Statistical efficiency of regenerative simulation methods for networks of queues

1983 ◽  
Vol 15 (1) ◽  
pp. 183-197 ◽  
Author(s):  
Donald L. Iglehart ◽  
Gerald S. Shedler
Keyword(s):  
Passage Time ◽  
General Function ◽  
Simulation Methods ◽  
Statistical Efficiency ◽  
Multiclass Networks ◽  
Regenerative Simulation ◽  
Time Information ◽  
General Service ◽  
Networks Of Queues ◽  
Passage Times

This paper is concerned with the assessment of the statistical efficiency of proposed regenerative simulation methods. We compare the efficiency of the ‘marked job' and ‘labelled jobs' methods for estimation of passage times in multiclass networks of queues with general service times. Using central limit theorem arguments, we show that the confidence intervals constructed for the expected value of a general function of the limiting passage time using the labelled jobs method are shorter than those obtained from the marked job method. This is consistent with intuition since the labelled jobs method extracts more passage-time information from a fixed-length simulation run.

Statistical efficiency of regenerative simulation methods for networks of queues

1983 ◽  
Vol 15 (01) ◽  
pp. 183-197 ◽  
Author(s):  
Donald L. Iglehart ◽  
Gerald S. Shedler
Keyword(s):  
Passage Time ◽  
General Function ◽  
Simulation Methods ◽  
Statistical Efficiency ◽  
Multiclass Networks ◽  
Regenerative Simulation ◽  
Time Information ◽  
General Service ◽  
Networks Of Queues ◽  
Passage Times

This paper is concerned with the assessment of the statistical efficiency of proposed regenerative simulation methods. We compare the efficiency of the ‘marked job' and ‘labelled jobs' methods for estimation of passage times in multiclass networks of queues with general service times. Using central limit theorem arguments, we show that the confidence intervals constructed for the expected value of a general function of the limiting passage time using the labelled jobs method are shorter than those obtained from the marked job method. This is consistent with intuition since the labelled jobs method extracts more passage-time information from a fixed-length simulation run.

scholarly journals A simple proof of a result of Iglehart and Shedler

1985 ◽  
Vol 17 (1) ◽  
pp. 239-241
Author(s):  
Mark Berman
Keyword(s):  
Confidence Intervals ◽  
Simple Proof ◽  
Passage Time ◽  
Alternative Proof ◽  
Multiclass Networks ◽  
Simple Alternative ◽  
General Service Times ◽  
Service Times ◽  
General Service ◽  
Networks Of Queues

Iglehart and Shedler (1983) prove that the ‘labelled jobs’ method for estimation of passage-time characteristics in closed multiclass networks of queues with general service times provides asymptotically shorter confidence intervals than does the ‘marked job’ method. A simple alternative proof of this result, under slightly more restrictive conditions, is given here.

scholarly journals A simple proof of a result of Iglehart and Shedler

1985 ◽  
Vol 17 (01) ◽  
pp. 239-241
Author(s):  
Mark Berman
Keyword(s):  
Confidence Intervals ◽  
Simple Proof ◽  
Passage Time ◽  
Alternative Proof ◽  
Multiclass Networks ◽  
Simple Alternative ◽  
General Service Times ◽  
Service Times ◽  
General Service ◽  
Networks Of Queues

Iglehart and Shedler (1983) prove that the ‘labelled jobs’ method for estimation of passage-time characteristics in closed multiclass networks of queues with general service times provides asymptotically shorter confidence intervals than does the ‘marked job’ method. A simple alternative proof of this result, under slightly more restrictive conditions, is given here.

First passage time for the state of exact chemical equilibrium

1980 ◽  
Vol 45 (3) ◽  
pp. 777-782 ◽  
Author(s):  
Milan Šolc
Keyword(s):  
Chemical Equilibrium ◽  
First Passage Time ◽  
Passage Time ◽  
The State ◽  
Recurrence Time ◽  
First Passage ◽  
First Order ◽  
The Mean ◽  
Passage Times ◽  
Number Of Particles

The establishment of chemical equilibrium in a system with a reversible first order reaction is characterized in terms of the distribution of first passage times for the state of exact chemical equilibrium. The mean first passage time of this state is a linear function of the logarithm of the total number of particles in the system. The equilibrium fluctuations of composition in the system are characterized by the distribution of the recurrence times for the state of exact chemical equilibrium. The mean recurrence time is inversely proportional to the square root of the total number of particles in the system.

Spectral Theory for Skip-Free Markov Chains

1989 ◽  
Vol 3 (1) ◽  
pp. 77-88 ◽  
Author(s):  
Joseph Abate ◽  
Ward Whitt
Keyword(s):  
Markov Chains ◽  
Spectral Theory ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage Times ◽  
Simple Relationship ◽  
First Passage ◽  
Birth And Death Processes ◽  
The Laplace Transform ◽  
Passage Times

The distribution of upward first passage times in skip-free Markov chains can be expressed solely in terms of the eigenvalues in the spectral representation, without performing a separate calculation to determine the eigenvectors. We provide insight into this result and skip-free Markov chains more generally by showing that part of the spectral theory developed for birth-and-death processes extends to skip-free chains. We show that the eigenvalues and eigenvectors of skip-free chains can be characterized in terms of recursively defined polynomials. Moreover, the Laplace transform of the upward first passage time from 0 to n is the reciprocal of the nth polynomial. This simple relationship holds because the Laplace transforms of the first passage times satisfy the same recursion as the polynomials except for a normalization.

scholarly journals Probing Protein Shelf Lives from Inverse Mean First Passage Times

2019 ◽  
Author(s):  
Vishal Singh ◽  
Parbati Biswas
Keyword(s):  
Protein Aggregation ◽  
Rate Constants ◽  
Survival Probability ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
First Order Kinetics ◽  
The Mean ◽  
Passage Times ◽  
Good Agreement

Protein aggregation is investigated theoretically via protein turnover, misfolding, aggregation and degradation. The Mean First Passage Time (MFPT) of aggregation is evaluated within the framework of Chemical Master Equation (CME) and pseudo first order kinetics with appropriate boundary conditions. The rate constants of aggregation of different proteins are calculated from the inverse MFPT, which show an excellent match with the experimentally reported rate constants and those extracted from the ThT/ThS fluorescence data. Protein aggregation is found to be practically independent of the number of contacts and the critical number of misfolded contacts. The age of appearance of aggregation-related diseases is obtained from the survival probability and the MFPT results, which matches with those reported in the literature. The calculated survival probability is in good agreement with the only available clinical data for Parkinson’s disease.<br>

Sign in / Sign up

Export Citation Format

Share Document