A single-server G-queue in discrete-time with geometrical arrival and service process

Atencia, Iván; Moreno, Pilar

doi:10.1016/j.peva.2004.07.019

Cited by 41 publications

(23 citation statements)

References 26 publications

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“…Intuitively, the introduction of the balking assumption makes the system less congested than if it was not present, thus the existence of balking provides a mechanism to control an excessive congestion at the system. There exist another queueing models where the customers can leave the system before completing his service, for instance, queues with negative customers [4,5], disasters [4] or impatient customers [8]. Unlike what happens in our model, in the case of negative arrivals or disasters, the abandonments are generated by external causes.…”

Section: Introductionmentioning

confidence: 99%

A discrete time single-server queue with balking: economic applications

Lozano

Moreno

2008

Applied Economics

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This article studies a discrete time single-server queue with finite and infinite buffer where the users have the option to leave the queue upon arrival (balking). We consider two variants of the model in accordance with the balking policies. Firstly, all the arriving customers balk with a constant probability. Secondly, arriving customers increase their balking probabilities as more customers join the system. Specifically, we find the ergodicity condition and closed-form expressions for the stationary distribution of the system size, of the waiting/spending time in the FCFS system and of the unfinished work. The mathematical model is applied in order to resolve several real-life problems in the economic field; in this sense, practical applications in the secondary and tertiary sector are shown. We also develop a cost model to determine the buffer capacity that minimizes certain cost function and give some numerical examples.

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Section: Introductionmentioning

confidence: 99%

A discrete time single-server queue with balking: economic applications

Lozano

Moreno

2008

Applied Economics

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“…Recently, the analysis of G-queues has been extended to the discrete-time situation in view of their applicability in the study of practical problems arise from telecommunication networks and computer networks [9,11]. In [9], the authors consider a discrete-time Geo/Geo/1 queue with negative customers and disasters, in which the RCH (removal of customers from the head of the queue) killing discipline, RCE (removal of customers from the end of the queue) killing discipline and disaster discipline are studied.…”

Section: Introductionmentioning

confidence: 99%

“…In [9], the authors consider a discrete-time Geo/Geo/1 queue with negative customers and disasters, in which the RCH (removal of customers from the head of the queue) killing discipline, RCE (removal of customers from the end of the queue) killing discipline and disaster discipline are studied. In a subsequent paper [11], the same authors analyze a discrete-time single-server queue with geometrical arrivals of both positive and negative customers. The RCE-inimmune servicing killing policy and RCE-immune servicing killing policy are investigated regarding a customer in service can and cannot be killed by a negative customer.…”

Section: Introductionmentioning

confidence: 99%

A single-server discrete-time retrial G-queue with server breakdowns and repairs

Wang

Zhang

2009

Acta Math. Appl. Sin. Engl. Ser.

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This paper concerns a discrete-time Geo/Geo/1 retrial queue with both positive and negative customers where the server is subject to breakdowns and repairs due to negative arrivals. The arrival of a negative customer causes one positive customer to be killed if any is present, and simultaneously breaks the server down. The server is sent to repair immediately and after repair it is as good as new. The negative customer also causes the server breakdown if the server is found idle, but has no effect on the system if the server is under repair. We analyze the Markov chain underlying the queueing system and obtain its ergodicity condition. The generating function of the number of customers in the orbit and in the system are also obtained, along with the marginal distributions of the orbit size when the server is idle, busy or down. Finally, we present some numerical examples to illustrate the influence of the parameters on several performance characteristics of the system.

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“…Most of the existing papers (see e.g. Artalejo et al 2005;Atencia and Moreno 2005;Wang and Zhao 2007 and their references) investigate single server models of Geo/G/1-type and mainly follows the methodology introduced in Yang and Li (1995). As an exception, we mention a few recent papers dealing with the multiserver case (Artalejo and Lopez-Herrero 2007b;Artalejo et al 2008) and the use of matrix-analytic methods (Alfa 2006).…”

Section: Introductionmentioning

confidence: 99%

Performance Analysis of a Block-Structured Discrete-Time Retrial Queue with State-Dependent Arrivals

Artalejo

2009

Discrete Event Dyn Syst

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In this paper, we introduce a new discrete block state-dependent arrival (D-BSDA) distribution which provides fresh insights leading to a successful generalization of the discrete-time Markovian arrival process (D-MAP). The D-BSDA distribution is related to structured Markov chains and the method of stages. The consideration of this new discrete-time state-dependent block description gives one the ability of construct new stochastic models. The retrial queue analyzed in this paper gives an example of application of the D-BSDA distribution to construct more general and sophisticated models. We assume that the primary arrivals and the retrials follow the D-BSDA description and the service times are of discrete phasetype (PH). We study the underlying level dependent Markov chain of M/G/1-type at the epochs immediately after the slot boundaries. To this end, we employ the ULtype RG-factorization which provides an expression for the stationary probabilities. We also perform an analysis of waiting times. Numerical experiments are presented to study the system performance.

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A single-server G-queue in discrete-time with geometrical arrival and service process

Cited by 41 publications

References 26 publications

A discrete time single-server queue with balking: economic applications

A discrete time single-server queue with balking: economic applications

A single-server discrete-time retrial G-queue with server breakdowns and repairs

Performance Analysis of a Block-Structured Discrete-Time Retrial Queue with State-Dependent Arrivals

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