On fair routing from emergency departments to hospital wards: QED queues with heterogeneous servers

Management Science

Volumn 58, Issue 7, 2012, Pages 1273-1291

  Mandelbaum, Avishai ^a   Momčilović, Petar ^b   Tseytlin, Yulia ^a,c  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^b J Crayton Pruitt Family Department of Biomedical Engineering   (United States)

^c UNIVERSITY OF HAIFA   (Israel)

Author keywords

Asymptotic analysis; Fairness; Healthcare; Heterogeneous servers; Hospital routing policies; Qualityand efficiency driven regime; Queueing systems

Indexed keywords

FAIRNESS; HETEROGENEOUS SERVERS; QUALITYAND EFFICIENCY-DRIVEN REGIME; QUEUEING SYSTEM; ROUTING POLICIES;

ASYMPTOTIC ANALYSIS; EMERGENCY ROOMS; HEALTH CARE; QUEUEING NETWORKS;

LAKES;

EID: 84864074121     PISSN: 00251909     EISSN: 15265501     Source Type: Journal    
DOI: 10.1287/mnsc.1110.1491     Document Type: Article

References (50)

1. Armony, M. 2005. Dynamic routing in large-scale service systems with heterogeneous servers. Queueing Syst. Theory Appl. 51 (3-4) 287-329.
2. Armony, M., A. Mandelbaum. 2012. Routing and staffing in largescale service systems: The case of homogeneous impatient customers and heterogeneous servers. Oper. Res. 59 (1) 50-65.
3. Armony, M., A. Ward. 2010. Fair dynamic routing policies in large-scale systems with heterogeneous servers. Oper. Res. 58 (3) 624-637.
4. Armony, M., S. Israelit, A. Mandelbaum, Y. Marmor, Y. Tseytlin, G. Yom-Tov. 2011. Patient flow in hospitals: A data-based queueing-science perspective. Working paper, New York University, New York.
5. Atar, R. 2008. Central limit theorem for a many-server queue with random service rates. Ann. Appl. Probab. 18 (4) 1548-1568.
6. Atar, R., Y. Y. Shaki, A. Shwartz. 2011. A blind policy for equalizing cumulative idleness. Queueing Systems Theory Appl. 67 (4) 275-293.
7. Avi-Itzhak, B., H. Levy. 2004. On measuring fairness in queues. Adv. Appl. Probab. 36 (3) 919-936.
8. Bekker, R., A. M. de Bruin. 2010. Time-dependent analysis for refused admissions in clinical wards. Ann. Oper. Res. 178 (1) 45-65.
9. Ben-Zrihen, M., J. Borsher, A. Reiss, Y. Tseytlin. 2007. Behavioral models in customer service centers. IE&M project, Industrial Engineering and Management, Technion, Haifa, Israel.
10. Borst, S., A. Mandelbaum, M. Reiman. 2004. Dimensioning of large call centers. Oper. Res. 52 (1) 17-34.
11. Cabral, F. B. 2005. The slow server problem for uninformed customers. Queueing Syst. Theory Appl. 50 (4) 353-370.
12. Cabral, F. B. 2007. Queues with heterogeneous servers and uninformed customers: Who works the most? Working paper, Universidade Federal de Pelotas, UNIPAMPA, Brazil.
13. Coffman, E. G., Jr., A. A. Puhalskii, M. I. Reiman. 1995. Polling systems with zero switchover times: A heavy-traffic averaging principle. Ann. Appl. Probab. 5 (3) 681-719.
14. Colquitt, J., D. Conlon, M. Wesson, C. Porter, K. Y. Ng. 2001. Justice at the millennium: A meta-analytic review of 25 years of organizational justice research. J. Appl. Psych. 86 (3) 425-445.
15. Dai, J., T. Tezcan. 2011. State space collapse in many-server diffusion limits of parallel server systems. Math Oper Res. 36 (2) 271-320.
16. de Bruin, A. M., R. Bekker, L. van Zanten, G. M. Koole. 2010. Dimensioning hospital wards using the Erlang loss model. Ann. Oper. Res. (1) 23-43.
17. de Véricourt, F., O. B. Jennings. 2011. Nurse staffing in medical units: A queueing perspective. Oper Res. 59 (6) 1320-1331.
18. Elkin, K., N. Rozenberg. 2007. Patients' flow from the emergency department to the internal wards. IE&M project, Industrial Engineering and Management, Technion, Haifa, Israel.
19. Erlang, A. K. 1948. On the rational determination of the number of circuits. E. Brockmeyer, H. L. Halstrom, A. Jensen, eds. The life and works of A. K. Erlang. Copenhagen Telephone Company, Copenhagen, 216-221.
20. Gans, N., G. Koole, A. Mandelbaum. 2003. Telephone call centers: Tutorial, review, and research prospects. Manufacturing Service Oper. Management 5 (2) 79-141.
21. González, P., C. Herrero. 2004. Optimal sharing of surgical costs in the presence of queues. Math. Methods Oper. Res. 59 (3) 435-446.
22. Green, L. V. 2004. Capacity planning and management in hospitals. M. L. Brandeau, F. Sainfort, W. P. Pierskalla, eds. Operations Research and Health Care: A Handbook of Methods and Applications. International Series in Operations Research & Management Science. Kluwer, Norwell, MA, 15-42.
