A discrete-time Geo/G/1 retrial queue with preferred and impatient 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.

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Performance Analysis of a Discrete-Time Retrial Queue with Bernoulli Feedback, Starting Failure and Single Vacation Policy

10.1007/978-3-030-68281-1_27 ◽

2021 ◽

pp. 365-379

Author(s):

Shweta Upadhyaya

Keyword(s):

Performance Analysis ◽

Discrete Time ◽

Retrial Queue ◽

Bernoulli Feedback ◽

Single Vacation ◽

Starting Failure

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Analysis of a retrial queue with group service of impatient customers

Journal of Ambient Intelligence and Humanized Computing ◽

10.1007/s12652-019-01318-x ◽

2019 ◽

Vol 11 (6) ◽

pp. 2591-2599 ◽

Cited By ~ 4

Author(s):

M. P. D’Arienzo ◽

A. N. Dudin ◽

S. A. Dudin ◽

R. Manzo

Keyword(s):

Retrial Queue ◽

Impatient Customers ◽

Group Service

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

Mathematical Problems in Engineering ◽

10.1155/2015/835158 ◽

2015 ◽

Vol 2015 ◽

pp. 1-12 ◽

Cited By ~ 1

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.

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