Fluid Flow Models and Queues—A Connection by Stochastic Coupling

Ahn, Soohan; Ramaswami, V.

doi:10.1081/stm-120023564

Cited by 84 publications

(76 citation statements)

References 18 publications

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“…[14], [8] and [9] respectively exhibit and exploit the similarity between stationary fluid queues in a finite Markovian environment and quasi-birthand-death processes. In [1], a direct connection by stochastic coupling is established between fluid queues and quasi-birth-and-death processes.…”

Section: Introductionmentioning

confidence: 99%

Maximum Level and Hitting Probabilities in Stochastic Fluid Flows Using Matrix Differential Riccati Equations

Séricola

Remiche

2009

Methodol Comput Appl Probab

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International audienceIn this work, we expose a clear methodology to analyze maximum level and hitting probabilities in a Markov driven fluid queue for various initial condition scenarios and in both cases of infinite and finite buffers. Step by step we build up our argument that finally leads to matrix differential Riccati equations for which there exists a unique solution. The power of the methodology resides in the simple probabilistic argument used that permits to obtain analytic solutions of these differential equations. We illustrate our results by a comprehensive fluid model that we exactly solve

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Section: Introductionmentioning

confidence: 99%

Maximum Level and Hitting Probabilities in Stochastic Fluid Flows Using Matrix Differential Riccati Equations

Séricola

Remiche

2009

Methodol Comput Appl Probab

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“…We invite to refer to the specifications for further clarification about the QoS model taken into account. Each network node must provide a service that matches, with some error bounds, the fluid model ( [24,25]) through the token bucket scheme with paramters (b, r, p), respectively the bucket size, the token rate and the peak rate. The QoS request includes a maximum end-to-end delay bound, d req , that shall be guaranteed between the application terminals.…”

Section: End-to-end Behaviourmentioning

confidence: 99%

A Proposal for End-to-End QoS Provisioning in Software-Defined Networks

Lucrezia¹,

Marchetto²,

Risso³

et al. 2017

IJECE

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This paper describes a framework application for the control plane of a network infrastructure; the objective is to feature end-user applications with the capability of requesting at any time a customised end-to-end Quality-of-Service profile in the context of dynamic Service-Level-Agreements. Our solution targets current and future real-time applications that require tight QoS parameters, such as a guaranteed end-to-end delay bound. These applications include, but are not limited to, health-care, mobility, education, manufacturing, smart grids, gaming and much more. We discuss the issues related to the previous Integrated Service and the reason why the RSVP protocol for guaranteed QoS did not take off. Then we present a new signaling and resource reservation framework based on the cutting-edge network controller ONOS. Moreover, the presented system foresees the need of considering the edges of the network, where terminal applications are connected to, to be piloted by distinct logically centralised controllers. We discuss a possible inter-domain communication mechanism to achieve the end-to-end QoS guarantee.Copyright c 201x Institute of Advanced Engineering and Science.All rights reserved.Corresponding Author: Name: Francesco Lucrezia Affiliation: Polytechnic of Turin, Italy Address. Corso Duca degli Abruzzi, 24, 10129 Torino, Italy Email: francesco.lucrezia@polito.it INTRODUCTIONInternet service providers (ISPs) are striving to innovate their network infrastructures at the pace content providers do with their services. Digital contents are consumed by smart phones and sophisticated terminal stations that continuously evolve together with the applications they host. Interestingly enough, the evolution of the OverThe-Top (OTT) services is mainly happening without the aid of network service providers, within the best-effort data traffic channel in the access networks. Recently, a new plethora of applications requiring a RTT delay of around 1ms have been grouped under the hat of tactile-internet applications: a tactile sensor reads information and a connected system reacts with actuators seen by a human within 1 ms [1]. Although we are still far from achieving end-to-end RTT of around 1ms with wireless communications, ISPs need to be ready to re-architect their software control-plane in order to fully exploit the enormous potentials offered by their infrastructures. The goal of this paper is to present the design and a prototype implementation of a control-plane network application for provisioning dynamic end-to-end QoS profiles to end-user applications. The current adoption of distributed control algorithms forces the use of the same signaling protocol (e.g. RSVP, BGP-LS) in all the data-path nodes, not taking into account the resistances inevitably present between device vendors and between administrative domains. For this reason the Service-Level-Agreements (SLAs) between a service provider and its customers or between providers are still mainly static. Moreover, the experience has shown that the scal...

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“…In the case of stationary analysis, the equations that describe a fluid model are ordinary differential equations (ODEs), and there is no initial condition. Indeed this problem has been solved for first order models by the analysis of first passage time probabilities, see for instance [23,11,2,8,7,12] and the references therein. The key of these solutions lies in the matrix characterization of the distribution of the phase visited at the end of a busy period of the fluid queue.…”

Section: Introductionmentioning

confidence: 99%

“…In [2] a direct connection by stochastic coupling is established between fluid queues and quasi birth and death processes.…”

Section: Introductionmentioning

confidence: 99%

Second order fluid models with general boundary behaviour

et al. 2007

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A crucial property of second order fluid models is the behaviour of the fluid level at the boundaries. Two cases have been considered: the reflecting and the absorbing boundary. This paper presents an approach for the stationary analysis of second order fluid models with any combination of boundary behaviours. The proposed approach is based on the solution of a linear system whose coefficients are obtained from a matrix exponent. A practical example demonstrates the suitability of the technique in performance modeling. AbstractA crucial property of second order fluid models is the behaviour of the fluid level at the boundaries. Two cases have been considered: the reflecting and the absorbing boundary. This paper presents an approach for the stationary analysis of second order fluid models with any combination of boundary behaviours. The proposed approach is based on the solution of a linear system whose coefficients are obtained from a matrix exponent. A practical example demonstrates the suitability of the technique in performance modeling.

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Fluid Flow Models and Queues—A Connection by Stochastic Coupling

Cited by 84 publications

References 18 publications

Maximum Level and Hitting Probabilities in Stochastic Fluid Flows Using Matrix Differential Riccati Equations

Maximum Level and Hitting Probabilities in Stochastic Fluid Flows Using Matrix Differential Riccati Equations

A Proposal for End-to-End QoS Provisioning in Software-Defined Networks

Second order fluid models with general boundary behaviour

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