The discrete-time Geo/Geo/1 queue with negative customers and disasters

Atencia, Iván; Moreno, Pilar

doi:10.1016/s0305-0548(03)00107-2

Cited by 76 publications

(32 citation statements)

References 10 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.…”

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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“…Nevertheless these studies only focused on the continuous time cases. As far as we know, Atencia and Moreno (2004) for the first time extend this topic to the discrete-time systems. Based on our best knowledge, the existing literature on discrete-time finite source queues does not cover the contribution of promoting disasters in the system.…”

Section: Introductionmentioning

confidence: 99%