Journal ArticleDOI
An m/g/1 retrial queue with general retrial times, working vacations and vacation interruption
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An M/G/1 ret trial queue with general retrial times is considered, and working vacations and vacation interruption policy is introduced into the retrial queue to prove the conditional stochastic decomposition for the queue length in orbit.Abstract:
We consider an M/G/1 retrial queue with general retrial times, and introduce working vacations and vacation interruption policy into the retrial queue. During the working vacation period, customers can be served at a lower rate. If there are customers in the system at a service completion instant, the vacation will be interrupted and the server will come back to the normal working level. Using supplementary variable method, we obtain the stationary probability distribution and some performance measures. Furthermore, we carry out the waiting time distribution and prove the conditional stochastic decomposition for the queue length in orbit. Finally, some numerical examples are presented.read more
Citations
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Journal ArticleDOI
A cold standby repairable system with working vacations and vacation interruption following Markovian arrival process
TL;DR: This paper studies a cold standby repairable system with working vacations and vacation interruptions, and builds a vector-valued Markov process constructed for this system using the matrix-analytic method.
Journal ArticleDOI
A study on M/G/1 feedback retrial queue with subject to server breakdown and repair under multiple working vacation policy
TL;DR: In this article, a single server feedback retrial queueing system with multiple working vacations and vacation interruption is considered and the steady state probability generating function for the system size is obtained by using the supplementary variable method.
Journal ArticleDOI
Analysis of an unreliable retrial G-queue with working vacations and vacation interruption under Bernoulli schedule
TL;DR: In this paper, a single server retrial queueing system with working vacations is considered, where the regular busy server is subjected to breakdown due to the arrival of negative customers, and the server goes for a working vacation when the orbit becomes empty at the time of service completion for a positive customer.
Journal ArticleDOI
Admission control for finite capacity queueing model with general retrial times and state-dependent rates
Madhu Jain,Sudeep Singh Sanga +1 more
Abstract: The finite state dependent queueing model with \begin{document}$ F $\end{document} -policy is investigated by considering the general retrial attempts. On arrival in the system, if the job finds the server engaged, it is forced to enter into the retrial orbit. After a random period of time, the job from the retrial orbit re-attempts for the service. According to \begin{document}$ F $\end{document} -policy, as the system attains its full capacity, the arrivals are restricted to join the system until the number of jobs comes down to the prefixed threshold value ' \begin{document}$ F $\end{document} '. The supplementary variable corresponding to the remaining retrial time is used to frame the governing equations which are solved by using Laplace-Stieltjes transform and then applying the recursive method. Special models for machine repair and time-sharing queue are deduced by setting the state dependent rates. Several system indices are obtained explicitly which are further used to facilitate the sensitivity analysis by considering a numerical illustration. A cost function is constructed and minimized for evaluating the optimal threshold parameter and optimal service rate.
Journal ArticleDOI
Supplementary variable technique (SVT) for non-Markovian single server queue with service interruption (QSI)
TL;DR: An overview and literature survey on the performance modeling and analysis of single server, general service queueing system with service interruption using supplementary variable technique and factors causing service interruption such as unreliable server and server vacation are presented.
References
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Queueing systems with vacations—a survey
TL;DR: This survey gives an overview of some general decomposition results and the methodology used to obtain these results for two vacation models and attempts to provide a methodological overview to illustrate how the seemingly diverse mix of problems is closely related in structure and can be understood in a common framework.
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A survey of retrial queues
TL;DR: A survey of the main results and methods of the theory of retrial queues, concentrating on Markovian single and multi-channel systems, as well as models with batch arrivals, multiclasses, customer impatience, double connection, control devices, two-way communication and buffer.
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A classified bibliography of research on retrial pueues: progress in 1990-1999
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Accessible bibliography on retrial queues: Progress in 2000-2009
TL;DR: A bibliography on retrial queues which updates the bibliography published in this journal in Artalejo (1999) is presented, focused on the progress made during the last decade 2000-2009.