Stationary analysis of a fluid queue driven by an <i>M</i> / <i>M</i> / 1 queue with working vacation

Vijayashree, K. V.; Anjuka, A.

doi:10.1080/16843703.2016.1208935

Cited by 9 publications

(5 citation statements)

References 27 publications

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“…Tian et al [4] reviewed the research on working vacation queueing systems. Recently, the survey on the works of queues with working vacation has been reported by [5][6][7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Preemptive Priority Markovian Queue Subject to Server Breakdown with Imperfect Coverage and Working Vacation Interruption

Liu

Hsu

et al. 2023

Computation

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This work considers a preemptive priority queueing system with vacation, where the single server may break down with imperfect coverage. Various combinations of server vacation priority queueing models have been studied by many scholars. A common assumption in these models is that the server will only resume its normal service rate after the vacation is over. However, such speculation is more limited in real-world situations. Hence, in this study, the vacation will be interrupted if a customer waits for service in the system at the moment of completion of service during vacation. The stationary probability distribution is derived by using the probability generating function approach. We also develop varieties of performance measures and provide a simple numerical example to illustrate these measures. Optimization analysis is finally carried out, including cost optimization and tri-object optimization.

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Section: Introductionmentioning

confidence: 99%

Preemptive Priority Markovian Queue Subject to Server Breakdown with Imperfect Coverage and Working Vacation Interruption

Liu

Hsu

et al. 2023

Computation

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“…Using the matrix geometric structure of the Laplace transform, they calculated the steady-state distribution of fluid buffer queue mean. In [20], a fluid model was investigated which was formulated with an M/M/1 queue subjected to working. The authors expressed the buffer content distribution based on a modified Bessel function of the first type, utilizing continuous fraction and generating function approaches.…”

Section: Introductionmentioning

confidence: 99%

“…The authors expressed the buffer content distribution based on a modified Bessel function of the first type, utilizing continuous fraction and generating function approaches. Impatience was also incorporated as a component in this system in reference [20], as discussed in their subsequent work in [21], since they presented a formula for the buffer content distribution based on the modified Bessel function of the first type, derived using the same approaches as presented in [22]. The authors in [23] delved into a fluid model directed by an M/M/1 queue with working vacations and unfavorable customer policies.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Vacation Fluid M/M/1 Queue in Multi-Phase Random Environment

Ammar,

Alharbi,

Zhao

2023

Mathematics

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An M/M/1 fluid queue with various vacations is studied in the context of a multi-phase random environment. When the system is in operation (i = 1, 2, …, n), it behaves according to the M/M/1 fluid queue model. However, in any other situation, the system is on vacation, so this leads it to transition into the vacation phase (i = 0). This transition occurs only when there is no data in the system. If the system returns from a vacation and finds it still empty of jobs, it will initiate a new vacation and continue in this pattern until jobs become available in the system, at which point it resumes working. When the vacation phase ends, the probability of the system transitioning to the operational phase is denoted as qi(i = 1, 2, …, n). Subsequently, we derive the stationary probability and analyze the buffer content in relation to the modified Bessel function of the first kind. We utilize the generating function approach and the Laplace–Stieltjes transform to achieve this, enabling us to accomplish our objectives. We provide numerical results to elucidate the overall behavior of the system under consideration.

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“…In recent years, many researchers investigated on fluid queueing systems subject to catastrophes or vacations. The analysis of fluid queueing system with vacations can be found in Ammar [23], Zhang and Shi [24], Xu et al [25], Mao et al [26], Xu et al [27], Mao et al [28], Vijayashree and Anjuka [29], and related references therein. Moreover, many researcher discussed the behaviour of fluid queueing syetms with catastrophes.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Stationary Fluid Queue Driven by State-Dependent Birth-Death Process Subject to Catastrophes

Ammar¹,

Samanta²,

Kilany³

et al. 2022

Scientia Iranica

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This paper investigates an infinite buffer fluid queueing model driven by a state-dependent birth-death process prone to catastrophes.We use the Laplace-Stieltjes transform and continued fraction approaches to establish precise expression for the joint probability of the content of the buffer and the number of customers in an / /1 MM queueing model. The importance of the proposed system is that, in numerous practical situation, the service facility has defence mechanisms in place to deal with long waits. Under the strain of a significant backlog of work, the servers may improve their service rate. Therefore,considering the state-dependent character of queueing systems is of relevance. For example, congestion control technologies prevent long queues forming in computer and communication systems by adjusting packet transmission speeds based on the length of the queue (of packets) at the source or destination. Theoretical results are supported by numerical illustrations.

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Stationary analysis of a fluid queue driven by an M / M / 1 queue with working vacation

Cited by 9 publications

References 27 publications

Preemptive Priority Markovian Queue Subject to Server Breakdown with Imperfect Coverage and Working Vacation Interruption

Preemptive Priority Markovian Queue Subject to Server Breakdown with Imperfect Coverage and Working Vacation Interruption

Analysis of Vacation Fluid M/M/1 Queue in Multi-Phase Random Environment

Analysis of Stationary Fluid Queue Driven by State-Dependent Birth-Death Process Subject to Catastrophes

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