About: Non-Stationary Queues with Batch Arrivals

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An Entity of Type : schema:ScholarlyArticle, within Data Space : covidontheweb.inria.fr associated with source document(s)

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type	Academic Article research paper schema:ScholarlyArticle
isDefinedBy	Covid-on-the-Web dataset
title	Non-Stationary Queues with Batch Arrivals
Creator	Daw, Andrew Fralix, Brian Pender, Jamol
source	ArXiv
abstract	Motivated by applications that involve setting proper staffing levels for multi-server queueing systems with batch arrivals, we present a thorough study of the queue-length process $/{Q(t); t /geq 0/}$, departure process $/{D(t); t /geq 0/}$, and the workload process $/{W(t); t /geq 0/}$ associated with the M$_{t}^{B_{t}}$/G$_{t}$/$/infty$ queueing system, where arrivals occur in batches, with the batch size distribution varying with time. Notably, we first show that both $Q(t)$ and $D(t)$ are equal in distribution to an infinite sum of independent, scaled Poisson random variables. When the batch size distribution has finite support, this sum becomes finite as well. We then derive the finite-dimensional distributions of both the queue-length process and the departure process, and we use these results to show that these finite-dimensional distributions converge weakly under a certain scaling regime, where the finite-dimensional distributions of the queue-length process converge weakly to a shot-noise process driven by a non-homogeneous Poisson process. Next, we derive an expression for the joint Laplace-Stieltjes transform of $W(t)$, $Q(t)$, and $D(t)$, and we show that these three random variables, under the same scaling regime, converge weakly, where the limit associated with the workload process corresponds to another Poisson-driven shot-noise process.
has issue date	2020-08-03(xsd:dateTime)
has license	arxiv
sha1sum (hex)	f82829db2cd70890b8b882d4bd9ff4f3e4fb4257
resource representing a document's title	Non-Stationary Queues with Batch Arrivals
resource representing a document's body	covid:f82829db2cd70890b8b882d4bd9ff4f3e4fb4257#body_text
is schema:about of	named entity 'shot-noise' named entity 'queueing systems' named entity 'non-homogeneous' named entity 'Poisson process' named entity 'exponentially distributed' »more»

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