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Retrial queue

About: Retrial queue is a research topic. Over the lifetime, 784 publications have been published within this topic receiving 12354 citations.


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Journal ArticleDOI
19 Aug 2020
TL;DR: The retrial queuing system with non-preemptive priority customer is developed and the steady state behaviour and average waiting time are obtained.
Abstract: We develop the retrial queuing system with non-preemptive priority customer.A batch of customer arriving in the system in which the nonpreemptive customer do not form any queue. A customer in first class find the server free and he completes his service leaves the system. A customer in second class waits a period of time until the customer in-service and obeys FCFS discipline. The joint probability generating functions are derived using the supplementary variable technique. In this model we obtain the steady state behaviour and average waiting time, finally some examples are presented to the effect of the system.
Posted Content
Quan-Lin Li1
TL;DR: This paper discusses tail probabilities in some basic queueing processes including QBD processes, Markov chains of GI/M/1 type and of M/G/ 1 type, and provides some effective and efficient algorithms for computing the tail probabilities by means of the matrix-geometric solution, the Matrix-iterative solution,The matrix-product solution and the two types of RG-factorizations.
Abstract: In the study of large scale stochastic networks with resource management, differential equations and mean-field limits are two key techniques. Recent research shows that the expected fraction vector (that is, the tailed probability vector) plays a key role in setting up mean-field differential equations. To further apply the technique of tailed probability vector to deal with resource management of large scale stochastic networks, this paper discusses tailed probabilities in some basic queueing processes including QBD processes, Markov chains of GI/M/1 type and of M/G/1 type, and also provides some effective and efficient algorithms for computing the tailed probabilities by means of the matrix-geometric solution, the matrix-iterative solution, the matrix-product solution and the two types of RG-factorizations. Furthermore, we consider four queueing examples: The M/M/1 retrial queue, the M(n)/M(n)/1 queue, the M/M/1 queue with server multiple vacations and the M/M/1 queue with repairable server, where the M/M/1 retrial queue is given a detailed discussion, while the other three examples are analyzed simply. Note that the results given in this paper will be very useful in the study of large scale stochastic networks with resource management, including the supermarket models and the work stealing models.
Journal ArticleDOI
TL;DR: In this paper , the authors considered a retrial queuing system with the help of two-way communication where the server is subject to random breakdowns and showed the effect of the different distributions of failure time on the main performance measures such as the mean waiting time of an arbitrary customer or the utilization of the service unit.
Abstract: In this paper a retrial queuing system is considered with the help of two-way communication where the server is subject to random breakdowns. This is a M/M/1//N type of system so the population of the source is finite. The server becoming idle enables calls the customers in the orbit (outgoing call or secondary customers). The service time of the primary and secondary customers follows exponential distribution with different rates μ1 and μ2 respectively. All the random variables included in the model construction are assumed to be totally independent of each other. The novelty of this paper is to show the effect of the different distributions of failure time on the main performance measures such as the mean waiting time of an arbitrary customer or the utilization of the service unit. In order to achieve a valid comparison a fitting process is done; thus, in case of every distribution the mean value and dispersion is the same. Graphical illustrations are given with the help of the self-developed simulation program.
Journal ArticleDOI
TL;DR: In this article, the steady-state behavior of a two-phase retrial queueing system with two phases of heterogeneous services and general retrial time is analyzed, and sensitivity analysis of performance measures and cost rate is done concerning arrival/retrial rates, feedback probabilities, and state-dependent admission in a telecommunication system.
Abstract: Today, real-world problems modeling is the first step in controlling, analyzing, and optimizing them. One of the applied techniques for modeling some of these problems is the queueing theory. Usually, the conditions such as lack of space, feedback, admission limits, etc. are the inseparable parts of these problems. This paper deals with modeling and analyzing the steady-state behavior of an $$M^{X} /G/ 1$$ retrial queueing system with two phases of heterogeneous services and general retrial time. The arriving batches join the system with dependent admission due to the server state. If the customers find the server busy, they join the orbit to repeat their request. Although, the first phase of service is essential for all customers, any customer has three options after the completion of the $$i$$ -th phase $$\left( {i = 1,2} \right)$$ . They may take the $$\left( {i + 1} \right)$$ -th phase of service with probability $${\uptheta }_{{\text{i}}}$$ , otherwise, return the orbit with probability $$p_{i} \left( {1 - \theta_{i} } \right)$$ or leave the system with probability $${ }\left( {1 - p_{i} } \right)\left( {1 - \theta_{i} } \right)$$ . In this paper, after finding the steady-state distributions and the probability generating functions of the system and orbit size, some important performance measures are found. Then, the sensitivity analysis of performance measures and cost rate is done concerning arrival/retrial rates, feedback probabilities, and state-dependent admission in a telecommunication system.

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202326
202259
202135
202056
201947
201844