Journal ArticleDOI
An Unreliable Server Retrial Queue with Two Phases of Service and General Retrial Times Under Bernoulli Vacation Schedule
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The steady state behavior of an M/G/1 retrial queue with two successive phases of service and general retrial times under Bernoulli vacation schedule for an unreliable server is dealt with.Abstract:
This paper deals with the steady state behavior of an M/G/1 retrial queue with two successive phases of service and general retrial times under Bernoulli vacation schedule for an unreliable server. While the server is working with any phase of service, it may breakdown at any instant and the service channel will fail for a short interval of time. The primary customers finding the server busy, down, or on vacation are queued in the orbit in accordance with the FCFS (first come, first served) retrial policy. After the completion of the second phase of service, the server either goes for a vacation of random length with probability p or serves the next unit, if any, with probability (1 – p). For this model, we first obtain the condition under which the system is stable. Then, we derive the system size distribution at a departure epoch and the probability generating function of the joint distributions of the server state and orbit size, and prove the decomposition property. We also provide a reliabili...read more
Citations
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Journal ArticleDOI
Analysis of a single server batch arrival unreliable queue with balking and general retrial time
TL;DR: This model has a potential applications in various fields, such as in the cognitive radio network and the manufacturing systems, and some important performance measures, stochastic decomposition property of the system size distribution and the reliability indices are obtained.
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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.
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An M/G/1 queue with two types of general heterogeneous service and optional repeated service subject to server’s breakdown and delayed repair
TL;DR: This model, which involves an M/G/1 queue with two types of general heterogeneous service and optional repeated service subject to server’s breakdowns occurring randomly at any instant while serving the customers and delayed repair, is studied.
Journal ArticleDOI
Performance of an M/M/1 Retrial Queue with Working Vacation Interruption and Classical Retrial Policy
Tao Li,Liyuan Zhang,Shan Gao +2 more
TL;DR: An M/M/1 retrial queue with working vacation interruption with probability generating functions of the number of customers in the orbit is considered and various system performance measures are developed.
Journal ArticleDOI
Reliability of a retrial system with mixed standby components and Bernoulli vacation
TL;DR: In this paper, a K − o u t − o f − N retrial system with mixed standby components and a single repairman under Bernoulli vacation schedule is studied. But the model is motivated by some machine repair syst...
References
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Journal ArticleDOI
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.
Journal ArticleDOI
Stochastic Decompositions in the M/G/1 Queue with Generalized Vacations
S. W. Fuhrmann,Robert B. Cooper +1 more
TL;DR: In this article, the authors considered a class of M/G/1 queueing models with a server who is unavailable for occasional intervals of time and showed that the stationary number of customers present in the system at a random point in time is distributed as the sum of two or more independent random variables.
Journal ArticleDOI
The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables
TL;DR: In this paper, it is shown that certain stochastic processes with discrete states in continuous time can be converted into Markov processes by the well-known method of including supplementary variables, and conditions under which it is possible to obtain a solution for arbitrary distributions are examined.
Journal ArticleDOI
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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