Scheduling in the High-Uncertainty Heavy Traffic Regime

References

• [1] Atar R, Dupuis P (2002) A differential game with constrained dynamics and viscosity solutions of a related HJB equation. Nonlinear Anal. 51(7):1105–1130.Crossref, Google Scholar
• [2] Atar R, Castiel E, Reiman M (2022) Asymptotic optimality of switched control policies in a simple parallel server system under an extended heavy traffic condition. Preprint, submitted July 16, https://arxiv.org/abs/2207.08010.Google Scholar
• [3] Atar R, Castiel E, Reiman M (2022) Parallel server systems under an extended heavy traffic condition: A lower bound. Preprint, submitted January 19, https://arxiv.org/abs/2201.07855.Google Scholar
• [4] 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. 31(3):1061–1099.Crossref, Google Scholar
• [5] Bandi C, Bertsimas D, Youssef N (2015) Robust queueing theory. Oper. Res. 63(3):676–700.Link, Google Scholar
• [6] Bassamboo A, Harrison JM, Zeevi A (2005) Dynamic routing and admission control in high-volume service systems: Asymptotic analysis via multi-scale fluid limits. Queueing Systems 51(3):249–285.Crossref, Google Scholar
• [7] Borodin A, Kleinberg J, Raghavan P, Sudan M, Williamson DP (1996) Adversarial queueing theory. Proc. Twenty-Eighth Annual ACM Sympos. Theory Comput. (ACM, New York), 376–385.Google Scholar
• [8] Budhiraja A, Dupuis P (2019) Analysis and Approximation of Rare Events: Representations and Weak Convergence Methods, vol. 94 (Springer, New York).Crossref, Google Scholar
• [9] Chen Y, Hasenbein JJ (2017) Staffing large-scale service systems with distributional uncertainty. Queueing Systems 87(1):55–79.Crossref, Google Scholar
• [10] Cohen A (2019) Asymptotic analysis of a multiclass queueing control problem under heavy traffic with model uncertainty. Stochastic Systems 9(4):359–391.Link, Google Scholar
• [11] Cohen A (2019) Brownian control problems for a multiclass M/M/1 queueing problem with model uncertainty. Math. Oper. Res. 44(2):739–766.Link, Google Scholar
• [12] Cohen A, Saha S (2021) Asymptotic optimality of the generalized cμ rule under model uncertainty. Stochastic Processes Their Appl. 136:206–236.Crossref, Google Scholar
• [13] Dupuis P (2003) Explicit solution to a robust queueing control problem. SIAM J. Control Optim. 42(5):1854–1875.Crossref, Google Scholar
• [14] Gamarnik D (2000) Using fluid models to prove stability of adversarial queueing networks. IEEE Trans. Automatic Control 45(4):741–746.Crossref, Google Scholar
• [15] Gilbarg D, Trudinger NS (1998) Elliptic Partial Differential Equations of Second Order, vol. 224 (Springer, Berlin).Google Scholar
• [16] Harrison JM, Zeevi A (2005) A method for staffing large call centers based on stochastic fluid models. Manufacturing Service Oper. Management 7(1):20–36.Link, Google Scholar
• [17] Jacod J, Shiryaev A (2013) Limit Theorems for Stochastic Processes, vol. 288 (Springer Science & Business Media, New York).Google Scholar
• [18] Jain A, Lim AE, Shanthikumar JG (2010) On the optimality of threshold control in queues with model uncertainty. Queueing Systems 65(2):157–174.Crossref, Google Scholar
• [19] Karatzas I, Shreve S (2014) Brownian Motion and Stochastic Calculus, vol. 113 (Springer Science & Business Media, New York).Google Scholar
• [20] Koçağa YL, Armony M, Ward AR (2015) Staffing call centers with uncertain arrival rates and co-sourcing. Production Oper. Management 24(7):1101–1117.Crossref, Google Scholar
• [21] Le Gall J-F (2016) Brownian Motion, Martingales, and Stochastic Calculus (Springer, Berlin).Crossref, Google Scholar
• [22] Reiman MI (1982) The heavy traffic diffusion approximation for sojourn times in Jackson networks. Disney RL, Ott TJ, eds. Applied Probability–Computer Science: The Interface, Progress in Computer Science, vol. 3 (Birkhäuser, Boston), 409–421.Crossref, Google Scholar
• [23] Rockafellar RT (1970) Convex Analysis (Princeton University Press, Princeton, NJ).Crossref, Google Scholar
• [24] Sheng D (1978) Some problems in the optimal control of diffusions. PhD thesis, Stanford University, Stanford, CA.Google Scholar
• [25] Sun X, Zhu X (2021) Dynamic control of a make-to-order system under model uncertainty. https://www.ise.ufl.edu/sun/files/2023/05/Dynamic_Control_of_a_Make_to_Order_System_Under_Model_Uncertainty.pdf.Google Scholar
• [26] Takács L (1961) The transient behavior of a single server queuing process with recurrent input and gamma service time. Ann. Math. Statist. 32(4):1286–1298.Crossref, Google Scholar
• [27] Whitt W (2006) Staffing a call center with uncertain arrival rate and absenteeism. Production Oper. Management 15(1):88–102.Crossref, Google Scholar