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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
TL;DR: It is shown that the joint stationary orbit queue length distribution at service completion epochs is determined by solving a Riemann boundary value problem.
Abstract: We mathematically investigate a single server system accepting two types of retrial customers and paired service. If upon arrival a customer finds the server busy, it is routed to an infinite capacity orbit queue according to each type. Upon a service completion epoch, if at least one orbit queue is non-empty, the server seeks to find customers from the orbits. If both orbit queues are non-empty, the seeking process will bring to the service area a pair of customers, one from each orbit. If there is only one non-empty, then a single customer from this orbit queue will be brought to the service area. However, if a primary customer arrives during the seeking process it will occupy the server immediately. It is shown that the joint stationary orbit queue length distribution at service completion epochs is determined by solving a Riemann boundary value problem. Stability condition is investigated, while generalizations of the main model are also discussed. A simple numerical example is obtained and yields insight into the behavior of the system.

26 citations

Journal ArticleDOI
TL;DR: The analytic analysis of tandem retrial queue is implemented under general assumptions about the system parameters and the feasibility of the proposed algorithms and importance of exact account of a nature of the arrival and service processes are illustrated.

26 citations

Journal ArticleDOI
TL;DR: This paper considers an M/G/1 retrial queue with vacations and derives several stochastic comparison properties in the sense of strong Stochastic ordering and convex ordering and provides simple insensitive bounds for the stationary queue length distribution.

26 citations

Journal ArticleDOI
TL;DR: This paper investigates the stationary distribution of the system state, the busy period and the waiting time of a discrete-time queue of Geo/Geo/c type with geometric repeated attempts, and proposes several algorithmic procedures for the efficient computation of the main performance measures.

25 citations

Journal ArticleDOI
TL;DR: In this article, a single-server retrial queue with two types of customers in which the server is subject to vacations along with breakdowns and repairs is studied, and explicit expressions are derived for the expected number of retrial customers of each type.
Abstract: A single-server retrial queue with two types of customers in which the server is subject to vacations along with breakdowns and repairs is studied. Two types of customers arrive to the system in accordance with two different independent Poisson flows. The service times of the two types of customers have two different independent general distributions. We assume that when a service is completed, the server will take vacations after an exponentially distributed reserved time. It is assumed that the server has an exponentially distributed lifetime, a generally distributed vacation time and a generally distributed repair time. There is no waiting space in front of the server, therefore, if the server is found busy, or on vacation, or down, the blocked two types of customers form two sources of repeated customers. Explicit expressions are derived for the expected number of retrial customers of each type. Additionally, by assuming both types of customers face linear costs for waiting and retrial, we discuss and compare the optimal and equilibrium retrial rates regarding the situations in which the customers are cooperative or noncooperative, respectively.

25 citations


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