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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 Article
TL;DR: In this paper, the authors considered a retrial queue with impatient customers, where the repair is not immediate and it starts after a random amount of time and the customer in service can either remain in service position or leave and return.
Abstract: Bulk arrival retrial queue with impatient customers is considered. The server is subject to breakdown and repair. The repair is not immediate and it starts after a random amount of time. While the server is being repaired, the customer in service can either remain in service position or leave and return. If the server is blocked upon the arrival of a batch, then the customers may leave the system without service or enter the orbit to retry for service after a random time. Upon retrial, the customer enters the service if the server is idle; otherwise goes back to the retrial orbit or renege the system. The condition for the system to be stable, analytical results for the queue length distribution and some performance measures are derived. Numerical results are presented.

3 citations

Proceedings ArticleDOI
04 Dec 2019
TL;DR: In this article, the authors considered a bulk arrival retrial queue with non-persistent customers and exponentially distributed multiple working vacation and obtained the probability generating function for the number of customers and the average number of users in the orbit.
Abstract: In this paper, we consider a bulk arrival retrial queue with non - persistent customers and exponentially distributed multiple working vacation. If the primary customer finds the server busy then the customer becomes impatient and may leave the system forever without service. After service completion epoch there is no customers in the orbit then the server takes vacation. During the vacation period, customers can be served at a lower rate. We obtain the probability generating function for the number of customers and the average number of customers in the orbit. Also, we discuss some particular cases of the model.

3 citations

Journal ArticleDOI
02 Jul 2012
TL;DR: In the present paper, a single server retrial queue with impatient customers is studied and Steady state solution of the number of busy servers is obtained.
Abstract: In the present paper, a single server retrial queue with impatient customers is studied. The primary arrivals and repeating calls follow the Poisson distribution. The service time is exponentially distributed. Explicit time-dependent probabilities of an exact number of arrivals and departures from the orbit are obtained by solving the differential-difference equations recursively. Steady state solution of the number of busy servers is obtained. The numerical results are graphically displayed to illustrate the effect of arrival rate, retrial rate and service rate on different probabilities against time. Some special cases of interest are also deduced.

3 citations

Journal ArticleDOI
TL;DR: In this article, the analysis of the waiting time distribution in the M/M/m retrial queue was studied and expressions for the Laplace-Stieltjes transform (LST) of the distribution were given.
Abstract: In this paper, we are concerned with the analysis of the waiting time distribution in the M/M/m retrial queue. We give expressions for the Laplace-Stieltjes transform (LST) of the waiting time distribution and then provide a numerical algorithm for calculating the LST of the waiting time distribution. Numerical inversion of the LSTs is used to calculate the waiting time distribution. Numerical results are presented to illustrate our results.

3 citations

Book ChapterDOI
01 Jan 2016
TL;DR: This paper considers a retrial queueing model for cloud computing systems where the processing unit (server) and the storage unit (buffer) are separated and presents a recursive scheme for computing the stationary probability of all the states.
Abstract: This paper considers a retrial queueing model for cloud computing systems where the processing unit (server) and the storage unit (buffer) are separated. Jobs that cannot occupy the server upon arrival are stored in the buffer from which they are sent to the server after some random time. After completing a service the server stays idle for a while waiting for either a new job or a job from the buffer. After the idle period, the server starts searching for a job from the buffer. We assume that the search time cannot be disregarded during which the server cannot serve a job. We model this system using a retrial queue with search for customers from the orbit and obtain an explicit solution in terms of partial generating functions. We present a recursive scheme for computing the stationary probability of all the states.

3 citations


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