Dynamic Equilibria in Fluid Queuing Networks

2014/01/27 by Roberto Cominetti, Cominetti, Roberto, José R. Correa +3
Mathematics · #FOS: Mathematics #Optimization and Control (math.OC) #math.OC

paper · pdf · doi:10.48550/arxiv.1401.6914

arxiv created 2014/01/27 · arxiv updated 2014/01/28

Abstract

This paper continues the study of equilibria for flows over time in the fluid queueing model recently considered by Koch and Skutella [10]. We provide a constructive proof for the existence and uniqueness of equilibria in the case of a single origin-destination with piecewise constant inflow rates, through a detailed analysis of the static flows obtained as derivatives of a dynamic equilibrium. We also give a nonconstructive existence proof of equilibria when the inflow rates belong to L^p including the extension to multiple origin-destinations.

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