A many-server functional strong law for a non-stationary loss model

Prakash Chakraborty; Harsha Honnappa

doi:10.1016/j.orl.2021.03.004

A many-server functional strong law for a non-stationary loss model

Prakash Chakraborty, Harsha Honnappa

Marcus Department of Industrial and Manufacturing Engineering

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

1 Scopus citations

Abstract

The purpose of this note is to show that it is possible to establish a many-server functional strong law of large numbers (FSLLN) for the fraction of occupied servers (i.e., the scaled number-in-system) without explicitly tracking through a measure valued process either the age or the residual service times of the jobs in a non-Markovian, non-stationary loss model. This considerable analytical simplification is achieved by exploiting a semimartingale representation. The fluid limit is shown to be the unique solution of a Volterra integral equation.

Original language	English (US)
Pages (from-to)	338-344
Number of pages	7
Journal	Operations Research Letters
Volume	49
Issue number	3
DOIs	https://doi.org/10.1016/j.orl.2021.03.004
State	Published - May 2021

All Science Journal Classification (ASJC) codes

Software
Management Science and Operations Research
Industrial and Manufacturing Engineering
Applied Mathematics

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10.1016/j.orl.2021.03.004

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AB - The purpose of this note is to show that it is possible to establish a many-server functional strong law of large numbers (FSLLN) for the fraction of occupied servers (i.e., the scaled number-in-system) without explicitly tracking through a measure valued process either the age or the residual service times of the jobs in a non-Markovian, non-stationary loss model. This considerable analytical simplification is achieved by exploiting a semimartingale representation. The fluid limit is shown to be the unique solution of a Volterra integral equation.

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A many-server functional strong law for a non-stationary loss model

Abstract

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