The analysis of unreliable M[X]/G/1 queuing system with loss, vacation and two delays of verification

Saggou, Hafida; Sadeg, Ines; Ourbih-Tari, Megdouda; Bourennane, El-Bay

doi:10.1080/03610918.2017.1414245

Cited by 4 publications

(1 citation statement)

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“…( 2018 ), Choudhury and Deka ( 2018 ), Saggou et al. ( 2019 ), Jain and Kaur ( 2020 ). To get a more comprehensive summary of the recent research work on the topic of the unreliable queue, interested readers may refer to the review paper done by Jain et al.…”

Section: Introductionmentioning

confidence: 99%

Analysis of a renewal batch arrival queue with a fault-tolerant server using shift operator method

Tang

2021

Oper Res Int J

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Motivated by the fault tolerance for manufacturing, we investigate a renewal input bulk arrival queue with a fault-tolerant server, in which the server can keep working with a low service rate even if the partial failure occurs. Only when there are no customers in the system, the partial failure can be removed. To explore the performance measures of the queue, a more generic and simpler algorithm based on the right shift operator method for solving difference equations is employed to obtain the queue-length distributions at different time epochs. The significant feature of this algorithm lies in that it does not require the derivation of the transition probability matrix for the corresponding embedded Markov chain. Furthermore, we can resort to the queue-length distribution at the pre-arrival epoch to quickly get the expected sojourn time for an arbitrary customer. Finally, with the help of Pad approximation, several representative numerical examples are illustrated in tables and graphs, under which we show how to verify the correctness of our theoretical results through Little’s law.

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