Asymptotically Optimal Clearing Control of Backlogs in Multiclass Processing Systems

References

• Argon NT, Ziya S, Righter R (2008) Scheduling impatient jobs in a clearing system with insights on patient triage in mass casualty incidents. Probability Engrg. Inform. Sci. 22(3):301–332.Crossref, Google Scholar
• Armony M, Maglaras C (2004) Contact centers with a call-back option and real-time delay information. Oper. Res. 52(4):527–545.Link, Google Scholar
• Atar R (2005) Scheduling control for queueing systems with many servers: Asymptotic optimality in heavy traffic. Ann. Appl. Probability 15(4):2606–2650.Crossref, Google Scholar
• Atar R (2012) A diffusion regime with nondegenerate slowdown. Oper. Res. 60(2):490–500.Link, Google Scholar
• Atar R, Gurvich I (2014) Scheduling parallel servers in the nondegenerate slowdown diffusion regime: Asymptotic optimality results. Ann. Appl. Probability 24(2):760–810.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, Giat C, Shimkin N (2011) On the asymptotic optimality of the cμ/θ rule under ergodic cost. Queueing Systems 67(2):127–144.Crossref, Google Scholar
• Atar R, Kaspi H, Shimkin N (2013) Fluid limits for many-server systems with reneging under a priority policy. Math. Oper. Res. 39(3):672–696.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. Probability 14(3):1084–1134.Crossref, Google Scholar
• Atkins D, Chen H (1995) Performance evaluation of scheduling control of queueing networks: Fluid model heuristics. Queueing Systems 21:391–413.Crossref, Google Scholar
• Bassamboo A, Randhawa RS (2015) Scheduling homogeneous impatient customers. Management Sci. 62(7):2129–2147.Link, Google Scholar
• Chan CW, Huang M, Sarhangian V (2021) Dynamic server assignment in multiclass queues with shifts, with applications to nurse staffing in emergency departments. Oper. Res. 69(6):1936–1959.Link, Google Scholar
• Chen H, Yao DD (1993) Dynamic scheduling of a multiclass fluid network. Oper. Res. 41(6):1104–1115.Link, Google Scholar
• Cox D, Smith W (1961) Queues (Chapman and Hall/CRC, Boca Raton, FL).Google Scholar
• Crosbie J (2017) Elon musk finally reveals the number of tesla model 3 reservations. Retrieved March 14, 2022, https://www.inverse.com/article/35011-tesla-model-3-reservations-number/.Google Scholar
• Dai JG, Meyn SP (1995) Stability and convergence of moments for multiclass queueing networks via fluid limit models. IEEE Trans. Automated Control 40(11):1889–1904.Crossref, Google Scholar
• Dupuis P (2003) Explicit solution to a robust queueing control problem. SIAM J. Control Optim. 42(5):1854–1875.Crossref, Google Scholar
• Field K (2016) 200,000 tesla model 3 reservations in less than 24 hours. Retrieved March 14, 2022, https://cleantechnica.com/2016/04/01/200000-tesla-model-3-reservations-less-24-hours/.Google Scholar
• Forbes (2021) Which used cars now cost more than new ones. Retrieved March 14, 2022, https://www.forbes.com/sites/jimgorzelany/2021/07/01/which-used-cars-now-cost-more-than-new-ones/?sh=155f01303ada.Google Scholar
• Garnett O, Mandelbaum A, Reiman MI (2002) Designing a call center with impatient customers. Manufacturing Service Oper. Management 4(3):208–227.Link, Google Scholar
• Gurman M, Wu D (2020) Apple supply chain braces for disruption from coronavirus. Retrieved March 14, 2022, https://www.bloomberg.com/news/articles/2020-01-28/apple-supply-chain-braces-for-disruption-from-coronavirus/.Google Scholar
• Gurvich I, Whitt W (2009) Scheduling flexible servers with convex delay costs in many-server service systems. Manufacturing Service Oper. Management 11(2):237–253.Link, Google Scholar
• Gurvich I, Armony M, Mandelbaum A (2008) Service-level differentiation in call centers with fully flexible servers. Management Sci. 54(2):279–294.Link, Google Scholar
• Hajzargarbashi E, Rashedi R, Pourafzali S, Esmailian M (2019) Waiting time for specialist consultation and visit requested in the emergency department: A cross-sectional study. Adv. J. Emergency Medicine 3(2):1–6.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
• Hu Y, Chan CW, Dong J (2019) Optimal scheduling of proactive care with patient deterioration. Technical report, Columbia University, New York.Google Scholar
• Hu Y, Dong J, Perry O (2022a) Asymptotic optimality of base-stock policies with idle times for stochastic economic lot scheduling problems. Working paper, Columbia University, New York.Google Scholar
• Hu Y, Dong J, Perry O (2022b) Asymptotic optimality of the binomial-exhaustive policy for polling systems with large switchover times. Ann. Appl. Probability 32(6):4803–4848.Crossref, Google Scholar
• Jagerman D, Altiok T (2003) Vessel arrival process and queueing in marine ports handling bulk materials. Queueing Systems 45(3):223–243.Crossref, Google Scholar
• Kang W, Ramanan K (2010) Fluid limits of many-server queues with reneging. Ann. Appl. Probability 20(6):2204–2260.Crossref, Google Scholar
