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.

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.

A multivariate reward process defined on a semi-Markov process and its first-passage-time distributions

1991 ◽  
Vol 28 (2) ◽  
pp. 360-373 ◽  
Author(s):  
Yasushi Masuda ◽  
Ushio Sumita
Keyword(s):  
Asymptotic Behavior ◽  
Markov Process ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
Renewal Equations ◽  
Supplementary Variables ◽  
Semi Markov Process ◽  
Reward Process

A multivariate reward process defined on a semi-Markov process is studied. Transform results for the distributions of the multivariate reward and related processes are derived through the method of supplementary variables and the Markov renewal equations. These transform results enable the asymptotic behavior to be analyzed. A class of first-passage time distributions of the multivariate reward processes is also investigated.

A multivariate reward process defined on a semi-Markov process and its first-passage-time distributions

1991 ◽  
Vol 28 (02) ◽  
pp. 360-373 ◽  
Author(s):  
Yasushi Masuda ◽  
Ushio Sumita
Keyword(s):  
Asymptotic Behavior ◽  
Markov Process ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
Renewal Equations ◽  
Supplementary Variables ◽  
Semi Markov Process ◽  
Reward Process

A multivariate reward process defined on a semi-Markov process is studied. Transform results for the distributions of the multivariate reward and related processes are derived through the method of supplementary variables and the Markov renewal equations. These transform results enable the asymptotic behavior to be analyzed. A class of first-passage time distributions of the multivariate reward processes is also investigated.

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.

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.

Sign in / Sign up

Export Citation Format

Share Document