Dynamic Scheduling of a Multiclass Queue in the Halfin–Whitt Regime: A Computational Approach for High-Dimensional Problems

References

• Aksin Z, Armony M, Mehrotra V (2007) The modern call center: A multi-disciplinary perspective on operations management research. Prod. Oper. Management 16(6):665–688.Crossref, Google Scholar
• Akşin Z, Ata B, Emadi SM, Su C-L (2013) Structural estimation of callers’ delay sensitivity in call centers. Management Sci. 59(12):2727–2746.Link, Google Scholar
• Ata B, Barjesteh N (2022) An approximate analysis of dynamic pricing, outsourcing, and scheduling policies for a multiclass make-to-stock queue in the heavy traffic regime. Oper. Res. 71(1):341–357. Link, Google Scholar
• Ata B, Gurvich I (2012) On optimality gaps in the Halfin–Whitt regime. Ann. Appl. Probab. 22(1):407–455.Crossref, Google Scholar
• Ata B, Kumar S (2005) Heavy traffic analysis of open processing networks with complete resource pooling: Asymptotic optimality of discrete review policies. Ann. Appl. Probab. 15(1A):331–391.Crossref, Google Scholar
• Ata B, Zhou Y (2025) Analysis and improvement of eviction enforcement. Preprint, submitted February 22, https://arxiv.org/abs/2502.16346.Google Scholar
• Ata B, Barjesteh N, Kumar S (2020) Dynamic dispatch and centralized relocation of cars in ride-hailing platforms. Preprint, submitted September 14, https://doi.org/10.2139/ssrn.3675888.Google Scholar
• Ata B, Harrison, JM, Si, N (2024) Drift control of high-dimensional reflected Brownian motion: A computational method based on neural networks. Stochastic Systems 15(2):111–146.Link, Google Scholar
• Atar R (2005) Scheduling control for queueing systems with many servers: Asymptotic optimality in heavy traffic. Ann. Appl. Probab. 15(4):2606–2650.Crossref, Google Scholar
• Atar R, Giat C, Shimkin N (2010) The cμ/θ rule for many-server queues with abandonment. Oper. Res. 58(5):1427–1439.Link, Google Scholar
• Atar R, Mandelbaum A, Reiman MI (2004) Scheduling a multi class queue with many exponential servers: Asymptotic optimality in heavy traffic. Ann. Appl. Probab. 14(3):1084–1134.Crossref, Google Scholar
• Beck C, Becker S, Cheridito P, Jentzen A, Neufeld A (2021) Deep splitting method for parabolic PDEs. SIAM J. Sci. Comput. 43(5):A3135–A3154.Crossref, Google Scholar
• 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
• Chevalier PB, Wein LM (1993) Scheduling networks of queues: Heavy traffic analysis of a multistation closed network. Oper. Res. 41(4):743–758.Link, Google Scholar
• Cox DR, Smith W (1961) Queues (Methuen & Co. Ltd, London).Google Scholar
• Dai JG, Gluzman M (2022) Queueing network controls via deep reinforcement learning. Stochastic Systems 12(1):30–67.Link, Google Scholar
• E W, Han J, Jentzen A (2017) Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations. Comm. Math. Statist. 5(4):349–380. Crossref, Google Scholar
• Fleming WH, Soner HM (2006) Controlled Markov Processes and Viscosity Solutions, vol. 25 (Springer Science & Business Media, New York).Google Scholar
• Gans N, Koole G, Mandelbaum A (2003) Telephone call centers: Tutorial, review, and research prospects. Manufacturing Service Oper. Management 5(2):79–141.Link, Google Scholar
• Garnett O, Mandelbaum A, Reiman M (2002) Designing a call center with impatient customers. Manufacturing Service Oper. Management 4(3):208–227.Link, Google Scholar
• Germain M, Pham H, Warin X (2022) Approximation error analysis of some deep backward schemes for nonlinear PDEs. SIAM J. Sci. Comput. 44(1):A28–A56.Crossref, Google Scholar
• Gilbarg D, Trudinger NS (2001) Elliptic Partial Differential Equations of Second Order, 2nd ed. (Springer, New York).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
• Han J, Jentzen A, E W (2018) Solving high-dimensional partial differential equations using deep learning. Proc. Natl. Acad. Sci. U S A. 115(34):8505–8510. 30082389.Crossref, Google Scholar
• Harrison JM (1988) Brownian models of queueing networks with heterogeneous customer populations. Fleming W, Lions PL, eds. Stochastic Differential Systems, Stochastic Control Theory Appl., The IMA Volumes in Mathematics and Its Applications, vol. 10 (Springer, New York), 147–186.Google Scholar
• Harrison JM (2000) Brownian models of open processing networks: Canonical representation of workload. Ann. Appl. Probab. 10(1):75–103.Crossref, Google Scholar
• Harrison JM (2003) A broader view of Brownian networks. Ann. Appl. Probab. 13(3):1119–1150.Crossref, Google Scholar
• Harrison JM, Wein LM (1990) Scheduling networks of queues: Heavy traffic analysis of a two-station closed network. Oper. Res. 38(6):1052–1064.Link, Google Scholar
• Harrison JM, Zeevi A (2004) Dynamic scheduling of a multiclass queue in the Halfin-Whitt heavy traffic regime. Oper. Res. 52(2):243–257.Link, Google Scholar
• He D, Li S, Shi W, Gao X, Zhang J, Bian J, Wang L, Liu T-Y (2023) Learning physics-informed neural networks without stacked back-propagation. Internat. Conf. Artificial Intelligence Statist. (PMLR, New York), 3034–3047.Google Scholar
• Hu Z, Shi Z, Karniadakis GE, Kawaguchi K (2024) Hutchinson trace estimation for high-dimensional and high-order physics-informed neural networks. Comput. Methods Appl. Mech. Engrg. 424:116883.Crossref, Google Scholar
• Koole GM, Li S (2023) A practice-oriented overview of call center workforce planning. Stochastic Systems 13(4):479–495.Link, Google Scholar
• Kumar S, Muthuraman K (2004) A numerical method for solving singular stochastic control problems. Oper. Res. 52(4):563–582.Link, Google Scholar
• Ma J, Protter P, Yong J (1994) Solving forward-backward stochastic differential equations explicitly—A four step scheme. Probab. Theory Related Fields 98(3):339–359.Crossref, Google Scholar
• Pardoux E, Peng S (1990) Adapted solution of a backward stochastic differential equation. Systems Control Lett. 14(1):55–61.Crossref, Google Scholar
• Raissi M, Perdikaris P, Karniadakis GE (2019) Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys. 378:686–707.Crossref, Google Scholar
• Stute W, Wang J-L (1994) The jackknife estimate of a Kaplan-Meier integral. Biometrika 81(3):602–606.Google Scholar
• Wein LM (1992) Dynamic scheduling of a multiclass make-to-stock queue. Oper. Res. 40(4):724–735.Link, Google Scholar