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Queuing Networks in Health Care Systems

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Handbook of Healthcare System Scheduling

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 168))

Abstract

Over the last decades, the concept of patient flow has received an increased amount of attention. Health care professionals have become aware that in order to analyze the performance of a single health care facility, its relationship with other health care facilities should also be taken into account. A natural choice for analysis of networks of health care facilities is queuing theory. With a queuing network a fast and flexible analysis is provided that discovers bottlenecks and allows for the evaluation of alternative set-ups of the network. In this chapter we describe how queuing theory, and networks of queues in particular, can be invoked to model, study, analyze, and solve health care problems. We describe important theoretical queuing results, give a review of the literature on the topic, discuss in detail two examples of how a health care problem is analyzed using a queuing network, and suggest directions for future research.

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Notes

  1. 1.

    We consider the system in statistical equilibrium only, as is customary in queuing theory. For the \(M/M/1\) queue, relaxation or convergence to equilibrium usually occurs fast. See Green et al. (2001) for a discussion on the validity of equilibrium analysis.

  2. 2.

    Many hospitals aim for a mean utilization of 85% and a blocking probability below 5% at the same time. This is only possible when the ward has a large (around 50) number of beds (Bruin et al. 2010).

References

  • Aaby K, Herrmann JW, Jordan CS, Treadwell M, Wood K (2006) Montgomery county’s public health service uses operations research to plan emergency mass dispensing and vaccination clinics. Interfaces 36(6):569–579

    Article  Google Scholar 

  • Adan I, van der Wal J (2011) Mean values techniques. In: Boucherie RJ, Dijk NM (eds) Queueing networks: a fundamental approach. Springer, New York

    Google Scholar 

  • Albin SL, Barrett J, Ito D, Mueller JE (1990) A queueing network analysis of a health center. Queueing Syst 7:51–61

    Article  Google Scholar 

  • American Society of Anesthesiologists (2011) www.asahq.org/For-Members/Clinical-Information/ASA-Physical-Status-Classification-System.aspx, Retrieved April 20, 2011

    Google Scholar 

  • Asaduzzaman Md, Chaussalet TJ, Robertson NJ (2010) A loss network model with overflow for capacity planning of a neonatal unit. Ann Oper Res 178:67–76

    Article  Google Scholar 

  • Asaduzzaman Md, Chaussalet TJ, Adeyemi S et al (2010) Towards effective capacity planning in a perinatal network centre. Arch Dis Child Fetal Neonatal 95:F283–287

    Article  Google Scholar 

  • Bailey NTJ (1952) A study of queues and appointment systems in hospital out-patient departments, with special reference to waiting-times. J Royal Stat Soc, Ser B-Stat Methodol 14(2):185–199

    Google Scholar 

  • Baskett F, Chandy KM, Muntz RR, Palacios FG (1975) Open, closed, and mixed networks of queues with different classes of customers. J Assoc Comput Mach 22(2):248–260

    Google Scholar 

  • Bitran GR, Morabito R (1996) Survey open queueing networks: optimization and performance evaluation models for discrete manufacturing systems. Prod Oper Manag 5(2):163–193

    Article  Google Scholar 

  • Blair EL, Lawrence CE (1981) A queueing network approach to health care planning with an application to burn care in New York state. Socio-Econ Plan Sci 15(5):207–216

    Article  Google Scholar 

  • Boucherie RJ, van Dijk NM (2011) Queueing networks: a fundamental approach. Springer, New York

    Book  Google Scholar 

  • Brockmeyer E, Halström HL, Jensen A (1948) The life and works of A.K. Erlang. Translations of the Danish academy of technical sciences 2

    Google Scholar 

  • de Bruin AM, Bekker R, van Zanten L, Koole GM (2010) Dimensioning hospital wards using the Erlang loss model. Ann Oper Res 178(1):23–43

    Article  Google Scholar 

  • Burke PJ (1956) The output of a queuing system. Oper Res 4(6):699–704

    Article  Google Scholar 

  • Buzacott JA, Shanthikumar JG (1993) Stochastic models of manufacturing systems. Prentice Hall, Englewood Cliffs

    Google Scholar 

  • Buzen JP (1973) Computational algorithms for closed queueing networks with exponential servers. Commun ACM 16(9):527–531

