Stability of a Subcritical Fluid Model for Fair Bandwidth Sharing with General File Size Distributions

References

• Bonald T, Massoulié L (2001) Impact of fairness on Internet performance. SIGMETRICS Performance Evaluation Rev. 29(1):82–91.Google Scholar
• Borst S, Egorova R, Zwart B (2014) Fluid limits for bandwidth-sharing networks in overload. Math. Oper. Res. 39(2):533–560.Google Scholar
• Bramson M (2008) Stability of queueing networks. Probab. Surveys 5:169–345.Google Scholar
• Bramson M (2010) Network stability under max–min fair bandwidth sharing. Ann. Appl. Probab. 20(3):1126–1176.Google Scholar
• Chiang M, Shah D, Tang A (2006) Stochastic stability under network utility maximization: General file size distribution. Proc. 44th Allerton Conf. Comm. Control Comput., vol. 5 (IEEE, Piscataway, NJ), 49–77.Google Scholar
• Dai JG (1995) On positive Harris recurrence of multiclass queueing networks: A unified approach via fluid limit models. Ann. Appl. Probab. 5(1):49–77.Google Scholar
• De Veciana G, Lee TJ, Konstantopoulos T (2001) Stability and performance analysis of networks supporting elastic services. IEEE/ACM Trans. Networks 9(1):2–14.Google Scholar
• Gromoll HC, Williams RJ (2008) Fluid Model for a Data Network with α-Fair Bandwidth Sharing and General Document Size Distributions: Two Examples of Stability, vol. 4 (Institute of Mathematical Statistics, Beachwood, OH), 253–265.Google Scholar
• Gromoll HC, Williams RJ (2009) Fluid limits for networks with bandwidth sharing and general document size distributions. Ann. Appl. Probab. 19(1):243–280.Google Scholar
• Gromoll HC, Puha AL, Williams RJ (2002) The fluid limit of a heavily loaded processor sharing queue. Ann. Appl. Probab. 12(3):797–859.Google Scholar
• Kelly FP, Williams RJ (2004) Fluid model for a network operating under a fair bandwidth-sharing policy. Ann. Appl. Probab. 14(3):1055–1083.Google Scholar
• Lee NH (2008) A sufficient condition for stochastic stability of an internet congestion control model in terms of fluid model stability. PhD thesis, Department of Mathematics, University of California, San Diego, San Diego.Google Scholar
• Massoulié L (2007) Structural properties of proportional fairness: Stability and insensitivity. Ann. Appl. Probab. 17(3):809–839.Google Scholar
• Massoulié L, Roberts J (2000) Bandwidth sharing and admission control for elastic traffic. Telecomm. Systems 15(1):185–201.Google Scholar
• Mo J, Walrand J (2000) Fair end-to-end window-based congestion control. IEEE/ACM Trans. Networks 8(5):556–567.Google Scholar
• Paganini F, Tang A, Ferragut A, Andrew LLH (2012) Network stability under alpha fair bandwidth allocation with general file size distribution. IEEE Trans. Automatic Control 57(3):579–591.Google Scholar
• Puha AL, Williams RJ (2016) Asymptotic behavior of a critical fluid model for a processor sharing queue via relative entropy. Stochastic Systems 6(2):251–300.Link, Google Scholar
• Ye HQ, Ou J, Yuan XM (2005) Stability of data networks: Stationary and bursty models. Oper. Res. 53(1):107–125.Link, Google Scholar