23. Green, L. V. 2008. Using operations research to reduce delays for healthcare. Z.-L. Chen, S. Raghavan, eds. Tutorials in Operations Research. INFORMS, Hanover, MD, 1-16.
24. Gurvich, I., W. Whitt. 2009. Queue-and-idleness-ratio controls in many-server service systems. Math. Oper. Res. 34 (2) 363-396.
25. Halfin, S., W. Whitt. 1981. Heavy-traffic limits for queues with many exponential servers. Oper. Res. 29 (3) 567-588.
26. Huseman, R. C., J. D. Hatfield, E. W. Miles. 1987. A new perspective on equity theory: The equity sensitivity construct. Acad. Management Rev. 12 (2) 222-234.
27. Joint Commission on the Accreditation of Healthcare Organizations (JCAHO). 2004. JCAHO requirement: New leadership standard on managing patient flow for hospitals. Joint Commission Perspectives 24 (2) 13-14.
28. Kc, D. S., C. Terwiesch. 2009. Impact of workload on service time and patient safety: An econometric analysis of hospital operations. Management Sci. 55 (9) 1486-1498.
29. Kelly, F. 1979. Reversibility and Stochastic Networks. Wiley, New York.
30. Larsen, R. L., A. K. Agrawala. 1983. Control of a heterogeneous two-server exponential queueing system. IEEE Trans. Software Engrg. 9 (4) 522-526.
31. Larson, R. C. 1987. Perspectives on queues: Social justice and the psychology of queueing. Oper. Res. 35 (6) 895-905.
32. Lin, W., P. R. Kumar. 1984. Optimal control of a queueing system with two heterogeneous servers. IEEE Trans. Automat. Control 29 (8) 696-703.
33. Litvak, E., M. C. Long, A. B. Cooper, M. L. McManus. 2001. Emergency department diversion: Causes and solutions. Acad. Emerg. Med. 8 (11) 1108-1110.
34. Mandelbaum, A., P. Momčilović, Y. Tseytlin. 2011. Online appendices to "On fair routing from emergency departments to hospital wards: QED queues with heterogeneous servers." http://iew3.technion. ac.il/serveng/References/.
35. McManus, M. L., M. C. Long, A. Cooper, E. Litvak. 2004. Queuing theory accurately models the need for critical care resources. Anesthesiology 100 (5) 1271-1276.
36. New York Times. 2002. 1 in 3 hospitals say they divert ambulances. (April 9), http://www.nytimes.com/2002/04/09/us/1-in-3-hospitals-say-they-divert- ambulances.html.
37. Rafaeli, A., G. Barron, K. Haber. 2002. The effects of queue structure on attitudes. J. Service Res. 5 (2) 125-139.
38. Ramakrishnan, M., D. Sier, P. G. Taylor. 2005. A two-time-scale model for hospital patient flow. IMA J. Management Math. 16 (3) 197-215.
39. Rubinovitch, M. 1985a. The slow server problem. J. Appl. Probab. 22 (1) 205-213.
40. Rubinovitch, M. 1985b. The slow server problem: A queue with stalling. J. Appl. Probab. 22 (4) 309-317.
41. Stockbridge, R. H. 1991. A martingale approach to the slow server problem. J. Appl. Probab. 28 (2) 480-486.
42. Tseytlin, Y. 2009. Queueing systems with heterogeneous servers: On fair routing of patients in emergency departments. M. Sc. thesis, Industrial Engineering and Management, Technion, Haifa, Israel.
43. Tseytlin, Y., A. Zviran. 2009. Simulation of patients routing from an emergency department to internal wards in Anonymous Hospital. IE&M project, Industrial Engineering and Management, Technion, Haifa, Israel.
44. Whitt, W. 2002. Stochastic-Process Limits: An Introduction to Stochastic-Process Limits and Their Application to Queues. Springer, New York.
45. Williams, R. 2000. It all adds up. Nurs. Stand. 14 (31) 12-13.
46. Wright, J., R. King. 2006. We All Fall Down: Goldratt's Theory of Constraints for Healthcare Systems. North River Press, Great Barrington, MA.
47. Yom-Tov, G. 2007. Queues in hospitals: Semi-open queueing networks in the QED regime. Technical report, Industrial Engineering and Management, Technion, Haifa, Israel.
48. Yom-Tov, G. 2010. Queues in hospitals: Queueing networks with ReEntering customers in the QED regime (QED =Quality-and Efficiency-Driven). Ph. D. thesis, Technion, Haifa, Israel.
49. Yom-Tov, G., A. Mandelbaum. 2011. Erlang-R: A time-varying queue with ReEntrant customers, in support of healthcare staffing. Working paper, Industrial Engineering and Management, Technion, Haifa, Israel.
50. Zhang, B., J. S. H. van Leeuwaarden, B. Zwart. 2012. Staffing call centers with impatient customers: Refinements to many-server asymptotics. Oper. Res 60 (2) 461-474.