    Article  Google Scholar 

  • Chaussalet TJ, Xie H, Millard P (2006) A closed queueing network approach to the analysis of patient flow in health care systems. Methods Info Med 45(5):492–497

    Google Scholar 

  • Cochran JK, Bharti A (2006) A multi-stage stochastic methodology for whole hospital bed planning under peak loading. Int J Ind Syst Eng 1(1-2):8–36

    Google Scholar 

  • Cochran JK, Bharti A (2006) Stochastic bed balancing of an obstetrics hospital. Health Care Manag Sci 9(1):31–45

    Article  Google Scholar 

  • Cochran JK, Roche KT (2008) A multi-class queueing network analysis methodology for improving hospital emergency department performance. Comput Oper Res 36(5):1497–1512

    Article  Google Scholar 

  • Cohen JW (1982) The single server queue, 8th edn. North-Holland Publishing Company, Amsterdam

    Google Scholar 

  • Creemers S, Lambrecht M Modeling a hospital queueing network. In: Boucherie RJ, Dijk NM (eds) Queueing networks: a fundamental approach. Springer, New York (2011)

    Google Scholar 

  • Fackrell M (2009) Modelling health care systems with phase-type distributions. Health Care Manag Sci 12(1):11–26

    Article  Google Scholar 

  • Ferschl MB, Tung A, Sweitzer B, Huo D, Glick DB (2005) Preoperative clinic visits reduce operating room cancellations and delays. Anesthesiology 103(4):855–859

    Article  Google Scholar 

  • Free University, Department of Mathematics, Erlang-C calculator, www.few.vu.nl/koole/ccmath/ErlangC/

    Google Scholar 

  • Gordon WJ, Newell GF (1967) Closed queuing systems with exponential servers. Oper Res 15(2):254–265

    Article  Google Scholar 

  • Green LV, Kolesar PJ, Soares J (2001) Improving the SIPP approach for staffing service systems that have cyclic demands. Oper Res 49(4):549–564

    Article  Google Scholar 

  • Green LV (2006) Queueing analysis in health care. In: Hall RW (eds) Patient flow: reducing delay in health care delivery. Springer, New York

    Google Scholar 

  • Green LV, Soares J, Giglio JF, Green RA (2006) Using queueing theory to increase the effectiveness of emergency department provider staffing. Acad Emerg Med 13(1):61–68

    Article  Google Scholar 

  • Gross D, Shortle JF, Harris CM (2008) Fundamentals of queueing theory, 4th edn. Wiley, Hoboken

    Google Scholar 

  • Jackson JR (1957) Networks of waiting lines. Oper Res 5(4):518–521

    Article  Google Scholar 

  • Jiang L, Giachetti RE (2007) A queueing network model to analyze the impact of parallelization of care on patient cycle time. Health Care Manag Sci 11(3):248–261

    Article  Google Scholar 

  • Kelly FP (1979) Reversibility and stochastic networks. Available online via www.statslab.cam.ac.uk/frank/rsn.html

    Google Scholar 

  • Kelly FP (1991) Loss networks. Ann Appl Probab 1(3):319–378

    Article  Google Scholar 

  • Kleinrock L (1967) Queuing systems: theory, vol 1. Wiley, New York

    Google Scholar 

  • Kleinrock L (1976) Queueing systems: computer applications, vol 2. Wiley, New York

    Google Scholar 

  • Koizumi N, Kuno E, Smith TE (2005) Modeling patient flows using a queueing network with blocking. Health Care Manag Sci 8(1):49–60

    Article  Google Scholar 

  • Latouche G, Ramaswami V (1999) Introduction to matrix analytic methods in stochastic modeling. American Statistical Association and the Society for Industrial and Applied Mathematics, USA

    Google Scholar 

  • Latouche G, Taylor P (2002) Matrix-analytic methods: theory and applications. In: Proceedings of the fourth international conference, Adelaide. Imperial College Press, London

    Google Scholar 

  • Law AM, Kelton WD (1991) Simulation modeling and analysis. McGraw-Hill, New York

    Google Scholar 

  • Lee DKK, Zenios SA (2009) Optimal capacity overbooking for the regular treatment of chronic conditions. Oper Res 57(4):852–865

    Article  Google Scholar 

  • Little JDC (1961) A proof for the queuing formula \(L = \lambda W\). Oper Res 9(3):383–387

    Google Scholar 

  • Nelson RD (1995) Probability, stochastic processes, and queueing theory: the mathematics of computer performance modelling. Springer, New York

