Analysis of an M [X] /G/1 unreliable retrial G -queue with orbital search and feedback under Bernoulli vacation schedule
TL;DR: This paper considers a batch arrival retrial queue with feedback under Bernoulli vacation schedule, where the busy server is subjected to breakdown due to the arrival of negative customers.
Abstract: In this paper, we consider a batch arrival retrial queue with feedback under Bernoulli vacation schedule, where the busy server is subjected to breakdown due to the arrival of negative customers. Any arriving batch of positive customers finds the server free, one of the customers from the batch enters into the service area and the rest of them join into the orbit. Arriving positive customers may balk (or renege) the system at particular times. After completion of service the unsatisfied positive customer may rejoin into the orbit to get another regular service as feedback customer. The server takes Bernoulli vacation after service completion of positive customers. After completion of service (if the server is not taking vacation), repair or vacation the server searches for the customers in the orbit or remains idle. The steady state probability generating function for the system size is obtained by using the supplementary variable method. Some system performance measures, reliability measures and stochastic decomposition law are discussed. Finally, some numerical examples and cost optimization analysis are presented.
Citations
More filters
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.
Abstract: In this paper, we consider a single server feedback retrial queueing system with multiple working vacations and vacation interruption. An arriving customer may balk the system at some particular times. As soon as orbit becomes empty at regular service completion instant, the server goes for a working vacation. The server works at a lower service rate during working vacation (WV) period. After completion of regular service, the unsatisfied customer may rejoin into the orbit to get another service as feedback customer. The normal busy server may get to breakdown and the service channel will fail for a short interval of time. The steady state probability generating function for the system size is obtained by using the supplementary variable method. Some important system performance measures are obtained. Finally, some numerical examples and cost optimization analysis are presented.
33 citations
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.
Abstract: This paper deals with a batch arrivals queue with general retrial time, breakdowns, repairs and reserved time Here we assume that customers arrive according to compound Poisson processes Any arri
21 citations
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.
20 citations
Cites background from "Analysis of an M [X] /G/1 unreliabl..."
...[16,17] have discussed different types of queueing models operating with the simultaneous presence of negative arrivals....
[...]
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.
Abstract: In most of the queueing models, service is considered to be complete without any interruption. But in reality, queueing systems are subject to interruptions due to failure of server or any other cause. In the present article, we present 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. The factors causing service interruption such as unreliable server and server vacation are elaborated. The brief of supplementary variable technique to establish the queue size distribution is explained for single server non-Markovian queueing models by incorporating the features of service interruption. The basic concepts and review of literature on the queues with server breakdown and/or vacationing server are described. The research works done during last 10 years (2010–2019) on queues with service interruption involving many other key concepts namely Bernoulli vacation, multiple vacation, bulk arrival, discouragement, etc. and queueing scenarios of service interruption are reported. Some specific applications are also highlighted.
16 citations
TL;DR: In this paper, the authors deal with an unreliable queueing system with Bernoulli feedback and discouraging behavior of the units arriving at the service system and use the maximum entropy principle to study the problem.
Abstract: This article deals with an unreliable queueing system with Bernoulli feedback and discouraging behavior of the units arriving at the service system. The maximum entropy principle is used to study t...
10 citations
References
More filters
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.
Abstract: This paper considers a class of M/G/1 queueing models with a server who is unavailable for occasional intervals of time. As has been noted by other researchers, for several specific models of this type, 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, one of which is the stationary number of customers present in the standard M/G/1 queue i.e., the server is always available at a random point in time. In this paper we demonstrate that this type of decomposition holds, in fact, for a very general class of M/G/1 queueing models. The arguments employed are both direct and intuitive. In the course of this work, moreover, we obtain two new results that can lead to remarkable simplifications when solving complex M/G/1 queueing models.
664 citations
Book•
07 May 2008
TL;DR: This book is intended for an audience ranging from advanced undergraduates to researchers interested in queueing theory, but also in applied probability, stochastic models of the operations research, and engineering.
Abstract: The application of auto-repeat facilities in telephone systems, as well as the use of random access protocols in computer networks, have led to growing interest in retrial queueing models. Since much of the theory of retrial queues is complex from an analytical viewpoint, with this book the authors give a comprehensive and updated text focusing on approximate techniques and algorithmic methods for solving the analytically intractable models.
Retrial Queueing Systems: A Computational Approach also
* Presents motivating examples in telephone and computer networks.
* Establishes a comparative analysis of the retrial queues versus standard queues with waiting lines and queues with losses.
* Integrates a wide range of techniques applied to the main M/G/1 and M/M/c retrial queues, and variants with general retrial times, finite population and the discrete-time case.
* Surveys basic results of the matrix-analytic formalism and emphasizes the related tools employed in retrial queues.
* Discusses a few selected retrial queues with QBD, GI/M/1 and M/G/1 structures.
* Features an abundance of numerical examples, and updates the existing literature.
The book is intended for an audience ranging from advanced undergraduates to researchers interested not only in queueing theory, but also in applied probability, stochastic models of the operations research, and engineering. The prerequisite is a graduate course in stochastic processes, and a positive attitude to the algorithmic probability.
419 citations
TL;DR: Find sufficient conditions for the ergodicity and recurrence of irreducible and aperiodic Markov chains and their use in discussing a certain class of queuing problem with state dependent service times is indicated.
Abstract: This paper finds sufficient conditions for the ergodicity and recurrence of irreducible and aperiodic Markov chains. They extend some of the ones commonly used. The paper also indicates their use in discussing a certain class of queuing problem with state dependent service times.
269 citations