Law of large numbers for the many-server earliest-deadline-first queue

RAMI ATAR; Anup Biswas; Haya Kaspi

doi:10.1016/j.spa.2017.09.009

Law of large numbers for the many-server earliest-deadline-first queue

RAMI ATAR, Anup Biswas, Haya Kaspi

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

A many-server queue operating under the earliest deadline first discipline, where the distributions of service time and deadline are generic, is studied at the law of large numbers scale. Fluid model equations, formulated in terms of the many-server transport equation and the recently introduced measure-valued Skorohod map, are proposed as a means of characterizing the limit. The main results are the uniqueness of solutions to these equations, and the law of large numbers scale convergence to the solutions.

Original language	English
Pages (from-to)	2270-2296
Number of pages	27
Journal	Stochastic Processes and their Applications
Volume	128
Issue number	7
DOIs	https://doi.org/10.1016/j.spa.2017.09.009
State	Published - Jul 2018

Keywords

Earliest-deadline-first
Fluid limits
Least-patient-first
Many-server queues
Many-server transport equation
Measure-valued Skorohod map
Measure-valued processes

All Science Journal Classification (ASJC) codes

Statistics and Probability
Modelling and Simulation
Applied Mathematics

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10.1016/j.spa.2017.09.009

Cite this

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title = "Law of large numbers for the many-server earliest-deadline-first queue",

abstract = "A many-server queue operating under the earliest deadline first discipline, where the distributions of service time and deadline are generic, is studied at the law of large numbers scale. Fluid model equations, formulated in terms of the many-server transport equation and the recently introduced measure-valued Skorohod map, are proposed as a means of characterizing the limit. The main results are the uniqueness of solutions to these equations, and the law of large numbers scale convergence to the solutions.",

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author = "RAMI ATAR and Anup Biswas and Haya Kaspi",

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year = "2018",

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AU - Biswas, Anup

AU - Kaspi, Haya

PY - 2018/7

Y1 - 2018/7

N2 - A many-server queue operating under the earliest deadline first discipline, where the distributions of service time and deadline are generic, is studied at the law of large numbers scale. Fluid model equations, formulated in terms of the many-server transport equation and the recently introduced measure-valued Skorohod map, are proposed as a means of characterizing the limit. The main results are the uniqueness of solutions to these equations, and the law of large numbers scale convergence to the solutions.

AB - A many-server queue operating under the earliest deadline first discipline, where the distributions of service time and deadline are generic, is studied at the law of large numbers scale. Fluid model equations, formulated in terms of the many-server transport equation and the recently introduced measure-valued Skorohod map, are proposed as a means of characterizing the limit. The main results are the uniqueness of solutions to these equations, and the law of large numbers scale convergence to the solutions.

KW - Earliest-deadline-first

KW - Fluid limits

KW - Least-patient-first

KW - Many-server queues

KW - Many-server transport equation

KW - Measure-valued Skorohod map

KW - Measure-valued processes

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U2 - 10.1016/j.spa.2017.09.009

DO - 10.1016/j.spa.2017.09.009

M3 - مقالة

SN - 0304-4149

VL - 128

SP - 2270

EP - 2296

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 7

ER -

Law of large numbers for the many-server earliest-deadline-first queue

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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