• Kim J, Randhawa RS, Ward AR (2018) Dynamic scheduling in a many-server, multiclass system: The role of customer impatience in large systems. Manufacturing Service Oper. Management 20(2):285–301.Link, Google Scholar
• Long Z, Shimkin N, Zhang H, Zhang J (2020) Dynamic scheduling of multiclass many-server queues with abandonment: The generalized cμ/h rule. Oper. Res. 68(4):1218–1230.Link, Google Scholar
• Long Z, Zhang H, Zhang J, Zhang ZG (2023) The generalized c/μ rule for queues with heterogeneous server pools. Oper. Res., ePub ahead of print May 17, https://doi.org/10.1287/opre.2023.2472.Google Scholar
• Maglaras C (2000) Discrete-review policies for scheduling stochastic networks: Trajectory tracking and fluid-scale asymptotic optimality. Ann. Appl. Probability 10(3):897–929.Crossref, Google Scholar
• Maglaras C (2006) Revenue management for a multiclass single-server queue via a fluid model analysis. Oper. Res. 54(5):914–932.Link, Google Scholar
• Maglaras C, Zeevi A (2004) Diffusion approximations for a multiclass Markovian service system with “guaranteed” and “best-effort” service levels. Math. Oper. Res. 29(4):786–813.Link, Google Scholar
• Maglaras C, Zeevi A (2005) Pricing and design of differentiated services: Approximate analysis and structural insights. Oper. Res. 53(2):242–262.Link, Google Scholar
• Mandelbaum A, Stolyar AL (2004) Scheduling flexible servers with convex delay costs: Heavy-traffic optimality of the generalized cμ-rule. Oper. Res. 52(6):836–855.Link, Google Scholar
• Matousek M (2019) Tesla told some $35,000 model 3 customers they were days away from getting their cars. Now, those customers don’t know when their orders will arrive. Retrieved March 14, 2022, https://www.businessinsider.com/tesla-standard-range-model-3-customers-face-extended-wait-2019-4.Google Scholar
• Pang G, Whitt W (2009) Service interruptions in large-scale service systems. Management Sci. 55(9):1499–1512.Link, Google Scholar
• Perry O, Whitt W (2009) Responding to unexpected overloads in large-scale service systems. Management Sci. 55(8):1353–1367.Link, Google Scholar
• Perry O, Whitt W (2011a) A fluid approximation for service systems responding to unexpected overloads. Oper. Res. 59(5):1159–1170.Link, Google Scholar
• Perry O, Whitt W (2011b) An ODE for an overloaded X model involving a stochastic averaging principle. Stochastic Systems 1(1):59–108.Link, Google Scholar
• Perry O, Whitt W (2012) A fluid limit for an overloaded X model via a stochastic averaging principle. Math. Oper. Res. 38(2).Link, Google Scholar
• Perry O, Whitt W (2015) Achieving rapid recovery in an overload control for large-scale service systems. INFORMS J. Comput. 27(3):491–506.Link, Google Scholar
• Pinedo M (1983) Stochastic scheduling with release dates and due dates. Oper. Res. 31(3):559–572.Link, Google Scholar
• Pino D (2021) The Los Angeles port situation is not improving. Retrieved March 14, 2022, https://www.nationalreview.com/corner/the-la-port-situation-is-not-improving/.Google Scholar
• Puha AL, Ward AR (2019) Scheduling an overloaded multiclass many-server queue with impatient customers. Operations Research & Management Science in the Age of Analytics (INFORMS, Catonsville, MD), 189–217.Link, Google Scholar
• Saraiva A (2021) Cargo ships waiting at la ports are skipping Oakland and returning to Asia. Retrieved March 14, 2022, https://www.bloomberg.com/news/articles/2021-11-29/oakland-vessel-calls-drop-43-in-october-as-ships-queue-in-l-a.Google Scholar
• Tezcan T, Dai J (2010) Dynamic control of n-systems with many servers: Asymptotic optimality of a static priority policy in heavy traffic. Oper. Res. 58(1):94–110.Link, Google Scholar
• Ursavas E (2015) Priority control of berth allocation problem in container terminals. Ann. Oper. Res. 317:805–824.Crossref, Google Scholar
• Van Mieghem JA (1995) Dynamic scheduling with convex delay costs: The generalized cμ rule. Ann. Appl. Probability 5(3):809–833.Crossref, Google Scholar
• Wang L, Ai W, Deng T, Shen ZJM, Hong C (2020) Optimal production ramp-up in the smartphone manufacturing industry. Naval Res. Logist. 67(8):685–704.Crossref, Google Scholar
• Ward AR, Glynn PW (2003) A diffusion approximation for a Markovian queue with reneging. Queueing Systems 43(1):103–128.Crossref, Google Scholar
• Ward AR, Glynn PW (2005) A diffusion approximation for a gi/gi/1 queue with balking or reneging. Queueing Systems 50(4):371–400.Crossref, Google Scholar
• Whitt W (2004) Efficiency-driven heavy-traffic approximations for many-server queues with abandonments. Management Sci. 50(10):1449–1461.Link, Google Scholar
• Yu L, Iravani S, Perry O (2022) A fluid-diffusion-hybrid limiting approximation for priority systems with fast and slow customers. Oper. Res. 70(4):2579–2596.Link, Google Scholar
• Zhang J (2013) Fluid models of many-server queues with abandonment. Queueing Systems 73(2):147–193.Crossref, Google Scholar