Many-Server Asymptotics for Join-the-Shortest-Queue in the Super-Halfin-Whitt Scaling Window

References

• [1] Adan I, Resing J (2015) Queueing systems. Eindhoven University of Technology, Eindhoven, Netherlands. https://iadan.win.tue.nl/queueing.pdf.Google Scholar
• [2] Atar R (2012) A diffusion regime with nondegenerate slowdown. Oper. Res. 60(2):490–500.Link, Google Scholar
• [3] Banerjee S, Mukherjee D (2019) Join-the-shortest queue diffusion limit in Halfin–Whitt regime: Tail asymptotics and scaling of extrema. Ann. Appl. Probab. 29(2):1262–1309.Crossref, Google Scholar
• [4] Banerjee S, Mukherjee D (2020) Join-the-shortest queue diffusion limit in Halfin–Whitt regime: Sensitivity on the heavy traffic parameter. Ann. Appl. Probab. 30(1):80–144.Crossref, Google Scholar
• [5] Billingsley P (2012) Probability and Measure, Wiley Series in Probability and Statistics (John Wiley & Sons, Hoboken, NJ).Google Scholar
• [6] Billingsley P (2013) Convergence of Probability Measures (John Wiley & Sons, Hoboken, NJ).Google Scholar
• [7] Bramson M (2011) Stability of join the shortest queue networks. Ann. Appl. Probab. 21(4):1568–1625.Crossref, Google Scholar
• [8] Braverman A (2020) Steady-state analysis of the join-the-shortest-queue model in the Halfin–Whitt regime. Math. Oper. Res. 45(3):1069–1103.Link, Google Scholar
• [9] Braverman A (2023) The join-the-shortest-queue system in the Halfin–Whitt regime: Rates of convergence to the diffusion limit. Stochastic Systems 13(1):1–39.Google Scholar
• [10] Budhiraja A, Lee C (2009) Stationary distribution convergence for generalized Jackson networks in heavy traffic. Math. Oper. Res. 34(1):45–56.Link, Google Scholar
• [11] Budhiraja A, Friedlander E, Wu R (2021) Many-server asymptotics for Join-the-shortest-queue: Large deviations and rare events. Ann. Appl. Probab. 31(5):2376–2419.Google Scholar
• [12] Ephremides A, Varaiya P, Walrand J (1980) A simple dynamic routing problem. IEEE Trans. Automatic Control 25(4):690–693.Crossref, Google Scholar
• [13] Eschenfeldt P, Gamarnik D (2018) Join the shortest queue with many servers. The heavy traffic-asymptotics. Math. Oper. Res. 43(3):867–886.Link, Google Scholar
• [14] Foschini GJ (1977) On heavy traffic diffusion analysis and dynamic routing in packet switched networks. Chandy KM, Reiser M, eds. Computer Performance (North Holland, Amsterdam), 499–513.Google Scholar
• [15] Foschini G, Salz J (1978) A basic dynamic routing problem and diffusion. IEEE Trans. Comm. 26(3):320–327.Crossref, Google Scholar
• [16] Gupta V, Walton N (2019) Load balancing in the nondegenerate slowdown regime. Oper. Res. 67(1):281–294.Link, Google Scholar
• [17] Gurvich I (2004) Design and control of the m/m/n queue with multi-class customers and many servers. MSc thesis, Technion – Israel Institute of Technology, Haifa, Israel.Google Scholar
• [18] Hunt P, Kurtz T (1994) Large loss networks. Stoch. Processes Appl. 53(2):363–378.Crossref, Google Scholar
• [19] Hurtado-Lange D, Maguluri ST (2020) Load balancing system under Join the Shortest Queue: Many-server-heavy-traffic asymptotics. Preprint, submitted April 9, http://arxiv.org/abs/2004.04826.Google Scholar
• [20] Hurtado-Lange D, Maguluri ST (2022) A load balancing system in the many-server heavy-traffic asymptotics. Queueing Systems 101(3):353–391.Google Scholar
