On System-Wide Safety Staffing of Large-Scale Parallel Server Networks

References

• Aghajani R, Ramanan K (2019) Ergodicity of an SPDE associated with a many-server queue. Ann. Appl. Probability 29(2):994–1045.Crossref, Google Scholar
• Aghajani R, Ramanan K (2020) The limit of stationary distributions of many-server queues in the Halfin-Whitt regime. Math. Oper. Res. 45(3):1016–1055.Link, Google Scholar
• Arapostathis A, Pang G (2016) Ergodic diffusion control of multiclass multi-pool networks in the Halfin-Whitt regime. Ann. Appl. Probability 26(5):3110–3153.Crossref, Google Scholar
• Arapostathis A, Pang G (2018) Infinite-horizon average optimality of the N-network in the Halfin-Whitt regime. Math. Oper. Res. 43(3):838–866.Link, Google Scholar
• Arapostathis A, Pang G (2019) Infinite horizon asymptotic average optimality for large-scale parallel server networks. Stochastic Processing Appl. 129(1):283–322.Crossref, Google Scholar
• Arapostathis A, Hmedi H, Pang G (2021) On uniform exponential ergodicity of Markovian multiclass many-server queues in the Halfin–Whitt regime. Math. Oper. Res. 46(2):772–796.Link, Google Scholar
• Arapostathis A, Pang G, Sandrić N (2019a) Ergodicity of a Lévy-driven SDE arising from multiclass many-server queues. Ann. Appl. Probability 29(2):1070–1126.Crossref, Google Scholar
• Arapostathis A, Pang G, Sandrić N (2020) Subexponential upper and lower bounds in Wasserstein distance for Markov processes. Preprint, submitted July 10, 2019, https://arxiv.org/abs/ 1907.05250.Google Scholar
• Arapostathis A, Hmedi H, Pang G, Sandrić N (2019b) Uniform polynomial rates of convergence for a class of Lévy-driven controlled SDEs arising in multiclass many-server queues. Modeling, Stochastic Control, Optimization, and Applications, vol. 164 The IMA Volumes in Mathematics and its Applications (Springer, Cham, Switzerland), 1–20. Crossref, Google Scholar
• Atar R (2005a) A diffusion model of scheduling control in queueing systems with many servers. Ann. Appl. Probab. 15(1B):820–852.Crossref, Google Scholar
• Atar R (2005b) Scheduling control for queueing systems with many servers: Asymptotic optimality in heavy traffic. Ann. Appl. Probab. 15(4):2606–2650.Crossref, Google Scholar
• Borst S, Mandelbaum A, Reiman MI (2004) Dimensioning large call centers. Oper. Res. 52(1):17–34.Link, Google Scholar
• Dieker AB, Gao X (2013) Positive recurrence of piecewise Ornstein-Uhlenbeck processes and common quadratic Lyapunov functions. Ann. Appl. Probab. 23(4):1291–1317.Crossref, Google Scholar
• Down D, Meyn SP, Tweedie RL (1995) Exponential and uniform ergodicity of Markov processes. Ann. Probab. 23(4):1671–1691.Crossref, Google Scholar
• Gamarnik D, Stolyar AL (2012) Multiclass multiserver queueing system in the Halfin-Whitt heavy traffic regime: Asymptotics of the stationary distribution. Queueing Systems 71(1-2):25–51.Crossref, Google Scholar
• Halfin S, Whitt W (1981) Heavy-traffic limits for queues with many exponential servers. Oper. Res. 29(3):567–588.Link, Google Scholar
• Hmedi H, Arapostathis A, Pang G (2019) Uniform stability of a class of large-scale parallel server networks. Preprint, submitted July 10, 2019, https://arxiv.org/abs/ 1907.04793.Google Scholar
• Kaspi H, Ramanan K (2011) Law of large numbers limits for many-server queues. Ann. Appl. Probab. 21(1):33–114.Crossref, Google Scholar
• Kaspi H, Ramanan K (2013) SPDE limits of many-server queues. Ann. Appl. Probab. 23(1):145–229.Crossref, Google Scholar
• Meyn SP, Tweedie RL (1993) Stability of Markovian processes. III. Foster-Lyapunov criteria for continuous-time processes. Adv. Appl. Probab. 25(3):518–548.Crossref, Google Scholar
• Stolyar AL (2015) Tightness of stationary distributions of a flexible-server system in the Halfin-Whitt asymptotic regime. Stochastic Systems 5(2):239–267.Link, Google Scholar
• Stolyar AL, Yudovina E (2013) Systems with large flexible server pools: Instability of “natural” load balancing. Ann. Appl. Probab. 23(5):2099–2138.Crossref, Google Scholar
• Whitt W (1992) Understanding the efficiency of multi-server service systems. Management Sci. 38(5):708–723.Link, Google Scholar
• Williams RJ (2000) On dynamic scheduling of a parallel server system with complete resource pooling. Analysis of Communication Networks: Call Centres, Traffic and Performance, vol. 28 of Fields Institute Communications (AMS, Providence, RI), 49–71.Crossref, Google Scholar