Introduction to the Theory and Application of the Laplace Transformation

Doetsch, Gustav; Debnath, Lokenath

doi:10.1109/tsmc.1977.4309792

Cited by 153 publications

(271 citation statements)

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“…As we will see, depending on whether the Lévy process has light tails or heavy tails, we need to apply two different methods to derive the asymptotics: for the light-tailed case specific techniques are available (cf. the 'Heaviside approach' in [1], relying on, e.g., [20]), which are intrinsically different from the Tauberian techniques to be used in the heavy-tailed case, see e.g. [11].…”

Section: Asymptotics Of the Downstream Queuementioning

confidence: 99%

Asymptotic analysis of Lévy-driven tandem queues

Lieshout

Mandjes

2008

Queueing Syst

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We analyze tail asymptotics of a two-node tandem queue with spectrallypositive Lévy input. A first focus lies in the tail probabilities of the type, for α ∈ (0, 1) and x large, and Q i denoting the steadystate workload in the ith queue. In case of light-tailed input, our analysis heavily uses the joint Laplace transform of the stationary buffer contents of the first and second queue; the logarithmic asymptotics can be expressed as the solution to a convex programming problem. In case of heavy-tailed input we rely on sample-path methods to derive the exact asymptotics. Then we specialize in the tail asymptotics of the downstream queue, again in case of both light-tailed and heavy-tailed Lévy inputs. It is also indicated how the results can be extended to tandem queues with more than two nodes.

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Section: Asymptotics Of the Downstream Queuementioning

confidence: 99%

Asymptotic analysis of Lévy-driven tandem queues

Lieshout

Mandjes

2008

Queueing Syst

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“…Later in our article we apply it for the specific case that s = 1/2; recall that (−1/2) = −2 √ . A formal justification of the above relation can be found in Doetsch [2] (Theorem 37.1). Following Miyazawa and Rolski [12] , we consider the following specific form.…”

Section: Tauberian-type Resultsmentioning

confidence: 93%

“…For this we first recall the concept of the -contour with an half-angle of opening /2 < ≤ , as depicted in Ref. [2] (Fig. 30, p. 240); also, ( ) is the region between the contour and the line (z) = 0.…”

Section: Tauberian-type Resultsmentioning

confidence: 99%

Quasi-Stationary Workload in a Lévy-Driven Storage System

2012

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Quasi-stationary workload in a Lévy-driven storage system Mandjes, M.R.H.; Palmowski, Z.; Rolski, T. General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. PLEASE SCROLL DOWN FOR ARTICLETaylor & Francis makes every effort to ensure the accuracy of all the information (the "Content") contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http:// www.tandfonline.com/page/terms-and-conditions

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“…The cumulant transform is then the Laplace transform of the probability density function p Zn (z), and the density function itself may be computed as an inverse Laplace transform [6], [7], namely…”

Section: Saddlepoint Approximation For the Errormentioning

confidence: 99%