A two-level traffic shaper for an on–off source

Adan, I.J.B.F.; Resing, Jacques

doi:10.1016/s0166-5316(00)00020-1

Cited by 14 publications

(9 citation statements)

References 11 publications

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“…More importantly, the work here sets the stage for transient results in Ref. [2] which are not obtainable by the approach of [1] base on long run average rewards only.…”

Section: Distributional Couplingmentioning

confidence: 98%

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Fluid Flow Models and Queues—A Connection by Stochastic Coupling

Ahn

Ramaswami

2003

Stochastic Models

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We establish in a direct manner that the steady state distribution of Markovian fluid flow models can be obtained from a quasi birth and death queue. This is accomplished through the construction of the processes on a common probability space and the demonstration of a distributional coupling relation between them. The results here provide an interpretation for the quasi-birth-and-death processes in the matrix-geometric approach of Ramaswami and subsequent results based on them obtained by Soares and Latouche.

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“…More importantly, the work here sets the stage for transient results in Ref. [2] which are not obtainable by the approach of [1] base on long run average rewards only.…”

Section: Distributional Couplingmentioning

confidence: 98%

“…Such a procedure has been considered by Adan and Resing in Ref. [1] in an operational manner; we thank Adan for bringing [1] to our attention. Our work here and in Ref.…”

Section: Distributional Couplingmentioning

confidence: 99%

Fluid Flow Models and Queues—A Connection by Stochastic Coupling

Ahn

Ramaswami

2003

Stochastic Models

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“…The fundamental idea of approximating a continuous variable using a number of discrete states and inferring a continuous distribution from the probability distribution of being in the states using the Erlang distribution is not new. This approach has for example been taken in [1]. Indeed, finding a desired distribution by summing over a set of Erlang distributions is a fundamental tool in stochastic modelling and can e.g.…”

Section: Introductionmentioning

confidence: 99%

First in Line Waiting Times as a Tool for Analysing Queueing Systems

Koole

Nielsen

2012

Operations Research

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We introduce a new approach to modelling queueing systems where the priority or the routing of customers depends on the time the first customer has waited in the queue. This past waiting time of the first customer in line, W FIL , is used as the primary variable for our approach. A Markov chain is used for modelling the system where the states represent both the number of free servers and a discrete approximation to W FIL. This approach allows us to obtain waiting time distributions for complex systems, such as the N-design routing scheme widely used in e.g. call centers and systems with dynamic priorities.

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“…Recently, Ahn and Ramaswami [2,3] provided an analysis based on matrix-geometric methods [14,15] in which a sequence of matrix-geometric queues are constructed as approximations to the fluid flow and then stochastic process limit theorems are used to obtain the (exact) results for the fluid model from those on the matrix-geometric queues. The approach of Ahn and Ramaswami was built on an earlier work of Ramaswami [17] which is the first systematic approach to fluid flows based on matrix-geometric methods, as well as on a stochastic discretization introduced by Adan and Resing [1] . Unfortunately, none of these approaches is elementary, particularly for classroom use, and our main purpose here is to provide an elementary exposition.…”

Section: Introductionmentioning

confidence: 99%