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

Author:

Zhang Feng1ORCID,Zhu Zhifeng1

Affiliation:

1. School of Science, North University of China, Taiyuan 030051, China

Abstract

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.

Publisher

Hindawi Limited

Subject

General Engineering,General Mathematics

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