Asymptotic Behavior of the Time-Dependent Solution of the M/G/1 Queueing Model with Second Optional Service

2015 ◽  
Vol 39 (1) ◽  
pp. 29-64 ◽  
Author(s):  
Ehmet Kasim ◽  
Geni Gupur
Keyword(s):  
Asymptotic Behavior ◽  
Time Dependent ◽  
Queueing Model ◽  
Optional Service ◽  
Second Optional Service ◽  
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.

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 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.

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