Performance Modeling of Rule-Based Architectures as Discrete-Time Quasi Birth-Death Processes

2006 ◽  
Author(s):  
S. Palugyai ◽  
M.J. Csorba
Keyword(s):  
Discrete Time ◽  
Performance Modeling ◽  
Rule Based ◽  
Birth Death

On the parity of individuals in a branching process

1976 ◽  
Vol 13 (02) ◽  
pp. 219-230 ◽  
Author(s):  
J. Gani ◽  
I. W. Saunders
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Branching Process ◽  
Yeast Cells ◽  
Death Process ◽  
Second Moments ◽  
The Mean ◽  
Watson Process ◽  
Number Of Cells ◽  
Birth Death

This paper is concerned with the parity of a population of yeast cells, each of which may bud, not bud or die. Two multitype models are considered: a Galton-Watson process in discrete time, and its analogous birth-death process in continuous time. The mean number of cells with parity 0, 1, 2, … is obtained in both cases; some simple results are also derived for the second moments of the two processes.

A birth and death model of neuron firing

1974 ◽  
Vol 11 (02) ◽  
pp. 369-373
Author(s):  
B. F. Logan ◽  
L. A. Shepp
Keyword(s):  
Discrete Time ◽  
Random Variables ◽  
Nerve Cells ◽  
Neuron Firing ◽  
The Times ◽  
Number Of Particles ◽  
Birth Death

A simple birth-death model of particle fluctuations is studied where at each discrete time a birth and/or death may occur. We show that if the probability of a birth does not depend on the number of particles present and if births and deaths are independent, then the times between successive deaths are independent geometrically distributed random variables, which is false in the general case. Since the above properties of the times between successive neuron firings have been observed in nerve cells, the model proposed in [2] obtains added credence.

Newton-Shamanskii Method for a Quadratic Matrix Equation Arising in Quasi-Birth-Death Problems

2014 ◽  
Vol 4 (4) ◽  
pp. 386-395
Author(s):  
Pei-Chang Guo
Keyword(s):  
Markov Chains ◽  
Stationary Distribution ◽  
Discrete Time ◽  
Matrix Equation ◽  
Nonnegative Solution ◽  
Minimal Nonnegative Solution ◽  
The Minimal Nonnegative Solution ◽  
Quadratic Matrix Equation ◽  
Quadratic Matrix ◽  
Birth Death

AbstractIn order to determine the stationary distribution for discrete time quasi-birth-death Markov chains, it is necessary to find the minimal nonnegative solution of a quadratic matrix equation. The Newton-Shamanskii method is applied to solve this equation, and the sequence of matrices produced is monotonically increasing and converges to its minimal nonnegative solution. Numerical results illustrate the effectiveness of this procedure.

A Rule-Based Evolutionary Approach to Music Performance Modeling

2012 ◽  
Vol 16 (1) ◽  
pp. 96-107 ◽  
Author(s):  
Rafael Ramirez ◽  
Esteban Maestre ◽  
Xavier Serra
Keyword(s):  
Performance Modeling ◽  
Music Performance ◽  
Evolutionary Approach ◽  
Rule Based

scholarly journals On the convergence to stationarity of birth-death processes

2001 ◽  
Vol 38 (03) ◽  
pp. 696-706 ◽  
Author(s):  
Pauline Coolen-Schrijner ◽  
Erik A. Van Doorn
Keyword(s):  
Discrete Time ◽  
Death Process ◽  
Speed Of Convergence ◽  
Recent Proposal ◽  
The Many ◽  
Birth Death

Taking up a recent proposal by Stadje and Parthasarathy in the setting of the many-server Poisson queue, we consider the integral ∫0∞[limu→∞E(X(u))-E(X(t))]dtas a measure of the speed of convergence towards stationarity of the process {X(t),t≥0}, and evaluate the integral explicitly in terms of the parameters of the process in the case that {X(t),t≥0} is an ergodic birth-death process on {0,1,….} starting in 0. We also discuss the discrete-time counterpart of this result, and examine some specific examples.

scholarly journals A REVIEW OF PARRONDO'S PARADOX

2002 ◽  
Vol 02 (02) ◽  
pp. R71-R107 ◽  
Author(s):  
GREGORY P. HARMER ◽  
DEREK ABBOTT
Keyword(s):  
Discrete Time ◽  
Brownian Ratchet ◽  
Rule Based ◽  
Paradoxical Situation ◽  
State Dependent ◽  
Parrondo’S Paradox ◽  
Coin Tossing ◽  
Biased Coin

Inspired by the flashing Brownian ratchet, Parrondo's games present an apparently paradoxical situation. The games can be realized as coin tossing events. Game A uses a single biased coin while game B uses two biased coins and has a state dependent rule based on the player's current capital. Playing each of the games individually causes the player to lose. However, a winning expectation is produced when randomly mixing games A and B. This phenomenon is investigated and mathematically analyzed to give explanations on how such a process is possible. The games are expanded to become dependent on other properties rather that the capital of the player. Some of the latest developments in Parrondian ratchet or discrete-time ratchet theory are briefly reviewed.

scholarly journals Weak convergence of conditioned birth-death processes in discrete time

1997 ◽  
Vol 34 (01) ◽  
pp. 46-53
Author(s):  
Pauline Schrijner ◽  
Erik A. Van Doorn
Keyword(s):  
Weak Convergence ◽  
Discrete Time ◽  
Transition Probabilities ◽  
Death Process ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Absorbing State ◽  
Limiting Behaviour ◽  
Necessary And Sufficient ◽  
Birth Death

We consider a discrete-time birth-death process on the non-negative integers with −1 as an absorbing state and study the limiting behaviour asn →∞ of the process conditioned on non-absorption until timen.By proving that a condition recently proposed by Martinez and Vares is vacuously true, we establish that the conditioned process is always weakly convergent when all self-transition probabilities are zero. In the aperiodic case we obtain a necessary and sufficient condition for weak convergence.

Sign in / Sign up

Export Citation Format

Share Document