Dynamic Server Assignment in Multiclass Queues with Shifts, with Applications to Nurse Staffing in Emergency Departments

References

• Anderson R, Gamarnik D (2015) Scheduling interns in hospitals: Queueing models and fluid approximations. Working Paper, Massachusetts Institute of Technology, Cambridge, MA.Google Scholar
• Armony M, Israelit S, Mandelbaum A, Marmor YN, Tseytlin Y, Yom-Tov GB (2015) On patient flow in hospitals: A data-based queueing-science perspective. Stochastic Systems 5(1):146–194.Link, 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
• Atlason J, Epelman MA, Henderson SG (2008) Optimizing call center staffing using simulation and analytic center cutting-plane methods. Management Sci. 54(2):295–309.Link, Google Scholar
• Avram F, Bertsimas D, Ricard M (1995) Fluid models of sequencing problems in open queueing networks; an optimal control approach. Kelly FP, Williams RJ, eds. Stochastic Networks (Springer, New York), 199–234.Crossref, Google Scholar
• 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
• Bassamboo A, Harrison JM, Zeevi A (2006) Design and control of a large call center: Asymptotic analysis of an LP-based method. Oper. Res. 54(3):419–435.Link, Google Scholar
• Batt RJ, Terwiesch C (2015) Waiting patiently: An empirical study of queue abandonment in an emergency department. Management Sci. 61(1):39–59.Link, Google Scholar
• Batt RJ, Kc DS, Staats BR, Patterson BW (2019) The effects of discrete work shifts on a nonterminating service system. Production Oper. Management 28(6):1528–1544.Crossref, Google Scholar
• Bäuerle N (2000) Asymptotic optimality of tracking policies in stochastic networks. Ann. Appl. Probab. 10(4):1065–1083.Crossref, Google Scholar
• Brusco MJ, Jacobs LW, Bongiorno RJ, Lyons DV, Tang B (1995) Improving personnel scheduling at airline stations. Oper. Res. 43(5):741–751.Link, Google Scholar
• Burke EK, De Causmaecker P, Berghe GV, Van Landeghem H (2004) The state of the art of nurse rostering. J. Scheduling 7(6):441–499.Crossref, Google Scholar
• Chan CW, Yom-Tov G, Escobar G (2014) When to use speedup: An examination of service systems with returns. Oper. Res. 62(2):462–482.Link, Google Scholar
• Chen RR, Meyn S (1999) Value iteration and optimization of multiclass queueing networks. Queueing Systems 32(1–3):65–97.Crossref, Google Scholar
• Dai JG (1995) On positive harris recurrence of multiclass queueing networks: A unified approach via fluid limit models. Ann. Appl. Probab. 5(1):49–77.Crossref, Google Scholar
• Dai J, Shi P (2019) Inpatient overflow: An approximate dynamic programming approach. Manufacturing Service Oper. Management 21(4):713–948.Link, Google Scholar
• Dai J, Tezcan T (2011) State space collapse in many-server diffusion limits of parallel server systems. Math. Oper. Res. 36(2):271–320.Link, Google Scholar
• Dai JG, Weiss G (2002) A fluid heuristic for minimizing makespan in job shops. Oper. Res. 50(4):692–707.Link, Google Scholar
• Down DG, Koole G, Lewis ME (2011) Dynamic control of a single-server system with abandonments. Queueing Systems 67(1):63–90.Crossref, Google Scholar
• Green LV (2010) Using Queueing Theory to Alleviate Emergency Department Overcrowding (Wiley, New York).Google Scholar
• Green L, Kolesar P (1989) Testing the validity of a queueing model of police patrol. Management Sci. 35(2):127–148.Link, Google Scholar
• Green LV, Soares J, Giglio JF, Green RA (2006) Using queueing theory to increase the effectiveness of emergency department provider staffing. Academic Emergency Medicine 13(1):61–68.Crossref, Google Scholar
• Gurvich I, Whitt W (2010) Service-level differentiation in many-server service systems via queue-ratio routing. Oper. Res. 58(2):316–328.Link, Google Scholar