    Google Scholar 

  • Organisation for Economic Co-operation and Development (2011) www.oecd.org, Retrieved on April 19, 2011

    Google Scholar 

  • Research Institute CHOIR, University of Twente, Enschede, The Netherlands (2011) ORchestra bibliography. www.utwente.nl/choir/en/orchestra/

    Google Scholar 

  • Osorio C, Bierlaire M (2009) An analytic finite capacity queueing network model capturing the propagation of congestion and blocking. Eur J Oper Res 196(3):996–1007

    Article  Google Scholar 

  • Patient Flow Improvement Center Amsterdam, Erlang-B calculator www.vumc.nl/afdelingen/pica/Software/erlang_b/

    Google Scholar 

  • QtsPlus Software, ftp://ftp.wiley.com/public/sci_tech_med/queuing_theory/

    Google Scholar 

  • Taha HA (1997) Operations research: an introduction. Prentice Hall, Englewood Cliffs

    Google Scholar 

  • Takagi H (2000) Analysis and application of polling models. In: Haring G, Lindemann C, Reiser M (eds) Performance evaluation: origins and directions. Lecture Notes in Computer Science 1769, Springer, Berlin

    Google Scholar 

  • Tijms HC (2003) A first course in stochastic models. Wiley, Chichester

    Book  Google Scholar 

  • Vanberkel PT, Boucherie RJ, Hans EW, Hurink JL, Litvak N (2010) A survey of health care models that encompass multiple departments. Int J Health Manag Info 1(1):37–69

    Google Scholar 

  • van Dijk NM, Kortbeek N (2009) Erlang loss bounds for OT–ICU systems. Queueing syst 63(1):253–280

    Article  Google Scholar 

  • Westbay Online Traffic Calculators, www.erlang.com/calculator

    Google Scholar 

  • Whitt W (1983) The queueing network analyzer. Bell Syst Tech J 62(9):2779–2815

    Google Scholar 

  • Winston WL (1994) Operations research: applications and algorithms, 3rd edn. Duxbury Press, Belmont

    Google Scholar 

  • Wolff RW (1989) Stochastic modeling and the theory of queues. Prentice Hall, Englewood Cliffs

    Google Scholar 

  • Xie H, Chaussalet T, Rees M (2007) A semi-open queueing network approach to the analysis of patient flow in health care systems. IEEE proceedings twentieth IEEE international symposium on computer-based medical systems, pp 719–724

    Google Scholar 

  • Zachary S, Ziedins I (2011) Loss networks. In: Boucherie RJ, Dijk NM (eds) Queueing networks: a fundamental approach. Springer, New York

    Google Scholar 

  • Zeng G (2003) Two common properties of the Erlang-B function, Erlang-C function, and Engset blocking function. Math Comput Model 37(12–13):1287–1296

    Article  Google Scholar 

  • Zonderland ME, Boer F, Boucherie RJ, de Roode A, van Kleef JW (2009) Redesign of a university hospital preanesthesia evaluation clinic using a queuing theory approach. Anesthesia Analg 109(5):1612–1621

    Article  Google Scholar 

  • Zonderland ME, Boucherie RJ, Litvak N, Vleggeert-Lankamp LCAM (2010) Planning and scheduling of semi-urgent surgeries. Health Care Manag Sci 13(3):256–267

    Article  Google Scholar 

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Authors and Affiliations

  1. Stochastic Operations Research & Center for Health Care Operations Improvement and Research, University of Twente, Postbox 217, 7500 AE, Enschede, The Netherlands

    Maartje E. Zonderland & Richard J. Boucherie

  2. Division I, Leiden University Medical Center, Postbox 9600, 2300 RC, Leiden, The Netherlands

    Maartje E. Zonderland

Authors
  1. Maartje E. Zonderland
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  2. Richard J. Boucherie
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Correspondence to Maartje E. Zonderland .

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  1. Viterbi School of Engineering, Dept. Industrial & Systems Engineering, University of Southern California, McClintock Ave. 3715, Los Angeles, 90089-0193, California, USA

    Randolph Hall

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Zonderland, M.E., Boucherie, R.J. (2012). Queuing Networks in Health Care Systems. In: Hall, R. (eds) Handbook of Healthcare System Scheduling. International Series in Operations Research & Management Science, vol 168. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-1734-7_9

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