A Two-Time-Scale Approach to Time-Varying Queues in Hospital Inpatient Flow Management

Published Online:https://doi.org/10.1287/opre.2016.1566

References

  • Armony M, Chan CW, Zhu B (2015a) Critical care in hospitals: When to introduce a step down unit? Working paper, New York University, New York.Google Scholar
  • Armony M, Israelit S, Mandelbaum A, Marmor YN, Tseytlin Y, Yom-Tov GB (2015b) On patient flow in hospitals: A data-based queueing-science perspective. Stochastic Systems 5(1):146–194.LinkGoogle Scholar
  • Bernstein SL, Aronsky D, Duseja R, Epstein S, Handel D, Hwang U, McCarthy Met al. Society for Academic Emergency Medicine, Emergency Department Crowding Task Force (2009) The effect of emergency department crowding on clinically oriented outcomes. Acad. Emergency Medicine 16(1):1–10.CrossrefGoogle Scholar
  • Bramson M (2008) Stability of Queueing Networks. Lecture Notes in Mathematics, Vol. 1950 (Springer, Berlin).Google Scholar
  • Braverman A, Dai JG (2017) Stein’s method for steady-state diffusion approximations. Annals Appl. Probab. Forthcoming.CrossrefGoogle Scholar
  • Chan CW, Dong J, Green LV (2016) Queues with time-varying arrivals and inspections with applications to hospital discharge policies. Oper. Res., ePub ahead of print October 27, https://doi.org/10.1287/opre.2016.1536.LinkGoogle Scholar
  • Choudhury G, Lucantoni D, Whitt W (1997) Numerical solution of piecewise-stationary Mt/Gt/1 queues. Oper. Res. 45(3):451–463.LinkGoogle Scholar
  • Clark GM (1981) Use of polya distributions in approximate solutions to nonstationary M/M/s queues. Commun. ACM 24(4):206–217.CrossrefGoogle Scholar
  • Feldman Z, Mandelbaum A, Massey WA, Whitt W (2008) Staffing of time-varying queues to achieve time-stable performance. Management Sci. 54(2):324–338.LinkGoogle Scholar
  • Gans N, Koole G, Mandelbaum A (2003) Telephone call centers: Tutorial, review, and research prospects. Manufacturing Service Oper. Management 5(2):79–141.LinkGoogle Scholar
  • Gao P, Wittevrongel S, Bruneel H (2004) Discrete-time multiserver queues with geometric service times. Comput. Oper. Res. 31(1):81–99.CrossrefGoogle Scholar
  • Green L, Kolesar PJ (1991) The pointwise stationary approximation for queues with nonstationary arrivals. Management Sci. 37(1):84–97.LinkGoogle Scholar
  • Green LV, Kolesar PJ (1997) The lagged PSA for estimating peak congestion in multiserver Markovian queues with periodic arrival rates. Management Sci. 43(1):80–87.LinkGoogle Scholar
  • Green LV, Kolesar PJ, Whitt W (2007) Coping with time-varying demand when setting staffing requirements for a service system. Production Oper. Management 16(1):13–39.CrossrefGoogle Scholar
  • Griffin J, Xia S, Peng S, Keskinocak P (2012) Improving patient flow in an obstetric unit. Health Care Management Sci. 15(1):1–14.CrossrefGoogle Scholar
  • Gross D, Harris CM (1985) Fundamentals of Queueing Theory (John Wiley & Sons, New York).Google Scholar
  • Gurvich I (2014) Diffusion models and steady-state approximations for exponentially ergodic Markovian queues. Ann. Appl. Probab. 24(6):2527–2559.CrossrefGoogle Scholar
  • Halfin S, Whitt W (1981) Heavy-traffic limits for queues with many exponential servers. Oper. Res. 29(3):567–588.LinkGoogle Scholar
  • Hoot N, Aronsky D (2008) Systematic review of emergency department crowding: Causes, effects, and solutions. Ann. Emergency Medicine 52(2):126–136.CrossrefGoogle Scholar
  • Huang Q, Thind A, Dreyer J, Zaric G (2010) The impact of delays to admission from the emergency department on inpatient outcomes. BMC Emergency Medicine 10:16.CrossrefGoogle Scholar
  • Ingolfsson A, Akhmetshina E, Budge S, Li Y, Wu X (2007) A survey and experimental comparison of service-level-approximation methods for nonstationary M(t)/M/s(t) queueing systems with exhaustive discipline. INFORMS J. Comput. 19(2):201–214.LinkGoogle Scholar
