic Distribution ◽  
Return Time ◽  
Limit Behavior ◽  
Asymptotic Independence ◽  
Renewal Theorem ◽  
Expected Return ◽  
Storage Model ◽  
Semi Markov Process ◽  
Regeneration Point

The limit behavior of the content of a subcriticai storage model defined on a semi-Markov process is examined. This is achieved by creating a renewal equation using a regeneration point (i0,0) of the process. By showing that the expected return time to (i0, 0) is finite, the conditions needed for the basic renewal theorem are established. The joint asymptotic distribution of the content of the storage at time t and the accumulated amount of the unmet (lost) demands during (0,t) is then established by showing the asymptotic independence of these two.

On the limit behavior of certain quantities in a subcritical storage model

1985 ◽  
Vol 17 (02) ◽  
pp. 443-459 ◽  
Author(s):  
Prem S. Puri ◽  
Eric S. Tollar
Keyword(s):  
Markov Process ◽  
Asymptotic Distribution ◽  
Return Time ◽  
Limit Behavior ◽  
Asymptotic Independence ◽  
Renewal Theorem ◽  
Expected Return ◽  
Storage Model ◽  
Semi Markov Process ◽  
Regeneration Point

The limit behavior of the content of a subcriticai storage model defined on a semi-Markov process is examined. This is achieved by creating a renewal equation using a regeneration point (i 0,0) of the process. By showing that the expected return time to (i 0, 0) is finite, the conditions needed for the basic renewal theorem are established. The joint asymptotic distribution of the content of the storage at time t and the accumulated amount of the unmet (lost) demands during (0,t) is then established by showing the asymptotic independence of these two.

A semi-Markov storage model

1973 ◽  
Vol 5 (02) ◽  
pp. 362-378 ◽  
Author(s):  
Jerome Senturia ◽  
Prem S. Puri
Keyword(s):  
Asymptotic Behavior ◽  
Markov Process ◽  
Laplace Transforms ◽  
Exact Distribution ◽  
Exponential Distributions ◽  
Random Inputs ◽  
Storage Model ◽  
Semi Markov Process ◽  
Negative Exponential ◽  
Independent Identically Distributed

In this paper a storage model is described in which fluctuations in the content are governed by a sequence of independent identically distributed (i.i.d.) random inputs and i.i.d. random releases. This sequence proceeds according to an underlying semi-Markov process. Laplace transforms of the exact distribution of the content are given for the case of negative exponential distributions for both inputs and releases. Exact expressions for limiting (in time) content distributions are found. In the general case, the asymptotic behavior of the content is described for critical and supercritical limiting conditions.

scholarly journals The Renewal Process Generated By Return Times of Semi-Markov Process in Reliability Models

2017 ◽  
Vol 43 (1) ◽  
pp. 365-380
Author(s):  
Franciszek Grabski
Keyword(s):  
Markov Process ◽  
Renewal Process ◽  
First Passage Time ◽  
Return Time ◽  
Passage Time ◽  
Reliability Theory ◽  
Systems Of Equations ◽  
Reliability Models ◽  
Return Times ◽  
Semi Markov Process

Abstract The renewal process generated by the return times of semi-Markov process to a given state is considered in the paper. The return time to a state j and also a first passage time from a given state i to the state j of semi-Markov process are basic concepts that are used to determine this process. The systems of equations for distributions, expectations and secondond moments of these random variables are presented. Theorem concerning the asymptotic distribution of the considered renewal process is presented in this article. Moreover an illustrative example from the reliability theory is presented in the paper.

A semi-Markov storage model

1973 ◽  
Vol 5 (2) ◽  
pp. 362-378 ◽  
Author(s):  
Jerome Senturia ◽  
Prem S. Puri
Keyword(s):  
Asymptotic Behavior ◽  
Markov Process ◽  
Laplace Transforms ◽  
Exact Distribution ◽  
Exponential Distributions ◽  
Random Inputs ◽  
Storage Model ◽  
Semi Markov Process ◽  
Negative Exponential ◽  
Independent Identically Distributed

In this paper a storage model is described in which fluctuations in the content are governed by a sequence of independent identically distributed (i.i.d.) random inputs and i.i.d. random releases. This sequence proceeds according to an underlying semi-Markov process. Laplace transforms of the exact distribution of the content are given for the case of negative exponential distributions for both inputs and releases. Exact expressions for limiting (in time) content distributions are found. In the general case, the asymptotic behavior of the content is described for critical and supercritical limiting conditions.

Partially observable semi-Markov reward processes

1993 ◽  
Vol 30 (3) ◽  
pp. 548-560 ◽  
Author(s):  
Yasushi Masuda
Keyword(s):  
Markov Process ◽  
Counting Process ◽  
Probabilistic Interpretation ◽  
Real Domain ◽  
Semi Markov Process ◽  
Reward Process ◽  
Markov Reward ◽  
Partially Observable ◽  
Joint Behavior

The main objective of this paper is to investigate the conditional behavior of the multivariate reward process given the number of certain signals where the underlying system is described by a semi-Markov process and the signal is defined by a counting process. To this end, we study the joint behavior of the multivariate reward process and the multivariate counting process in detail. We derive transform results as well as the corresponding real domain expressions, thus providing clear probabilistic interpretation.

Continuous Semi-Markov Process by HARLAMOV, B.

Biometrics ◽  
2008 ◽  
Vol 64 (4) ◽  
pp. 1301-1301
Author(s):  
Mei-Jie Zhang
Keyword(s):  
Markov Process ◽  
Semi Markov Process
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