scholarly journals ALTERNATIVE ANALYSIS OF FINITE-TIME PROBABILITY DISTRIBUTIONS OF RENEWAL THEORY

2014 ◽  
Vol 28 (2) ◽  
pp. 183-201 ◽  
Author(s):  
Percy H. Brill
Keyword(s):  
Operations Research ◽  
Stochastic Models ◽  
Probability Distributions ◽  
Renewal Theory ◽  
Regenerative Process ◽  
Renewal Processes ◽  
Level Crossing ◽  
Alternative Analysis ◽  
Level Crossing Analysis ◽  
Total Life

We introduce a level-crossing analysis of the finite time-t probability distributions of the excess life, age, total life, and related quantities of renewal processes. The technique embeds the renewal process as one cycle of a regenerative process with a barrier at level t, whose limiting probability density function leads directly to the time-t quantities. The new method connects the analysis of renewal processes with the analysis of a large class of stochastic models of Operations Research. Examples are given.

scholarly journals On the level crossing of multi-dimensional delayed renewal processes

1997 ◽  
Vol 10 (4) ◽  
pp. 355-361 ◽  
Author(s):  
Jewgeni H. Dshalalow
Keyword(s):  
Renewal Process ◽  
Stochastic Models ◽  
First Passage Time ◽  
Passage Time ◽  
The Other ◽  
Renewal Processes ◽  
Active Components ◽  
Level Crossing ◽  
First Passage ◽  
Informal Discussion

The paper studies the behavior of an (l+3)th-dimensional, delayed renewal process with dependent components, the first three (called active) of which are to cross one of their respective thresholds. More specifically, the crossing takes place when at least one of the active components reaches or exceeds its assigned level. The values of the other two active components, as well as the rest of the components (passive), are to be registered. The analysis yields the joint functional of the “crossing level” and other characteristics (some of which can be interpreted as the first passage time) in a closed form, refining earlier results of the author. A brief, informal discussion of various applications to stochastic models is presented.

scholarly journals Level crossing analysis of Burgers equation in 1 + 1 dimensions

2006 ◽  
Vol 39 (15) ◽  
pp. 3903-3909 ◽  
Author(s):  
M Sadegh Movahed ◽  
A Bahraminasab ◽  
H Rezazadeh ◽  
A A Masoudi
Keyword(s):  
Burgers Equation ◽  
Level Crossing ◽  
Level Crossing Analysis

Analysis of an M/G/1 queue with two types of impatient units

1995 ◽  
Vol 27 (03) ◽  
pp. 840-861 ◽  
Author(s):  
M. Martin ◽  
J. R. Artalejo
Keyword(s):  
Markov Chain ◽  
Performance Measures ◽  
Mathematical Analysis ◽  
Service System ◽  
Probability Distributions ◽  
Embedded Markov Chain ◽  
Renewal Processes ◽  
Stationary Probability ◽  
Markov Renewal Processes ◽  
Specific Performance

This paper deals with a service system in which the processor must serve two types of impatient units. In the case of blocking, the first type units leave the system whereas the second type units enter a pool and wait to be processed later. We develop an exhaustive analysis of the system including embedded Markov chain, fundamental period and various classical stationary probability distributions. More specific performance measures, such as the number of lost customers and other quantities, are also considered. The mathematical analysis of the model is based on the theory of Markov renewal processes, in Markov chains of M/G/l type and in expressions of ‘Takács' equation' type.

Stochastic models in cell kinetics

1988 ◽  
Vol 25 (A) ◽  
pp. 91-111
Author(s):  
Peter J. Brockwell
Keyword(s):  
Life Cycle ◽  
Stochastic Models ◽  
Death Rate ◽  
Cell Kinetics ◽  
Branching Processes ◽  
Experimental Studies ◽  
Renewal Theory ◽  
Biological Cell ◽  
Age Dependent

We discuss the role of stochastic processes in modelling the life-cycle of a biological cell and the growth of cell populations. Results for multiphase age-dependent branching processes have proved invaluable for the interpretation of many of the basic experimental studies of the life-cycle. Moreover problems from cell kinetics, in particular those related to diurnal rhythm in cell-growth, have stimulated research into ‘periodic' renewal theory, and the asymptotic behaviour of populations of cells with periodic death rate.

