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Limit Theorems for Markovian Bandwidth-Sharing Networks with Rate Constraints

Author

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  • Josh Reed

    (Stern School of Business, New York University, New York, New York 10012)

  • Bert Zwart

    (Centrum Wiskunde & Informatica (CWI), Amsterdam, The Netherlands)

Abstract

Bandwidth-sharing networks provide a natural modeling framework for describing the dynamic flow-level interaction among elastic data transfers in computer and communication systems, and can be used to develop traffic pricing/charging mechanisms. At the same time, such models are exciting from an operations research perspective because their analysis requires techniques from stochastic modeling and optimization.In this paper, we develop a framework to approximate bandwidth-sharing networks under the assumption that the number of users as well as the capacities of the system are large, and the assumption that the traffic that each user is allowed to submit is bounded above by some rate, which is standard in practice. We also assume that customers on each route in the network abandon according to exponential patience times. Under Markovian assumptions, we develop fluid and diffusion approximations, which are quite tractable: for most parameter combinations, the invariant distribution is multivariate normal, with mean and diffusion coefficients that can be computed in polynomial time as a function of the size of the network.

Suggested Citation

  • Josh Reed & Bert Zwart, 2014. "Limit Theorems for Markovian Bandwidth-Sharing Networks with Rate Constraints," Operations Research, INFORMS, vol. 62(6), pages 1453-1466, December.
    • Handle: RePEc:inm:oropre:v:62:y:2014:i:6:p:1453-1466
    DOI: 10.1287/opre.2014.1321
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    References listed on IDEAS

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    1. Maria Remerova & Josh Reed & Bert Zwart, 2014. "Fluid Limits for Bandwidth-Sharing Networks with Rate Constraints," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 746-774, August.
    2. Heng-Qing Ye & David D. Yao, 2010. "Utility-Maximizing Resource Control: Diffusion Limit and Asymptotic Optimality for a Two-Bottleneck Model," Operations Research, INFORMS, vol. 58(3), pages 613-623, June.
    3. 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.
    4. Heng-Qing Ye & David D. Yao, 2008. "Heavy-Traffic Optimality of a Stochastic Network Under Utility-Maximizing Resource Allocation," Operations Research, INFORMS, vol. 56(2), pages 453-470, April.
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    6. Urtzi Ayesta & Michel Mandjes, 2009. "Bandwidth-sharing networks under a diffusion scaling," Annals of Operations Research, Springer, vol. 170(1), pages 41-58, September.
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