Discrete-time retrial queue with Bernoulli vacation, preemptive resume and feedback customers

Peishu Chen, Yongwu Zhou, Changwen Li

Abstract


Purpose: We consider a discrete-time Geo/G/1 retrial queue where the retrial time follows a general distribution, the server subject to Bernoulli vacation policy and the customer has preemptive resume priority, Bernoulli feedback strategy. The main purpose of this paper is to derive the generating functions of the stationary distribution of the system state, the orbit size and some important performance measures.

Design/methodology: Using probability generating function technique, some valuable and interesting performance measures of the system are obtained. We also investigate two stochastic decomposition laws and present some numerical results.

Findings: We obtain the probability generating functions of the system state distribution as well as those of the orbit size and the system size distributions. We also obtain some analytical expressions for various performance measures such as idle and busy probabilities, mean orbit and system sizes.

Originality/value: The analysis of discrete-time retrial queues with Bernoulli vacation, preemptive resume and feedback customers is interesting and to the best of our knowledge, no other scientific journal paper has dealt with this question. This fact gives the reason why efforts should be taken to plug this gap.


Keywords


Discrete-time queue, Bernoulli vacation, preemptive resume, Bernoulli feedback, general retrial time, stochastic decomposition

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DOI: http://dx.doi.org/10.3926/jiem.1487


Licencia de Creative Commons 

This work is licensed under a Creative Commons Attribution 4.0 International License

Journal of Industrial Engineering and Management, 2008-2019

Online ISSN: 2013-0953; Print ISSN: 2013-8423; Online DL: B-28744-2008

Publisher: OmniaScience