Large Deviations for the Single-Server Queue and the Reneging Paradox

References

• [1] Atar R, Kaspi H, Shimkin N (2014) Fluid limits for many-server systems with reneging under a priority policy. Math. Oper. Res. 39(3):672–696.Google Scholar
• [2] Atar R, Budhiraja A, Dupuis P, Wu R (2021) Robust bounds and optimization at the large deviations scale for queueing models via Rényi divergence. Ann. Appl. Probab. Forthcoming.Google Scholar
• [3] Budhiraja A, Dupuis P (2019) Analysis and Approximation of Rare Events: Representations and Weak Convergence Methods, vol. 94 (Springer, New York).Crossref, Google Scholar
• [4] Budhiraja A, Chen J, Dupuis P (2013) Large deviations for stochastic partial differential equations driven by a Poisson random measure. Stochastic Processes Their Appl. 123(2):523–560.Crossref, Google Scholar
• [5] Budhiraja A, Dupuis P, Ganguly A (2016) Moderate deviation principles for stochastic differential equations with jumps. Ann. Probab. 44(3):1723–1775.Crossref, Google Scholar
• [6] Budhiraja A, Dupuis P, Maroulas V (2011) Variational representations for continuous time processes. Annales de l’Institut Henri Poincaré(B). Probabilités et Statistiques 47(3):725–747.Google Scholar
• [7] Dupuis P, Ellis RS (1997) A Weak Convergence Approach to the Theory of Large Deviations (John Wiley & Sons, New York).Crossref, Google Scholar
• [8] Dupuis P, Ishii H (1991) On Lipschitz continuity of the solution mapping to the Skorokhod problem, with applications. Stochastics 35(1):31–62.Google Scholar
• [9] Ikeda N, Watanabe S (1981) Stochastic Differential Equations and Diffusion Processes, North-Holland Mathematical Library, vol. 24 (Elsevier, New York).Google Scholar
• [10] Kang W, Ramanan K (2010) Fluid limits of many-server queues with reneging. Ann. Appl. Probab. 20(6):2204–2260.Google Scholar
• [11] Karatzas I, Shreve SE (1991) Brownian Motion and Stochastic Calculus, Graduate Texts in Mathematics, vol. 113 (Springer, New York).Google Scholar
• [12] Kaspi H, Ramanan K (2011) Law of large numbers limits for many-server queues. Ann. Appl. Probab. 21(1):33–114.Crossref, Google Scholar
• [13] Kaspi H, Ramanan K (2013) SPDE limits of many-server queues. Ann. Appl. Probab. 23(1):145–229.Google Scholar
• [14] Kurtz TG (1981) Approximation of Population Processes, CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 36 (SIAM, Philadelphia).Crossref, Google Scholar
• [15] Puha AL, Ward AR (2019) Scheduling an overloaded multiclass many-server queue with impatient customers. Netessine S, ed. Operations Research & Management Science in the Age of Analytics (INFORMS, Catonsville, MD), 189–217.Link, Google Scholar
• [16] Reed J (2009) The G/GI/N queue in the Halfin-Whitt regime. Ann. Appl. Probab. 19(6):2211–2269.Google Scholar
• [17] Troutman JL (2012) Variational Calculus and Optimal Control: Optimization with Elementary Convexity (Springer, New York).Google Scholar
• [18] Ward AR (2012) Asymptotic analysis of queueing systems with reneging: A survey of results for FIFO, single class models. Surveys Oper. Res. Management Sci. 17(1):1–14.Crossref, Google Scholar