Fluid Limit of a PS-queue with Multistage Service

Maria Remerova; Bert Zwart

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arXiv · 1604.05464

Fluid Limit of a PS-queue with Multistage Service

Maria Remerova·Bert Zwart

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Abstract

The PS-model treated in this paper is motivated by freelance job websites where multiple freelancers compete for a single job. In the context of such websites, multistage service of a job means collection of applications from multiple freelancers. Under Markovian stochastic assumptions, we develop fluid limit approximations for the PS-model in overload. Based on this approximation, we estimate what proportion of freelancers get the jobs they apply for. In addition, the PS-model studied here is an instant of PS with routing and impatience, for which no Lyapunov function is known, and we suggest some partial solutions.

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Maria Remerova, Bert Zwart. 2016-04-19. Fluid Limit of a PS-queue with Multistage Service. https://arxiv.org/abs/1604.05464

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