A loss network model with overflow for capacity planning of a neonatal unit

Abstract

The main aim of this paper is to derive a solution to the capacity problem faced by many perinatal networks in the United Kingdom. We propose a queueing model to determine the number of cots at all care units for any desired overflow and rejection probability in a neonatal unit. The model formulation is developed, being motivated by overflow models in telecommunication systems. Exact expressions for the overflow and rejection probabilities are derived. The model is then applied to a neonatal unit of a perinatal network in the UK.

This is a preview of subscription content, access via your institution.

References

  1. Abdalla, N., & Boucherie, R. J. (2002). Blocking probabilities in mobile communications networks with time-varying rates and redialing subscribers. Annals of Operations Research, 112, 15–34.

    Article  Google Scholar 

  2. Asaduzzaman, M., & Chaussalet, T. J. (2008). Modelling and performance measure of a perinatal network centre in the United Kingdom. In Proceedings of the 21th IEEE international symposium on computer-based medical systems (pp. 506–511).

  3. BLISS (2005). Neonatal Services—are they improving? BLISS—The Premature Baby Charity.

  4. Boucherie, R. J., & Mandjes, M. (1998). Estimation of performance measures for product form cellular mobile communications networks. Telecommunication Systems, 10, 321–354.

    Article  Google Scholar 

  5. Chaussalet, T. J., Xie, H., & Millard, P. (2006). A closed queueing approach to the analysis of patient flow in health care systems. Methods of Information in Medicine, 5, 492–497.

    Google Scholar 

  6. Davis, J. L., Massey, W. A., & Whitt, W. (1995). Sensitivity to the service-time distribution in the nonstationary Erlang loss model. Management Science, 41(6), 1107–1116.

    Article  Google Scholar 

  7. DH (2005). Report of the neonatal intensive care services review group. Department of Health.

  8. Erhardsson, T. (2001). On the number of lost customers in stationary loss systems in the light traffic case. Queueing Systems, 38(1), 25–47.

    Article  Google Scholar 

  9. Ferreira, R. B., Coelli, F. C., Pereira, W. C., & Almeida, R. M. (2008). Optimizing patient flow in a large hospital surgical centre by means of discrete-event computer simulation models. Journal of Evaluation in Clinical Practice, 14, 1031–1037.

    Article  Google Scholar 

  10. Gła̧bowski, M., Kubasik, K., & Stasiak, M. (2008). Modeling of systems with overflow multi-rate traffic. Telecommunication Systems, 37, 85–96.

    Article  Google Scholar 

  11. Griffiths, J. D., Price-Lloyds, N., Smithies, M., & Williams, J. (2006). A queueing model of activities in an intensive care unit. IMA Journal of Management Mathematics, 17(3), 277–288.

    Article  Google Scholar 

  12. Jiang, L., & Giachetti, R. E. (2008). A queueing network model to analyze the impact of parallelization of care on patient cycle time. Health Care Management Science, 11, 248–261.

    Article  Google Scholar 

  13. Kelly, F. P. (1979). Reversibility and stochastic networks. Chichester: Wiley.

    Google Scholar 

  14. Kelly, F. P. (1991). Loss network. Annals of Applied Probability, 1(3), 319–378.

    Article  Google Scholar 

  15. Kim, S. C., Horowitz, I., Young, K. K., & Buckley, T. A. (1999). Analysis of capacity management of the intensive care unit in a hospital. European Journal of Operational Research, 115(1), 36–46.

    Article  Google Scholar 

  16. Koizumi, N., Kuno, E., & Smith, T. E. (2005). Modelling patient flows using a queuing network with blocking. Health Care Management Science, 8(1), 49–60.

    Article  Google Scholar 

  17. Kortbeek, N., & van Dijk, N. M. (2007). On dimensioning intensive care units. AENORM, 57, 22–26.

    Google Scholar 

  18. Litvak, N., van Rijsbergen, M., Boucherie, R. J., & van Houdenhoven, M. (2008). Managing the over flow of intensive care patients. European Journal of Operational Research, 185(3), 998–1010.

    Article  Google Scholar 

  19. Parmanum, J., Field, D., Rennie, J., & Steer, P. (2000). National census of availability of neonatal intensive care. British Medical Journal, 321(7263), 727–729.

    Article  Google Scholar 

  20. RCPCH (2007). Modelling the future: A consultation paper on the future of children’s health services. Royal College of Paediatrics and Child Health.

  21. Ridge, J., Jones, S., Nielsen, M., & Shahani, A. (1998). Capacity planning for intensive care units. European Journal of Operational Research, 105(2), 346–355.

    Article  Google Scholar 

  22. Sendfeld, P. (2008). Two queues with weighted one-way overflow. Methodology and Computing in Applied Probability, 10(4), 531–555.

    Article  Google Scholar 

  23. van Dijk, N. M. (1993). Queueing networks and product forms: a systems approach. Chichester: Wiley.

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Md Asaduzzaman.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Asaduzzaman, M., Chaussalet, T.J. & Robertson, N.J. A loss network model with overflow for capacity planning of a neonatal unit. Ann Oper Res 178, 67–76 (2010). https://doi.org/10.1007/s10479-009-0548-x

Download citation

Keywords

  • Neonatal unit
  • Overflow probability
  • Rejection probability
  • Queueing network
  • OR in health care