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Fluid Limit of a PS-queue with Multistage Service

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.

preprint2016arXivOpen access
Maria RemerovaBert Zwart
math.PR
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Open access2 authors1 topic
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Maria RemerovaBert Zwart

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