scholarly journals Interest of Boundary Kernel Density Techniques in Evaluating an Approximation Error of Queueing Systems Characteristics

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Aïcha Bareche ◽  
Djamil Aïssani
Keyword(s):  
Comparative Study ◽  
Density Function ◽  
Numerical Evaluation ◽  
Queueing Systems ◽  
Approximation Error ◽  
Kernel Density ◽  
Nonparametric Methods ◽  
Simulation Studies ◽  
Stationary Distributions ◽  
Numerical Examples

We show the interest of nonparametric methods taking into account the boundary correction techniques for a numerical evaluation of an approximation error between the stationary distributions ofG/M/1andM/M/1queueing systems, when the density function of the general arrivals lawGin theG/M/1system is unknown and defined on a bounded support. To compute this error, we use two kinds of norms: theL1norm and the weight norm. Numerical examples based on simulation studies are presented for the two cases of considered norms. A comparative study of the results has been provided.

scholarly journals KAPABILITAS PROSES DENGAN ESTIMASI FUNGSI DENSITAS KERNEL PADA PRODUKSI DENIM DI PT APAC INTI CORPORA

2018 ◽  
Vol 7 (3) ◽  
pp. 326-336
Author(s):  
Puput Ramadhani ◽  
Dwi Ispriyanti ◽  
Diah Safitri
Keyword(s):  
Quality Control ◽  
Production Process ◽  
Density Function ◽  
Control Chart ◽  
Cross Validation ◽  
Kernel Density ◽  
Process Capability ◽  
Conformity Index ◽  
Denim Fabric ◽  
Kernel Density Function

The quality of production becomes one of the basic factors of consumer decisions in choosing a product. Quality control is needed to control the production process. Control chart is a tool used in performing statistical quality control. One of the alternatives used when the data obtained is not known distribution is analyzed by nonparametric approach based on estimation of kernel density function. The most important thing in estimating kernel density function is optimal bandwidth selection (h) which minimizes Cross Validation (CV) value. Some of the kernel functions used in this research are Rectangular, Epanechnikov, Triangular, Biweight, and Gaussian. If the process control chart is statistically controlled, a process capability analysis can be calculated using the process conformity index to determine the nature of the process capability. In this research, the kernel control chart and process conformity index were used to analyze the slope shift of Akira-F style fabric and Corvus-SI style on the production of denim fabric at PT Apac Inti Corpora. The results of the analysis show that the production process for Akira-F style is statistically controlled, but Ypk > Yp is 0.889823 > 0,508059 indicating that the process is still not in accordance with the specified limits set by the company, while for Corvus- SI is statistically controlled and Ypk < Yp is 0.637742 < 0.638776 which indicates that the process is in accordance with the specification limits specified by the company. Keywords:     kernel density function estimation, Cross Validation, kernel control chart, denim fabric, process capability

scholarly journals On Truncation of the Matrix-Geometric Stationary Distributions

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 798 ◽  
Author(s):  
Naumov ◽  
Gaidamaka ◽  
Samouylov
Keyword(s):  
Finite Number ◽  
Stationary Distribution ◽  
Queueing Systems ◽  
Death Process ◽  
Birth And Death Process ◽  
Loss System ◽  
Stationary Distributions ◽  
Open Network ◽  
The Matrix

In this paper, we study queueing systems with an infinite and finite number of waiting places that can be modeled by a Quasi-Birth-and-Death process. We derive the conditions under which the stationary distribution for a loss system is a truncation of the stationary distribution of the Quasi-Birth-and-Death process and obtain the stationary distributions of both processes. We apply the obtained results to the analysis of a semi-open network in which a customer from an external queue replaces a customer leaving the system at the node from which the latter departed.

Numerical simulations of non-stationary distributions of electrochemical potentials in SOFC

2017 ◽  
Vol 34 (6) ◽  
pp. 1956-1988 ◽  
Author(s):  
Mayu Muramatsu ◽  
Keiji Yashiro ◽  
Tatsuya Kawada ◽  
Kenjiro Tarada
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Chemical Potential ◽  
Simulation Method ◽  
Open Circuit ◽  
Operating Conditions ◽  
Stationary Distributions ◽  
Experimental Conditions ◽  
Content Type ◽  
Numerical Examples

Purpose The purpose of this study is to develop a simulation method to calculate non-stationary distributions of the chemical potential of oxygen in a solid oxide fuel cell (SOFC) under operation. Design/methodology/approach The initial-boundary value problem was appropriately formulated and the appropriate boundary conditions were implemented so that the problem of non-stationary behavior of SOFC can be solved in accordance with actual operational and typical experimental conditions. The dependencies of the material properties on the temperature and partial pressure of oxygen were also elaborately introduced to realize actual material responses. The capability of the proposed simulation method was demonstrated under arbitrary operating conditions. Findings The steady state calculated with the open circuit voltage condition was conformable with the analytical solution. In addition, the transient states of the spatial distributions of potentials and currents under the voltage- and current-controlled conditions were successfully differentiated, even though they eventually became the same steady state. Furthermore, the effects of dense materials assumed for interconnects and current collectors were found to not be influential. It is thus safe to conclude that the proposed method enables us to simulate any type of transient simulations regardless of controlling conditions. Practical implications Although only uniaxial models were tested in the numerical examples in this paper, the proposed method is applicable for arbitrary shapes of SOFC cells. Originality/value The value of this paper is that adequate numerical simulations by the proposed method properly captured the electrochemical transient transport phenomena in SOFC under various operational conditions, and that the applicability was confirmed by some numerical examples.

scholarly journals Bounds on the rate of convergence for one class of inhomogeneous Markovian queueing models with possible batch arrivals and services

2018 ◽  
Vol 28 (1) ◽  
pp. 141-154 ◽  
Author(s):  
Alexander Zeifman ◽  
Rostislav Razumchik ◽  
Yacov Satin ◽  
Ksenia Kiseleva ◽  
Anna Korotysheva ◽  
...  
Keyword(s):  
Rate Of Convergence ◽  
Queueing Systems ◽  
Approximation Error ◽  
Linear Operators ◽  
Upper And Lower Bounds ◽  
Logarithmic Norm ◽  
Batch Arrivals ◽  
State Dependent ◽  
The Mean ◽  
Number Of Customers

AbstractIn this paper we present a method for the computation of convergence bounds for four classes of multiserver queueing systems, described by inhomogeneous Markov chains. Specifically, we consider an inhomogeneous M/M/S queueing system with possible state-dependent arrival and service intensities, and additionally possible batch arrivals and batch service. A unified approach based on a logarithmic norm of linear operators for obtaining sharp upper and lower bounds on the rate of convergence and corresponding sharp perturbation bounds is described. As a side effect, we show, by virtue of numerical examples, that the approach based on a logarithmic norm can also be used to approximate limiting characteristics (the idle probability and the mean number of customers in the system) of the systems considered with a given approximation error.

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