FLUID LIMIT OF A PS-QUEUE WITH MULTISTAGE SERVICE

Maria Frolkova; Bert Zwart

doi:10.1017/S0269964817000456

FLUID LIMIT OF A PS-QUEUE WITH MULTISTAGE SERVICE

Maria Frolkova, Bert Zwart

Mathematics

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Abstract

We consider a variation of the processor-sharing (PS) queue, inspired by freelance job websites where multiple freelancers compete for a single job. We develop fluid limit approximations for the overloaded PS-model with multiple (possibly infinitely many) service stages. Based on this approximation, we estimate what proportion of freelancers get the job they apply for. In addition, the PS model studied here is an instance of PS with routing and impatience, for which no Lyapunov function is known, and we suggest some partial solutions.

Original language	English
Pages (from-to)	1-27
Number of pages	27
Journal	Probability in the Engineering and Informational Sciences
Volume	33
Issue number	1
Early online date	20 Dec 2017
DOIs	https://doi.org/10.1017/S0269964817000456
Publication status	Published - Jan 2019

Keywords

fluid limits
freelance job websites
Lyapunov functions
processor-sharing
routing

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1017/S0269964817000456

fluid-limit-of-a-ps-queue-with-multistage-serviceFinal published version, 358 KBLicence: Article 25fa Dutch Copyright Act

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FLUID LIMIT OF A PS-QUEUE WITH MULTISTAGE SERVICE

Abstract

Keywords

UN SDGs

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