Sojourn time asymptotics in a parking lot network |
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Authors: | Regina Egorova " target="_blank">Bert Zwart |
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Institution: | (1) CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands;(2) Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands;(3) Stewart School of Industrial and Systems Engineering, Georgia University of Technology, 765 Ferst Drive, Atlanta, GA 30332, USA |
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Abstract: | For a two-class two-node bandwidth sharing network called parking lot network we investigate the tail behavior of the queue
length and sojourn time under light-tailed assumptions. These results extend previous results in the literature obtained for
a single-node network. Explicit conditions are given that indicate whether congestion at the second node influences the large
deviations behavior or not. To overcome the complexities that arise when moving away from the single node case, we rely on
recent results on overloaded bandwidth sharing networks obtained by Borst et al. (2009), and a comparison with the modified
proportional fairness discipline, as introduced by Massoulié (Ann Appl Probab 17: 809–839, 2007). Specifically, our results include upper bounds for the distribution of the number of flows in the network, finiteness of
the moment generating function of the workload, and large-deviations asymptotics for the sojourn time assuming flow size distributions
having a bounded hazard rate. |
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Keywords: | |
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