scholarly journals Fuzzy Availability Assessment for Discrete Time Multi-State System under Minor Failures and Repairs by Using Fuzzy Lz-transform.

2017 ◽  
Vol 19 (2) ◽  
pp. 179-190 ◽  
Author(s):  
Linmin Hu
Keyword(s):  
Discrete Time ◽  
State System ◽  
Fuzzy Availability ◽  
Availability Assessment

Quantized state simulation of spiking neural networks

SIMULATION ◽  
2011 ◽  
Vol 88 (3) ◽  
pp. 299-313 ◽  
Author(s):  
Guillermo L Grinblat ◽  
Hernán Ahumada ◽  
Ernesto Kofman
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Discrete Event ◽  
State System ◽  
Spiking Neurons ◽  
Spiking Neural Networks ◽  
Computational Costs ◽  
Simulation Results ◽  
Neuroscience Community

In this work, we explore the usage of quantized state system (QSS) methods in the simulation of networks of spiking neurons. We compare the simulation results obtained by these discrete-event algorithms with the results of the discrete time methods in use by the neuroscience community. We found that the computational costs of the QSS methods grow almost linearly with the size of the network, while they grows at least quadratically in the discrete time algorithms. We show that this advantage is mainly due to the fact that QSS methods only perform calculations in the components of the system that experience activity.

On steady-state queue size distributions of the discrete-time GI/G/1 queue

1996 ◽  
Vol 28 (04) ◽  
pp. 1177-1200 ◽  
Author(s):  
Tao Yang ◽  
M. L. Chaudhry
Keyword(s):  
Steady State ◽  
Discrete Time ◽  
Linear Transformation ◽  
State System ◽  
Interarrival Time ◽  
Steady State Distribution ◽  
State Distribution ◽  
The Matrix ◽  
Matrix Geometric Solution ◽  
System Length

In this paper, we present results for the steady-state system length distributions of the discrete-timeGI/G/1 queue. We examine the system at customer arrival epochs (customer departure epochs) and use the residual service time (residual interarrival time) as the supplementary variable. The embedded Markov chain is ofGI/M/1 type if the embedding points are arrival epochs and is ofM/G/1 type if the embedding points are departure epochs. Using the matrix analytic method, we identify the necessary and sufficient condition for both Markov chains to be positive recurrent. For theGI/M/1 type chain, we derive a matrix-geometric solution for its steady-state distribution and for theM/G/1 type chain, we develop a simple linear transformation that relates it to theGI/M/1 type chain and leads to a simple analytic solution for its steady-state distribution. We also show that the steady-state system length distribution at an arbitrary point in time can be obtained by a simple linear transformation of the matrix-geometric solution for theGI/M/1 type chain. A number of applications of the model to communication systems and numerical examples are also discussed.

Reliability modeling for a discrete time multi-state system with random and dependent transition probabilities

2019 ◽  
Vol 233 (5) ◽  
pp. 747-760 ◽  
Author(s):  
Linmin Hu ◽  
Rui Peng
Keyword(s):  
Discrete Time ◽  
Power Distribution ◽  
State Transition ◽  
Transition Probabilities ◽  
Survival Function ◽  
Copula Function ◽  
State System ◽  
Dependence Structure ◽  
Reliability Modeling ◽  
Dynamic Reliability

In a random environment, state transition probabilities of a multi-state system can change as the environment changes. Thus, a dynamic reliability model with random and dependent transition probabilities is developed for non-repairable discrete-time multi-state system in this article. The dependence among the random state transition probabilities of the system is modeled by a copula function. By probability argument and random process theory, we obtain explicit expressions of some reliability characteristics and joint survival function of random time spent by the system in all working states (partially and completely working states). A special case is considered when the state transition probabilities are dependent random variables with power distribution, and the dependence structure is modeled by Farlie–Gumbel–Morgenstern copula. Numerical examples are also presented to demonstrate the developed model and perform a comparison for the models with random and fixed transition probabilities.

