Non-Uniqueness of the Minimal Realization Problem Representation of the Markovian Arrival Process of Order 2 and Moment Fitting

2021 ◽  
Vol 46 (3) ◽  
pp. 1-8
Author(s):  
Sunkyo Kim
Keyword(s):  
Markovian Arrival Process ◽  
Problem Representation ◽  
Arrival Process ◽  
Minimal Realization ◽  
Realization Problem

scholarly journals Shock models under a Markovian arrival process

2009 ◽  
Vol 50 (5-6) ◽  
pp. 879-884 ◽  
Author(s):  
Rafael Pérez-Ocón ◽  
Maria del Carmen Segovia
Keyword(s):  
Markovian Arrival Process ◽  
Arrival Process ◽  
Shock Models

A minimal realization for affine control systems on connected Lie groups

2017 ◽  
Vol 14 (09) ◽  
pp. 1750126
Author(s):  
A. Kara Hansen ◽  
S. Selcuk Sutlu
Keyword(s):  
Control System ◽  
Control Systems ◽  
Lie Groups ◽  
Lie Group ◽  
Canonical Projection ◽  
Minimal Realization ◽  
Realization Problem ◽  
Affine Control Systems ◽  
Affine Control System ◽  
Connected Lie Group

In this work, we study minimal realization problem for an affine control system [Formula: see text] on a connected Lie group [Formula: see text]. We construct a minimal realization by using a canonical projection and by characterizing indistinguishable points of the system.

scholarly journals Descriptors for point processes based on runs: the Markovian arrival process

1996 ◽  
Vol 9 (4) ◽  
pp. 469-488 ◽  
Author(s):  
Marcel F. Neuts
Keyword(s):  
Point Process ◽  
Point Processes ◽  
General Purpose ◽  
Markovian Arrival Process ◽  
The Other ◽  
Arrival Process ◽  
Qualitative Behavior ◽  
Regular Grid ◽  
Matrix Analytic Methods ◽  
Process Map

This paper is part of a broader investigation of properties of a point process that can be identified by imagining that the process is involved in a competition for the generation of runs of events. The general purpose of that methodology is to quantify the prevalence of gaps and bursts in realizations of the process. The Markovian arrival process (MAP) is highly versatile in qualitative behavior and its analysis is numerically tractable by matrix-analytic methods. It can therefore serve well as a benchmark process in that investigation. In this paper, we consider the MAP and a regular grid competing for runs of lengths at least r1 and r2, respectively. A run of length r in one of the processes is defined as a string of r successive events occurring without an intervening event in the other process.This article is dedicated to the memory of Roland L. Dobrushin.

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