A Survey for Stochastic Decomposition in Vacation Queues

2019 ◽  
pp. 134-158
Author(s):  
Naishuo Tian ◽  
Xiuli Xu ◽  
Zhanyou Ma ◽  
Shunfu Jin ◽  
Wei Sun
Keyword(s):  
Stochastic Decomposition

scholarly journals Sojourn Times in A Queueing System with Breakdowns and General Retrial Times

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2882
Author(s):  
Ivan Atencia ◽  
José Luis Galán-García
Keyword(s):  
Steady State ◽  
Discrete Time ◽  
Queueing System ◽  
Retrial Queue ◽  
Stochastic Decomposition ◽  
Discrete Time System ◽  
Main Research ◽  
Extensive Analysis ◽  
Complete Study ◽  
Number Of Customers

This paper centers on a discrete-time retrial queue where the server experiences breakdowns and repairs when arriving customers may opt to follow a discipline of a last-come, first-served (LCFS)-type or to join the orbit. We focused on the extensive analysis of the system, and we obtained the stationary distributions of the number of customers in the orbit and in the system by applying the generation function (GF). We provide the stochastic decomposition law and the application bounds for the proximity between the steady-state distributions for the queueing system under consideration and its corresponding standard system. We developed recursive formulae aimed at the calculation of the steady-state of the orbit and the system. We proved that our discrete-time system approximates M/G/1 with breakdowns and repairs. We analyzed the busy period of an auxiliary system, the objective of which was to study the customer’s delay. The stationary distribution of a customer’s sojourn in the orbit and in the system was the object of a thorough and complete study. Finally, we provide numerical examples that outline the effect of the parameters on several performance characteristics and a conclusions section resuming the main research contributions of the paper.

Inventory control for a MARKOVIAN remanufacturing system with stochastic decomposition process

2007 ◽  
Vol 108 (1-2) ◽  
pp. 416-425 ◽  
Author(s):  
Katsuhiko Takahashi ◽  
Katsumi Morikawa ◽  
Myreshka ◽  
Daisuke Takeda ◽  
Akihiko Mizuno
Keyword(s):  
Inventory Control ◽  
Decomposition Process ◽  
Stochastic Decomposition

scholarly journals A Discrete-TimeGeo/G/1 Retrial Queue with Two Different Types of Vacations

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Feng Zhang ◽  
Zhifeng Zhu
Keyword(s):  
Discrete Time ◽  
Queueing System ◽  
Retrial Queue ◽  
System Size ◽  
Stochastic Decomposition ◽  
Continuous Time Model ◽  
Time Model ◽  
Different Types ◽  
Number Of Customers ◽  
The Relationship

We analyze a discrete-timeGeo/G/1 retrial queue with two different types of vacations and general retrial times. Two different types of vacation policies are investigated in this model, one of which is nonexhaustive urgent vacation during serving and the other is normal exhaustive vacation. For this model, we give the steady-state analysis for the considered queueing system. Firstly, we obtain the generating functions of the number of customers in our model. Then, we obtain the closed-form expressions of some performance measures and also give a stochastic decomposition result for the system size. Moreover, the relationship between this discrete-time model and the corresponding continuous-time model is also investigated. Finally, some numerical results are provided to illustrate the effect of nonexhaustive urgent vacation on some performance characteristics of the system.

Stochastic Decomposition

1996 ◽  
Author(s):  
Julia L. Higle ◽  
Suvrajeet Sen
Keyword(s):  
Stochastic Decomposition
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