• [21] Karatzas I, Shreve S (2014) Brownian Motion and Stochastic Calculus, Graduate Texts in Mathematics (Springer, New York).Google Scholar
• [22] Kleinrock L (1975) Queueing Systems: Theory, vol. 1 (Wiley-Interscience, New York).Google Scholar
• [23] Lakatos L, Szeidl L, Telek M (2019) Introduction to Queueing Systems with Telecommunication Applications (Springer, Cham, Switzerland).Crossref, Google Scholar
• [24] Liptser R, Shiryayev AN (2012) Theory of Martingales, Mathematics and Its Applications, vol. 49 (Springer, Dordrecht, Netherlands).Google Scholar
• [25] Liu X, Ying L (2019) A simple steady-state analysis of load balancing algorithms in the sub-Halfin–Whitt regime. Sigmetrics Performance Evaluation Rev. 46(2):15–17.Crossref, Google Scholar
• [26] Liu X, Ying L (2022) Universal scaling of distributed queues under load balancing in the super-Halfin–Whitt regime. IEEE/ACM Trans. Networking 30(1):190–201.Crossref, Google Scholar
• [27] Maglaras C, Yao J, Zeevi A (2018) Optimal price and delay differentiation in large-scale queueing systems. Management Sci. 64(5):2427–2444.Link, Google Scholar
• [28] Mandelbaum A (2008) QED Q’s: Quality- and efficiency-driven queues. Accessed May 2021, https://iew.technion.ac.il/serveng/References/Lecture_QED_Qs_Scientific_TAU.pdf.Google Scholar
• [29] Mandelbaum A, Shaikhet G (2004) Private communication to Rami Atar.Google Scholar
• [30] McDiarmid C (1998) Concentration (Springer, Berlin, Heidelberg).Crossref, Google Scholar
• [31] Meyn SP, Tweedie RL (2012) Markov Chains and Stochastic Stability (Springer-Verlag, London).Google Scholar
• [32] Mukherjee D, Borst SC, Van Leeuwaarden JSH, Whiting PA (2016) Universality of load balancing schemes on the diffusion scale. J. Appl. Probab. 53(4):1111–1124.Crossref, Google Scholar
• [33] Mukherjee D, Borst SC, van Leeuwaarden JSH, Whiting PA (2018) Universality of power-of-D load balancing in many-server systems. Stochastic Systems 8(4):265–292.Link, Google Scholar
• [34] Pang G, Talreja R, Whitt W (2007) Martingale proofs of many-server heavy-traffic limits for Markovian queues. Probab. Surveys 4:193–267.Crossref, Google Scholar
• [35] Reiman MI (1984) Some diffusion approximations with state space collapse. Modelling and Performance Evaluation Methodology (Springer, Berlin, Heidelberg), 207–240.Crossref, Google Scholar
• [36] Roberts GO, Tweedie RL (1996) Exponential convergence of Langevin distributions and their discrete approximations. Bernoulli 2(4):341–363.Crossref, Google Scholar
• [37] Rogers LCG, Williams D (2000) Diffusions, Markov Processes, and Martingales, Cambridge Mathematical Library, vol. 1, 2nd ed. (Cambridge University Press, Cambridge, UK).Google Scholar
• [38] van der Boor M, Borst S, van Leeuwaarden J, Mukherjee D (2022) Scalable load balancing in networked systems: A survey of recent advances. SIAM Rev. 64(3):554–622.Google Scholar
• [39] Whitt W (2003) How multiserver queues scale with growing congestion-dependent demand. Oper. Res. 51(4):531–542.Link, Google Scholar
• [40] Whitt W (2007) Proofs of the martingale FCLT. Probab. Surveys 4:268–302.Crossref, Google Scholar
• [41] Winston W (1977) Optimality of the shortest line discipline. J. Appl. Probab. 14(1):181–189.Crossref, Google Scholar
• [42] Zhang H, Hsu GH, Wang R (1995) Heavy traffic limit theorems for a sequence of shortest queueing systems. Queueing Systems 21(1):217–238.Crossref, Google Scholar