A Framework for Decision-Based Engineering Design

1998 ◽  
Vol 120 (4) ◽  
pp. 653-658 ◽  
Author(s):  
G. A. Hazelrigg
Keyword(s):  
Engineering Design ◽  
Operations Research ◽  
Quality Function Deployment ◽  
Value Theory ◽  
Decision Making Process ◽  
Design Decisions ◽  
Decision Sciences ◽  
Research Decision ◽  
Decision Based Design ◽  
Total Life

Engineering design is increasingly recognized as a decision-making process. This recognition brings with it the richness of many well-developed theories and methods from economics, operations research, decision sciences, and other disciplines. Done correctly, it forces the process of engineering design into a total systems context, and demands that design decisions account for a product’s total life cycle. It also provides a theory of design that is based on a rigorous set of axioms that underlie value theory. But the rigor of decision-based design also places stringent conditions on the process of engineering design that eliminate popular approaches such as Quality Function Deployment. This paper presents the underlying notions of decision-based design, points to some of the axioms that underlie the theory of decision-based design, and discusses the consequences of the theory on engineering education.

scholarly journals Nuclear spin-hyperpolarization generated in a flavoprotein under illumination: experimental field-dependence and theoretical level crossing analysis

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Yonghong Ding ◽  
Alexey S. Kiryutin ◽  
Alexandra V. Yurkovskaya ◽  
Denis V. Sosnovsky ◽  
Renad Z. Sagdeev ◽  
...  
Keyword(s):  
Electron Transfer ◽  
Solid State ◽  
Magnetic Fields ◽  
Nuclear Spin ◽  
Flavin Mononucleotide ◽  
Magic Angle ◽  
Residual Water ◽  
Theoretical Level ◽  
Level Crossing ◽  
Level Crossing Analysis

AbstractThe solid-state photo-chemically induced dynamic nuclear polarization (photo-CIDNP) effect generates non-equilibrium nuclear spin polarization in frozen electron-transfer proteins upon illumination and radical-pair formation. The effect can be observed in various natural photosynthetic reaction center proteins using magic-angle spinning (MAS) nuclear magnetic resonance (NMR) spectroscopy, and in a flavin-binding light-oxygen-voltage (LOV) domain of the blue-light receptor phototropin. In the latter system, a functionally instrumental cysteine has been mutated to interrupt the natural cysteine-involving photochemistry allowing for an electron transfer from a more distant tryptophan to the excited flavin mononucleotide chromophore. We explored the solid-state photo-CIDNP effect and its mechanisms in phototropin-LOV1-C57S from the green alga Chlamydomonas reinhardtii by using field-cycling solution NMR. We observed the 13C and, to our knowledge, for the first time, 15N photo-CIDNP signals from phototropin-LOV1-C57S. Additionally, the 1H photo-CIDNP signals of residual water in the deuterated buffer of the protein were detected. The relative strengths of the photo-CIDNP effect from the three types of nuclei, 1H, 13C and 15N were measured in dependence of the magnetic field, showing their maximum polarizations at different magnetic fields. Theoretical level crossing analysis demonstrates that anisotropic mechanisms play the dominant role at high magnetic fields.

scholarly journals Joint simulation of backward and forward recurrence times in a superposition of independent renewal processes

1991 ◽  
Vol 28 (04) ◽  
pp. 930-933
Author(s):  
C. Y. Teresa Lam
Keyword(s):  
Joint Distribution ◽  
Random Variables ◽  
Independent Random Variables ◽  
Renewal Processes ◽  
Life Distribution ◽  
Recurrence Times ◽  
Joint Simulation ◽  
Total Life

It is shown that, in a superposition of finitely many independent renewal processes, an observation from the limiting (when t →∞) joint distribution of backward and forward recurrence times at t can be simulated by simulating an observation of the pair (UW, (1 – U)W), where U and Ware independent random variables with U ~ uniform(0, 1) and W distributed according to the limiting total life distribution of the superposition process.

Stochastic models in cell kinetics

1988 ◽  
Vol 25 (A) ◽  
pp. 91-111
Author(s):  
Peter J. Brockwell
Keyword(s):  
Life Cycle ◽  
Stochastic Models ◽  
Death Rate ◽  
Cell Kinetics ◽  
Branching Processes ◽  
Experimental Studies ◽  
Renewal Theory ◽  
Biological Cell ◽  
Age Dependent

We discuss the role of stochastic processes in modelling the life-cycle of a biological cell and the growth of cell populations. Results for multiphase age-dependent branching processes have proved invaluable for the interpretation of many of the basic experimental studies of the life-cycle. Moreover problems from cell kinetics, in particular those related to diurnal rhythm in cell-growth, have stimulated research into ‘periodic' renewal theory, and the asymptotic behaviour of populations of cells with periodic death rate.

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