On steady-state queue size distributions of the discrete-time GI/G/1 queue

1996 ◽  
Vol 28 (4) ◽  
pp. 1177-1200 ◽  
Author(s):  
Tao Yang ◽  
M. L. Chaudhry
Keyword(s):  
Steady State ◽  
Discrete Time ◽  
Linear Transformation ◽  
State System ◽  
Interarrival Time ◽  
Steady State Distribution ◽  
State Distribution ◽  
The Matrix ◽  
Matrix Geometric Solution ◽  
System Length

In this paper, we present results for the steady-state system length distributions of the discrete-time GI/G/1 queue. We examine the system at customer arrival epochs (customer departure epochs) and use the residual service time (residual interarrival time) as the supplementary variable. The embedded Markov chain is of GI/M/1 type if the embedding points are arrival epochs and is of M/G/1 type if the embedding points are departure epochs. Using the matrix analytic method, we identify the necessary and sufficient condition for both Markov chains to be positive recurrent. For the GI/M/1 type chain, we derive a matrix-geometric solution for its steady-state distribution and for the M/G/1 type chain, we develop a simple linear transformation that relates it to the GI/M/1 type chain and leads to a simple analytic solution for its steady-state distribution. We also show that the steady-state system length distribution at an arbitrary point in time can be obtained by a simple linear transformation of the matrix-geometric solution for the GI/M/1 type chain. A number of applications of the model to communication systems and numerical examples are also discussed.

scholarly journals On the Steady-State System Size Distribution for a Discrete-Time Geo/G/1 Repairable Queue

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Renbin Liu ◽  
Zhaohui Deng
Keyword(s):  
Steady State ◽  
Size Distribution ◽  
Discrete Time ◽  
Queueing System ◽  
System Size ◽  
State System ◽  
System Capacity ◽  
Analysis Method ◽  
Network Access ◽  
Capacity Design

This paper studies a discrete-time N-policy Geo/G/1 queueing system with feedback and repairable server. With a probabilistic analysis method and renewal process theory, the steady-state system size distribution is derived. Further, the steady-state system size distribution derived in this work is extremely suitable for numerical calculations. Numerical example illustrates the important application of steady-state system size distribution in system capacity design for a network access proxy system.

scholarly journals Fuzzy Availability Assessment for a Repairable Multistate Series-Parallel System

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Linmin Hu ◽  
Dequan Yue ◽  
Ruiling Tian
Keyword(s):  
Parametric Programming ◽  
Parallel System ◽  
Function Technique ◽  
Extension Principle ◽  
Programming Technique ◽  
Assessment Approach ◽  
Fuzzy Availability ◽  
Special Assessment ◽  
Fuzzy State ◽  
Availability Assessment

This paper considers a repairable multistate series-parallel system (RMSSPS) with fuzzy parameters. It is assumed that the system components are independent, and their state transition rates and performance rates are fuzzy values. The fuzzy universal generating function technique is adopted to determine fuzzy state probability and fuzzy performance rate of the system. On the basis ofα-cut approach and the extension principle, parametric programming technique is employed to obtain theα-cuts of some indices for the system. The system fuzzy availability is defined as the ability of the system to satisfy fuzzy consumer demand. A special assessment approach is developed for evaluating the fuzzy steady-state availability of the system with the fuzzy demand. A flow transmission system with three components is presented to demonstrate the validity of the proposed method.

The Effect of Partly Missing Covariates on Statistical Power in Randomized Controlled Trials With Discrete-Time Survival Endpoints

Methodology ◽  
2017 ◽  
Vol 13 (2) ◽  
pp. 41-60
Author(s):  
Shahab Jolani ◽  
Maryam Safarkhani
Keyword(s):  
Randomized Controlled Trials ◽  
Discrete Time ◽  
Treatment Effect ◽  
Survival Data ◽  
Controlled Trials ◽  
Missing Covariates ◽  
Indicator Method ◽  
Imputation Methods ◽  
Randomized Controlled ◽  
Baseline Covariates

Abstract. In randomized controlled trials (RCTs), a common strategy to increase power to detect a treatment effect is adjustment for baseline covariates. However, adjustment with partly missing covariates, where complete cases are only used, is inefficient. We consider different alternatives in trials with discrete-time survival data, where subjects are measured in discrete-time intervals while they may experience an event at any point in time. The results of a Monte Carlo simulation study, as well as a case study of randomized trials in smokers with attention deficit hyperactivity disorder (ADHD), indicated that single and multiple imputation methods outperform the other methods and increase precision in estimating the treatment effect. Missing indicator method, which uses a dummy variable in the statistical model to indicate whether the value for that variable is missing and sets the same value to all missing values, is comparable to imputation methods. Nevertheless, the power level to detect the treatment effect based on missing indicator method is marginally lower than the imputation methods, particularly when the missingness depends on the outcome. In conclusion, it appears that imputation of partly missing (baseline) covariates should be preferred in the analysis of discrete-time survival data.

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