Well-posedness and asymptotic behavior of the time-dependent solution of an M/G/1 queueing model

2018 ◽  
Vol 10 (1) ◽  
pp. 49-92 ◽  
Author(s):  
Nurehemaiti Yiming ◽  
Geni Gupur
Keyword(s):  
Asymptotic Behavior ◽  
Time Dependent ◽  
Well Posedness ◽  
Queueing Model ◽  
Time Dependent Solution

SEMIGROUP METHODS FOR A PARALLEL MAINTENANCE SYSTEM WITH TWO COMPONENTS

2010 ◽  
Vol 08 (04) ◽  
pp. 363-386 ◽  
Author(s):  
ABDUKERIM HAJI ◽  
BILIKIZ YUNUS
Keyword(s):  
Asymptotic Behavior ◽  
Spectral Theory ◽  
Positive Operators ◽  
Time Dependent ◽  
Well Posedness ◽  
Maintenance System ◽  
Time Dependent Solution

By using the theory of C0-semigroups and spectral theory of positive operators, we prove well-posedness of the parallel maintenance system with two components and study the asymptotic behavior of the time-dependent solution.

scholarly journals Semigroup Methods for the M/G/1 Queueing Model with Working Vacation and Vacation Interruption

2016 ◽  
Vol 8 (5) ◽  
pp. 56 ◽  
Author(s):  
Ehmet Kasim
Keyword(s):  
Semigroup Theory ◽  
Steady State Solution ◽  
Linear Operators ◽  
Time Dependent ◽  
Queueing Model ◽  
Working Vacation ◽  
Positive Time ◽  
Vacation Interruption ◽  
Vacation Period ◽  
Time Dependent Solution

By using the strong continuous semigroup theory of linear operators we prove that the M/G/1 queueing model with working vacation and vacation interruption has a unique positive time dependent solution which satisfies probability conditions. When the both service completion rate in a working vacation period and in a regular busy period are constant, by investigating the spectral properties of an operator corresponding to the model we obtain that the time-dependent solution of the model strongly converges to its steady-state solution.

The well-Posedness of a Two-Unit Standby Redundant Electronic Equipment System

2013 ◽  
Vol 325-326 ◽  
pp. 315-318
Author(s):  
Xing Qiao ◽  
Yan Wang ◽  
Dan Ma ◽  
Zhuang Liu
Keyword(s):  
Steady State ◽  
Electronic Equipment ◽  
Time Dependent ◽  
Well Posedness ◽  
Reliability Study ◽  
Reliability Indices ◽  
Unique Existence ◽  
Human Failure ◽  
Time Dependent Solution ◽  
Equipment System

In this paper, we deal with a two-unit standby redundant electronic equipment system under human failure. In reliability study, it is ordinary to substitute the steady-state reliability indices for dynamic ones because the time-dependent solution is difficult to get. But this replacement should be based on some conditions in general. Therefore it is important to study the unique existence and the expression of the dynamic solution and it is the same with its stability.

Asymptotic behavior of small solutions of the Benjamin–Ono equation with time-dependent coefficients

2015 ◽  
Vol 21 (1) ◽  
Author(s):  
Youcef Mammeri
Keyword(s):  
Asymptotic Behavior ◽  
Time Scale ◽  
Time Dependent ◽  
Continuous Case ◽  
Well Posedness ◽  
Natural Time

AbstractWe study the behavior of small solutions depending on time of the generalized and regularized Benjamin–Ono equation in both continuous and periodic context. In particular, we prove that these solutions remain small for a time scale improving the natural time given by the local well-posedness. In the continuous case, the result becomes global-in-time.

scholarly journals Further Research on the M/G/1 Retrial Queueing Model with Server Breakdowns

2012 ◽  
Vol 2012 ◽  
pp. 1-16
Author(s):  
Ehmet Kasim ◽  
Geni Gupur
Keyword(s):  
Spectral Properties ◽  
Imaginary Axis ◽  
Time Dependent ◽  
Queueing Model ◽  
Asymptotically Stable ◽  
Resolvent Set ◽  
Retrial Queueing ◽  
Time Dependent Solution

We study spectral properties of the operator which corresponds to the M/G/1 retrial queueing model with server breakdowns and obtain that all points on the imaginary axis except zero belong to the resolvent set of the operator and 0 is not an eigenvalue of the operator. Our results show that the time-dependent solution of the model is probably strongly asymptotically stable.

scholarly journals Semigroup Method on aMX/G/1 Queueing Model

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Alim Mijit
Keyword(s):  
Functional Analysis ◽  
Time Dependent ◽  
Queueing Model ◽  
Semigroup Method ◽  
Time Dependent Solution

By using the Hille-Yosida theorem, Phillips theorem, and Fattorini theorem in functional analysis we prove that theMX/G/1 queueing model with vacation times has a unique nonnegative time-dependent solution.

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