Invariant States of Hydrodynamic Limits of Randomized Load-Balancing Networks

References

• [1] Agarwal P, Ramanan K (2020) Invariant states of hydrodynamic limits of randomized load balancing networks. Preprint, submitted August 19, https://arxiv.org/abs/2008.08510.Google Scholar
• [2] Aghajani R, Ramanan K (2019) The hydrodynamic limit of a randomized load balancing network. Ann. Appl. Probab. 29(4):2114–2174.Crossref, Google Scholar
• [3] Aghajani R, Li X, Ramanan K (2015) Mean-field dynamics of load-balancing networks with general service distributions. Preprint, submitted December 16, https://arxiv.org/abs/1512.05056.Google Scholar
• [4] Aghajani R, Li X, Ramanan K (2017) The PDE method for the analysis of randomized load balancing networks. Proc. ACM Measurement Anal. Comput. Systems 1(2):38:1–38:28.Google Scholar
• [5] Atar R, Kang W, Kaspi H, Ramanan K (2023) Long-time limit of nonlinearly coupled measure-valued equations that model many-server queues with reneging. SIAM J. Math. Anal. 55(6):7189–7239.Crossref, Google Scholar
• [6] Bramson M (2011) Stability of join the shortest queue networks. Ann. Appl. Probab. 21(4):1568–1625.Crossref, Google Scholar
• [7] Bramson M, Lu Y, Prabhakar B (2010) Randomized load balancing with general service time distributions. SIGMETRICS Performance Evaluation Rev. 38(1):275–286.Crossref, Google Scholar
• [8] Bramson M, Lu Y, Prabhakar B (2012) Asymptotic independence of queues under randomized load balancing. Queueing Systems 71(3):247–292.Crossref, Google Scholar
• [9] Bramson M, Lu Y, Prabhakar B (2013) Decay of tails at equilibrium for FIFO join the shortest queue networks. Ann. Appl. Probab. 23(5):1841–1878.Crossref, Google Scholar
• [10] Brown L, Gans N, Mandelbaum A, Sakov A, Shen H, Zeltyn S, Zhao L (2005) Statistical analysis of a telephone call center: A queueing-science perspective. J. Amer. Statist. Assoc. 100(469):36–50.Crossref, Google Scholar
• [11] Chen S, Sun Y, Kozat UC, Huang L, Sinha P, Liang G, Liu X, Shroff NB (2014) When queueing meets coding: Optimal-latency data retrieving scheme in storage clouds. Preprint, submitted April 26, https://arxiv.org/abs/1404.6687.Google Scholar
• [12] Folland GB (1999) Real Analysis: Modern Techniques and Their Applications, Pure and Applied Mathematics, 2nd ed. (John Wiley & Sons, Inc., New York).Google Scholar
• [13] Kang W, Ramanan K (2010) Fluid limits of many-server queues with reneging. Ann. Appl. Probab. 20(6):2204–2260.Crossref, Google Scholar
• [14] Kang W, Ramanan K (2012) Asymptotic approximations for stationary distributions of many-server queues with abandonment. Ann. Appl. Probab. 22(2):477–521.Crossref, Google Scholar
• [15] Kaspi H, Ramanan K (2011) Law of large numbers limits for many-server queues. Ann. Appl. Probab. 21(1):33–114.Crossref, Google Scholar
• [16] Kolesar P (1984) Stalking the endangered cat: A queueing analysis of congestion at automatic teller machines. Interfaces 14(6):16–26.Link, Google Scholar
• [17] Li QL, Lui JC, Wang Y (2010) A matrix-analytic solution for randomized load balancing models with PH service times. Hummel KA, Hlavacs H, Gansterer W, eds. Performance Evaluation Comput. Comm. Systems. Milestones Future Challenges. PERFORM 2010, Lecture Notes in Computer Science, vol. 6821 (Springer, Berlin, Heidelberg), 240–253.Google Scholar
• [18] Liang G, Kozat UC (2014) TOFEC: Achieving optimal throughput-delay trade-off of cloud storage using erasure codes. IEEE INFOCOM 2014 - IEEE Conf. Comput. (IEEE, Piscataway, NJ), 826–834.Google Scholar
• [19] Mitzenmacher M (2001) The power of two choices in randomized load balancing. IEEE Trans. Parallel Distribution Systems 12(10):1094–1104.Crossref, Google Scholar
• [20] Narasimhan R, Nievergelt Y (2001) Complex Analysis in One Variable, 2nd ed. (Birkhäuser, Boston).Crossref, Google Scholar
• [21] Stanley RP (1986) Enumerative Combinatorics, The Wadsworth & Brooks/Cole Mathematics Series, vol. I (Springer, Boston).Crossref, Google Scholar
• [22] Vasantam T, Mukhopadhyay A, Mazumdar RR (2018) The mean-field behavior of processor sharing systems with general job lengths under the sq (d) policy. Performance Evaluation 127:120–153.Crossref, Google Scholar
• [23] Vasantam T, Mukhopadhyay A, Mazumdar RR (2019) Insensitivity of the mean field limit of loss systems under SQ(d) routeing. Adv. Appl. Probab. 51(4):1027–1066.Crossref, Google Scholar
• [24] Vvedenskaya ND, Dobrushin RL, Karpelevich FI (1996) A queueing system with a choice of the shorter of two queues—An asymptotic approach. Problemy Peredachi Informatsii 32(1):20–34.Google Scholar