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Sojourn time asymptotics in a parking lot network

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  • Regina Egorova
  • Bert Zwart

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. Copyright Springer-Verlag 2011

Suggested Citation

  • Regina Egorova & Bert Zwart, 2011. "Sojourn time asymptotics in a parking lot network," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(2), pages 163-190, October.
    • Handle: RePEc:spr:mathme:v:74:y:2011:i:2:p:163-190
    DOI: 10.1007/s00186-011-0351-8
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    Cited by:

    1. Sem Borst & Regina Egorova & Bert Zwart, 2014. "Fluid Limits for Bandwidth-Sharing Networks in Overload," Mathematics of Operations Research, INFORMS, vol. 39(2), pages 533-560, May.

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