Reliability modelling using G-queues

Harrison, Peter G.; Patel, Niki; Pitel, Edwige

doi:10.1016/s0377-2217(99)00478-6

Cited by 42 publications

(19 citation statements)

References 11 publications

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“…For instance, in [25], they are used to model a multimedia server system in which customers require "documents" that are transmitted on the shared media. Several other applications of G-networks have been presented in the literature by various authors (see [17,2,29,27]). Following on from the seminal works of [13,14], a number of extensions have been proposed.…”

Section: Introductionmentioning

confidence: 99%

Analysis of stochastic Petri nets with signals

Marin¹,

Balsamo²,

Harrison³

2012

Performance Evaluation

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Section: Introductionmentioning

confidence: 99%

Analysis of stochastic Petri nets with signals

Marin¹,

Balsamo²,

Harrison³

2012

Performance Evaluation

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“…Another example, in a manufacturing system where a negative arrival represents a cancellation of a job. These lead to many applications in the modelling of manufacturing systems, telecommunication systems and many others such as reliability models [8]. Theoretical results including the stability analysis has been discussed by Gelenbe et al [4,5,6].…”

Section: Introductionmentioning

confidence: 99%

Fast solvers for queueing systems with negative customers

Wen

Ching

2006

Proceedings of the 1st International Conference on Performance Evaluation Methodolgies and Tools - Valuetools '06

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In this paper, we are interested in solving Markovian queueing systems having Poisson batch arrivals, exponential servers and negative customers. Preconditioned conjugate gradient method is applied to solving the steady-state probability distribution of queueing system. Preconditioner were constructed by exploiting near-Toeplitz structure of the generator matrix and the Gohberg-Semumcul formula. We proved the preconditioned system has its spectrum clustered around one. Numerical results are given to demonstrate the efficient of our method.

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“…The pioneering work on discrete-time considering negative arrivals without retrials was done by Atencia and Moreno (2004;2005), who considered several killing strategies for negative customers. For a survey on this topics we refer to Gelenbe and Labed (1998) or Artalejo (2000), for applications in engineering to Chao et al (1999), and for application in communication networks and packet transmission systems to Harrison et al (2000), Park et al (2009), or Piórkowski andWerewka (2010).…”

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confidence: 99%

A discrete-time queueing system with changes in the vacation times

Atencia

2016

International Journal of Applied Mathematics and Computer Science

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This paper considers a discrete-time queueing system in which an arriving customer can decide to follow a last come first served (LCFS) service discipline or to become a negative customer that eliminates the one at service, if any. After service completion, the server can opt for a vacation time or it can remain on duty. Changes in the vacation times as well as their associated distribution are thoroughly studied. An extensive analysis of the system is carried out and, using a probability generating function approach, steady-state performance measures such as the first moments of the busy period of the queue content and of customers delay are obtained. Finally, some numerical examples to show the influence of the parameters on several performance characteristics are given.

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Reliability modelling using G-queues

Cited by 42 publications

References 11 publications

Analysis of stochastic Petri nets with signals

Analysis of stochastic Petri nets with signals

Fast solvers for queueing systems with negative customers

A discrete-time queueing system with changes in the vacation times

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