Discrete-time retrial queue with Bernoulli vacation, preemptive resume and feedback customers
Abstract: 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
Author: Peishu Chen, Yongwu
Zhou, Changwen Li
Journal Code: jptindustrigg150084
