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FLUID LIMIT OF A PS-QUEUE WITH MULTISTAGE SERVICE

Published online by Cambridge University Press:  20 December 2017

Maria Frolkova  and
Bert Zwart
Maria Frolkova
Affiliation:
Department of Mathematics at Vrije Universiteit Amsterdam, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands E-mail: m.frolkova@vu.nl
Bert Zwart
Affiliation:
Centrum Wiskunde en Informatica, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands and Eindhoven University of Technology, Eindhoven, The Netherlands E-mail: Bert.Zwart@cwi.nl
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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.

Keywords

fluid limitsfreelance job websitesLyapunov functionsprocessor-sharingrouting
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 33 , Issue 1 , January 2019 , pp. 1 - 27
Copyright
Copyright © Cambridge University Press 2017 

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