• Harrison JM (1996) The BIGSTEP approach to flow management in stochastic processing networks. Stochastic Networks Theory Appl. 4:147–186.Google Scholar
• Harrison JM (1998) Heavy traffic analysis of a system with parallel servers: asymptotic optimality of discrete-review policies. Ann. Appl. Probab. 8(3):822–848.Crossref, 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
• 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
• Huang J, Carmeli B, Mandelbaum A (2015) Control of patient flow in emergency departments, or multiclass queues with deadlines and feedback. Oper. Res. 63(4):892–908.Link, Google Scholar
• Ingolfsson A, Haque MA, Umnikov A (2002) Accounting for time-varying queueing effects in workforce scheduling. Eur. J. Oper. Res. 139(3):585–597.Crossref, Google Scholar
• Jouini O, Dallery Y, Nait-Abdallah R (2008) Analysis of the impact of team-based organizations in call center management. Management Sci. 54(2):400–414.Link, Google Scholar
• Kim SH, Whitt W (2014) Are call center and hospital arrivals well modeled by nonhomogeneous Poisson processes? Manufactuing Service Oper. Management 16(3):464–480.Link, Google Scholar
• Kolesar PJ, Rider KL, Crabill TB, Walker WE (1975) A queuing-linear programming approach to scheduling police patrol cars. Oper. Res. 23(6):1045–1062.Link, Google Scholar
• Larranaga M, Ayesta U, Verloop IM (2013) Dynamic fluid-based scheduling in a multi-class abandonment queue. Performance Evaluation 70(10):841–858.Crossref, Google Scholar
• Maglaras C (2000) Discrete-review policies for scheduling stochastic networks: Trajectory tracking and fluid-scale asymptotic optimality. Ann. Appl. Probab. 10(3):897–929.Crossref, Google Scholar
• Mandelbaum A, Stolyar AL (2004) Scheduling flexible servers with convex delay costs: Heavy-traffic optimality of the generalized ccμ-rule. Oper. Res. 52(6):836–855.Link, Google Scholar
• Mandelbaum A, Massey WA, Reiman MI (1998) Strong approximations for Markovian service networks. Queueing Systems 30(1):149–201.Crossref, Google Scholar
• Martonosi SE (2011) Dynamic server allocation at parallel queues. IIE Trans. 43(12):863–877.Crossref, Google Scholar
• Meyn S (1997) Stability and optimization of queueing networks and their fluid models. Yin GG, Zhang Q, eds. Mathematics of Stochastic Manufacturing Systems (American Mathematical Society, Providence, RI), 175–200.Google Scholar
• 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
• Saghafian S, Hopp WJ, Van Oyen MP, Desmond JS, Kronick SL (2012) Patient streaming as a mechanism for improving responsiveness in emergency departments. Oper. Res. 60(5):1080–1097.Link, Google Scholar
• Song H, Tucker AL, Murrell KL (2015) The diseconomies of queue pooling: An empirical investigation of emergency department length of stay. Management Sci. 61(12):3032–3053.Link, Google Scholar
• Tirdad A, Grassmann WK, Tavakoli J (2016) Optimal policies of M(t)/M/c/cqueues with two different levels of servers. Eur. J. Oper. Res. 249(3):1124–1130.Crossref, Google Scholar
• Van Mieghem JA (1995) Dynamic scheduling with convex delay costs: The generalizedcμrule. Ann. Appl. Probab. 5(3):809–833.Crossref, Google Scholar
• Véricourt Fd, Jennings OB (2011) Nurse staffing in medical units: A queueing perspective. Oper. Res. 59(6):1320–1331.Link, Google Scholar
• Yankovic N, Green LV (2011) Identifying good nursing levels: A queuing approach. Oper. Res. 59(4):942–955.Link, Google Scholar
• Yom-Tov GB, Mandelbaum A (2014) Erlang-R: A time-varying queue with reentrant customers, in support of healthcare staffing. Manufacturing Service Oper. Management 16(2):283–299.Link, Google Scholar