Heavy-Traffic Insensitive Bounds for Weighted Proportionally Fair Bandwidth Sharing Policies
References
- [1] (2007) Beyond processor sharing. ACM SIGMETRICS Performance Evaluation Rev. 34(4):36–43.Crossref, Google Scholar
- [2] (2003) Applied Probability and Queues (Springer-Verlag, New York).Google Scholar
- [3] (2001) Performance of multiclass Markovian queueing networks via piecewise linear Lyapunov functions. Ann. Appl. Probabilities 11(4):1384–1428.Crossref, Google Scholar
- [4] (1971) Weak Convergence of Measures: Applications in Probability (Society for Industrial and Applied Mathematics, Philadelphia).Crossref, Google Scholar
- [5] (2001) Impact of fairness on Internet performance. Proc. ACM SIGMETRICS Internat. Conf. Measurement and Modeling of Comput. Systems (ACM, New York), 82–91.Google Scholar
- [6] (2003) Insensitive bandwidth sharing in data networks. Queueing Systems 44(1):69–100.Crossref, Google Scholar
- [7] (1998) State space collapse with application to heavy traffic limits for multiclass queueing networks. Queueing Systems 30(1/2):89–148.Crossref, Google Scholar
- [8] (2010) Network stability under max-min fair bandwidth sharing. Adv. Appl. Probabilities 20(3):1126–1176.Google Scholar
- [9] (2001) Stability and performance analysis of networks supporting elastic services. IEEE/ACM Trans. Networks 9(1):2–14.Crossref, Google Scholar
- [10] (2012) Asymptotically tight steady-state queue length bounds implied by drift conditions. Queueing Systems 72(3-4):311–359.Crossref, Google Scholar
- [11] (2020) Stability of a subcritical fluid model for fair bandwidth sharing with general file size distributions. Stochastic Systems 10(3):251–273.Link, Google Scholar
- [12] (2004) Diffusion approximation for a processor sharing queue in heavy traffic. Ann. Appl. Probabilities 14(2):555–611.Crossref, Google Scholar
- [13] (2008) Fluid Model for a Data Network with α-Fair Bandwidth Sharing and General Document Size Distributions: Two Examples of Stability, vol. 4 of Collections (Institute of Mathematical Statistics, Beachwood, OH), 253–265.Google Scholar
- [14] (1982) Hitting-time and occupation-time bounds implied by drift analysis with applications. Adv. Appl. Probabilities 14(3):502–525.Crossref, Google Scholar
- [15] (1987) Multidimensional reflected Brownian motions having exponential stationary distributions. Ann. Probabilities 15(1):115–137.Crossref, Google Scholar
- [16] (2009) State space collapse and diffusion approximation for a network operating under a fair bandwidth sharing policy. Ann. Appl. Probabilities 19(5):1719–1780.Crossref, Google Scholar
- [17] (2012) Markov Chain Models—Rarity and Exponentiality, vol. 28 (Springer Science & Business Media, New York).Google Scholar
- [18] (1997) Charging and rate control for elastic traffic. Eur. Trans. Telecommun. 8(1):33–37.Crossref, Google Scholar
- [19] (2005) On the use of SoS methods for analysis of connection-level stability in the Internet. Proc. Amer. Control Conf., Portland, OR, vol. 4 (IEEE), 2705–2708.Google Scholar
- [20] (2017) On optimal weighted-delay scheduling in input-queued switches. Preprint, submitted April 7 and updated September 27, https://arxiv.org/abs/1704.02302.Google Scholar
- [21] (1969) Optimization by Vector Space Methods (John Wiley & Sons, Hoboken, NJ).Google Scholar
- [22] (2016) Heavy traffic queue length behavior in a switch under the maxweight algorithm. Stochastic Systems 6(1):211–250.Link, Google Scholar
- [23] (2016) Optimal heavy-traffic queue length scaling in an incompletely saturated switch. Proc. ACM SIGMETRICS Internat. Conf. Measurement and Modeling of Comput Systems (ACM), 13–24.Google Scholar
- [24] (2014) Heavy traffic optimal resource allocation algorithms for cloud computing clusters. Performance Evaluation 81:20–39.Crossref, Google Scholar
- [25] (2007) Structural properties of proportional fairness: Stability and insensitivity. Ann. Appl. Probabilities 17(3):809–839.Crossref, Google Scholar
- [26] (2000) Bandwidth sharing and admission control for elastic traffic. Telecomm. Systems 15(1):185–201.Crossref, Google Scholar
- [27] (2000) Fair end-to-end window-based congestion control. IEEE/ACM Trans. Networks 8(5):556–567.Crossref, Google Scholar
- [28] (2012) Network stability under alpha fair bandwidth allocation with general file size distribution. IEEE Trans. Automated Control 57(3):579–591.Crossref, Google Scholar
- [29] (1996) Queue-length distribution for the discriminatory processor-sharing queue. Oper. Res. 44(4):653–657.Link, Google Scholar
- [30] (2014) Qualitative properties of α-fair policies in bandwidth-sharing networks. Ann. Appl. Probabilities 24(1):76–113.Google Scholar
- [31] (1990) Mathematical Control Theory: Deterministic Finite Dimensional Systems (Springer-Verlag, New York).Crossref, Google Scholar
- [32] (2004) Asymptotic regimes and approximations for discriminatory processor sharing. ACM SIGMETRICS Performance Evaluation Rev. 32(2):44–46.Crossref, Google Scholar
- [33] (2014) Insensitivity of proportional fairness in critically loaded bandwidth sharing networks. Preprint, submitted November 18 and updated June 17, https://arxiv.org/abs/1411.4841.Google Scholar
- [34] (2011) Insensitive, maximum stable allocations converge to proportional fairness. Queueing Systems 68(1):51.Crossref, Google Scholar
- [35] (2017) Heavy traffic queue length behavior in switches with reconfiguration delay. Proc. IEEE Internat. Conf. Comput. Comm., Atlanta, GA (IEEE).Google Scholar
- [36] (2018) Heavy-traffic delay insensitivity in connection-level models of data transfer with proportionally fair bandwidth sharing. ACM SIGMETRICS Performance Evaluation Rev. 45(3):232–245.Crossref, Google Scholar
- [37] (2016) MapTask scheduling in MapReduce with data locality: Throughput and heavy-traffic optimality. IEEE/ACM Trans. Networks 24:190–203.Crossref, Google Scholar
- [38] (1987) Reflected Brownian motion with skew symmetric data in a polyhedral domain. Probability Theory Related Fields 75(4):459–485.Crossref, Google Scholar
- [39] (1998) Diffusion approximations for open multiclass queueing networks: sufficient conditions involving state space collapse. Queueing Systems 30(1):27–88.Crossref, Google Scholar
- [40] (2016) Stochastic processing networks. Annu. Rev. Statist. Appl. 3(1):323–345.Crossref, Google Scholar
- [41] (2015) Priority algorithm for near-data scheduling: Throughput and heavy-traffic optimality. Proc. IEEE Internat. Conf. Comput. Comm., Hong Kong, China (IEEE), 963–972.Google Scholar
- [42] (2012) A stochastic network under proportional fair resource control–diffusion limit with multiple bottlenecks. Oper. Res. 60(3):716–738.Link, Google Scholar
- [43] (2016) Diffusion limit of fair resource control–stationarity and interchange of limits. Math. Oper. Res. 41(4):1161–1207.Link, Google Scholar