  • Jennings OB, Mandelbaum A, Massey WA, Whitt W (1996) Server staffing to meet time-varying demand. Management Sci. 42(10):1383–1394.LinkGoogle Scholar
  • Liu SW, Thomas SH, Gordon JA, Hamedani AG, Weissman JS (2009) A pilot study examining undesirable events among emergency department-boarded patients awaiting inpatient beds. Ann. Emergency Medicine 54(3):381–385.CrossrefGoogle Scholar
  • Liu Y, Whitt W (2011a) Large-time asymptotics for the Gt/Mt/st + GIt many-server fluid queue with abandonment. Queueing Systems 67(2):145–182.CrossrefGoogle Scholar
  • Liu Y, Whitt W (2011b) Nearly periodic behavior in the overloaded G/D/s + GI queue. Stochastic Systems 1(2):340–410.LinkGoogle Scholar
  • Liu Y, Whitt W (2011c) A network of time-varying many-server fluid queues with customer abandonment. Oper. Res. 59(4):835–846.LinkGoogle Scholar
  • Liu Y, Whitt W (2012a) Stabilizing customer abandonment in many-server queues with time-varying arrivals. Oper. Res. 60(6):1551–1564.LinkGoogle Scholar
  • Liu Y, Whitt W (2012b) The Gt/GI/st + GI many-server fluid queue. Queueing Systems 71:405–444.CrossrefGoogle Scholar
  • Mandelbaum A, Momcilovic P, Tseytlin Y (2012) On fair routing from emergency departments to hospital wards: QED queues with heterogeneous servers. Management Sci. 58(7):1273–1291.LinkGoogle Scholar
  • Massey WA, Whitt W (1994) An analysis of the modified offered-load approximation for the nonstationary Erlang loss model. Ann. Appl. Probab. 4(4):1145–1160.CrossrefGoogle Scholar
  • Pines JM, Batt RJ, Hilton JA, Terwiesch C (2011) The financial consequences of lost demand and reducing boarding in hospital emergency departments. Ann. Emergency Medicine 58(4):331–340.CrossrefGoogle Scholar
  • Powell ES, Khare RK, Venkatesh AK, Van Roo BD, Adams JG, Reinhardt G (2011) The relationship between inpatient discharge timing and emergency department boarding. J. Emergency Medicine 42(2):186–196.CrossrefGoogle Scholar
  • Ramakrishnan M, Sier D, Taylor P (2005) A two-time-scale model for hospital patient flow. IMA J. Management Math. 16(3):197–215.CrossrefGoogle Scholar
  • Ross N (2011) Fundamentals of Stein’s method. Probab. Surv. 8:210–293.CrossrefGoogle Scholar
  • Rothkopf MH, Oren SS (1979) A closure approximation for the nonstationary M/M/s queue. Management Sci. 25(6):522–534.LinkGoogle Scholar
  • Shi P (2013) Stochastic modeling and decision making in two healthcare applications: Inpatient flow management and influenza pandemics. Ph.D. thesis, Georgia Institute of Technology, Atlanta.Google Scholar
  • Shi P, Chou M, Dai JG, Ding D, Sim J (2016) Models and insights for hospital inpatient operations: Time-dependent ED boarding time. Management Sci. 62(1):1–28.LinkGoogle Scholar
  • Shi P, Dai JG, Ding D, Ang J, Chou M, Xin J, Sim J (2014) Patient flow from emergency department to inpatient wards: Empirical observations from a Singaporean hospital. https://ssrn.com/abstract_id=2517050.Google Scholar
  • Singer AJ, Thode J Henry C, Viccellio P, Pines JM (2011) The association between length of emergency department boarding and mortality. Acad. Emergency Medicine 18(12):1324–1329.CrossrefGoogle Scholar
  • U.S. Centers for Disease Control and Prevention (2010) Health, United States. http://www.cdc.gov/nchs/data/hus/hus10.pdf.Google Scholar
  • U.S. General Accounting Office (2003) Hospital Emergency Departments: Crowded Conditions Vary Among Hospitals and Communities. United States General Accounting Office, Washington, DC.Google Scholar
  • Whitt W (1991) The pointwise stationary approximation for Mt/Mt/s queues is asymptotically correct as the rates increases. Management Sci. 37(3):307–314.LinkGoogle 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.LinkGoogle Scholar
  • Zacharias C, Armony M (2016) Joint panel sizing and appointment scheduling in outpatient care. Management Sci., ePub ahead of print September 12, https://doi.org/10.1287/mnsc.2016.2532.LinkGoogle Scholar
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