A factorization property for BMAP/G/1 vacation queues under variable service speed

Baek, Jung Woo; Lee, Ho Woo; Lee, Se Won; Ahn, Soohan

doi:10.1007/s10479-007-0292-z

Cited by 9 publications

(4 citation statements)

References 23 publications

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“…Remark 3.2 Equation (3.39) shows that the vector LST u * (θ ) of the fluid level at an arbitrary time point is factored into two parts, one of which is the vector LST u * idle (θ ) of the fluid level at an arbitrary idle time point. This factorization is very similar to the factorization of the BMAP/G/1 queue with generalized vacations (Baek et al 2008 andChang et al 2002).…”

Section: Theorem 34mentioning

confidence: 54%

“…More details about vacation queues can be found in Doshi (1986), Heyman (1977), Lee and Srinivasan (1989) and Levy and Yechiali (1975). Studies on the MAP(BMAP)/G/1 queue with a server vacation model can be found in Baek et al (2008), Chang et al (2002), Lee and Baek (2005) and Lee et al (2001).…”

Section: Introductionmentioning

confidence: 99%

“…It is known that the vector Laplace Stieltjes transform (LST) of the queue length and the workload distributions for many of the MAP(BMAP)/G/1 vacation queues is factored into two parts (Baek et al 2008;Chang et al 2002 andLee et al 2001) one of which is the LST of the queue length or the workload at an arbitrary time during the idle period. Readers will see that the vector LST of the fluid level of our system is also factored into a similar form.…”

Section: Introductionmentioning

confidence: 99%

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A MAP-modulated fluid flow model with multiple vacations

Baek

Lee

et al. 2012

Ann Oper Res

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We consider a MAP-modulated fluid flow queueing model with multiple vacations. As soon as the fluid level reaches zero, the server leaves for repeated vacations of random length V until the server finds any fluid in the system. During the vacation period, fluid arrives from outside according to the MAP (Markovian Arrival Process) and the fluid level increases vertically at the arrival instance. We first derive the vector Laplace-Stieltjes transform (LST) of the fluid level at an arbitrary point of time in steady-state and show that the vector LST is decomposed into two parts, one of which the vector LST of the fluid level at an arbitrary point of time during the idle period. Then we present a recursive moments formula and numerical examples.

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Section: Theorem 34mentioning

confidence: 54%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A MAP-modulated fluid flow model with multiple vacations

Baek

Lee

et al. 2012

Ann Oper Res

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“…The model can be reduced to the single (the timer of infinite-duration) or multiple vacation case (zero-length timer duration). In Baek et al (2008Baek et al ( , 2013 queueing models with server vacations are considered, in which the input flow of packets is described by MAP-type process. The M/G/1/N -type finite-buffer model, which is considered in the paper, is also investigated e.g.…”

mentioning

confidence: 99%

Transient workload distribution in the $$M/G/1$$ M / G / 1 finite-buffer queue with single and multiple vacations

Kempa

2015

Ann Oper Res

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A finite-buffer M/G/1-type queueing system with exhaustive service and server vacations is considered. The single and multiple vacation policies are investigated separately. In the former case a single vacation is being initialized every time when the system becomes empty. After the vacation the server waits on standby for packets to start the service process. In the multiple vacation policy the server begins successive single vacation periods until at least one packet is present in the system. For both vacation policies systems of integral equations for the transient virtual waiting time v(t) distributions, conditioned by the numbers of packets present in the system at the start epoch, are found. The representations for the twofold Laplace transforms of the conditional distributions of v(t) are obtained and written in compact forms, convenient in numerical treatment. From these formulae stationary distributions of v(t) and their means can be computed via usual operations on transforms. Some numerical illustrations of theoretical results are attached as well.

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Batch Markovian Arrival Processes (BMAP)

Cordeiro

Kharoufeh

2011

Wiley Encyclopedia of Operations Research and Management Science

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This article describes the batch Markovian arrival process (BMAP), a point process that is characterized by Markov‐modulated batch arrivals of random size. The BMAP is a generalization of many well‐known processes including the Markovian arrival process (MAP), the Poisson process, and the Markov‐modulated Poisson process. It provides a common framework for modeling arrival processes in a variety of applications. We formally define the continuous‐ and discrete‐time BMAP, review a few basic results for each, and show how these processes generalize many common point processes. Additionally, we provide suggestions for further reading on the subject.

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A factorization property for BMAP/G/1 vacation queues under variable service speed

Cited by 9 publications

References 23 publications

A MAP-modulated fluid flow model with multiple vacations

A MAP-modulated fluid flow model with multiple vacations

Transient workload distribution in the $$M/G/1$$ M / G / 1 finite-buffer queue with single and multiple vacations

Batch Markovian Arrival Processes (BMAP)

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