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A Skorokhod map on measure valued paths with applications to priority queues Kaspi, Haya
Description
The Skorokhod map on the half-line has proved to be a useful tool for studying processes with non-negativity constraints. In this work we introduce a measure-valued analog of this map that transforms each element ? of a certain class of c`adl`ag paths that take values in the space of signed measures on [0, ?) to a c\'ad\'ag path that takes values in the space of non-negative measures on $[0, \infty)$ in such a way that for each $x>0$, the path $t\to \zeta_t [0, x]$ is transformed via a Skorokhod map on the half-line, and the regulating functions for different $x>0$ are coupled. We establish regularity properties of this map and show that the map provides a convenient tool for studying queueing systems in which tasks are prioritized according to a continuous parameter. One such priority assignment rule is the well known earliest-deadline-first priority rule. We study it both for the single and the many server queueing systems. We show how the map provides a framework within which to form fluid model equations, prove uniqueness of solutions to these equations and establish convergence of scaled state processes to the fluid model. In particular, for these models, we obtain new convergence results in time-inhomogeneous settings, which appear to fall outside the purview of existing approaches and is essential when studying the EDF policy for many servers queues. Based on Joint work with Rami Atar, Anup Biswas and Kavita Ramanan.
Item Metadata
Title |
A Skorokhod map on measure valued paths with applications to priority queues
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2017-10-26T09:49
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Description |
The Skorokhod map on the half-line has proved to be a useful tool
for studying processes with non-negativity constraints. In this work we
introduce a measure-valued analog of this map that transforms each
element ? of a certain class of c`adl`ag paths that take values in the space
of signed measures on [0, ?) to a c\'ad\'ag path that takes values in the
space of non-negative measures on $[0, \infty)$ in such a way that for each
$x>0$, the path $t\to \zeta_t [0, x]$ is transformed via a Skorokhod map on the
half-line, and the regulating functions for different $x>0$ are coupled.
We establish regularity properties of this map and show that the map
provides a convenient tool for studying queueing systems in which tasks
are prioritized according to a continuous parameter. One such priority
assignment rule is the well known earliest-deadline-first priority rule.
We study it both for the single and the many server queueing systems.
We show how the map provides a framework within which to form
fluid model equations, prove uniqueness of solutions to these equations
and establish convergence of scaled state processes to the fluid model.
In particular, for these models, we obtain new convergence results in
time-inhomogeneous settings, which appear to fall outside the purview
of existing approaches and is essential when studying the EDF policy
for many servers queues.
Based on Joint work with Rami Atar, Anup Biswas and Kavita Ramanan.
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Extent |
46 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Technion
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Series | |
Date Available |
2018-04-25
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0365987
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International