3,895
Views
10
CrossRef citations to date
0
Altmetric
Original Articles

Infinite-server queueing models of demand in healthcare: A review of applications and ideas for further work

, &
Pages 1145-1160 | Received 02 Mar 2018, Accepted 13 Apr 2019, Published online: 31 May 2019

References

  • Alnowibet, K., & Perros, H. (2009). Nonstationary analysis of the loss queue and of queueing networks of loss queues. European Journal of Operational Research, 196(3), 1015–1030. doi: 10.1016/j.ejor.2007.10.066
  • Bagust, A., Place, M., & Posnett, J. W. (1999). Dynamics of bed use in accommodating emergency admissions: Stochastic simulation model. British Medical Journal, 319(7203), 155–158. doi: 10.1136/bmj.319.7203.155
  • Bekker, R., & de Bruin, A. M. (2010). Time-dependent analysis for refused admissions in clinical wards. Annals of Operations Research, 178(1), 45–65. doi: 10.1007/s10479-009-0570-z
  • Chow, V. S., M. L., Puterman, N., Salehirad, W., Huang, & Atkins, D. (2011). Reducing surgical ward congestion through improved surgical scheduling and uncapacitated simulation. Production and Operations Management, 20(3), 418–430. doi: 10.1111/j.1937-5956.2011.01226.x
  • de Bruin, A. M., Bekker, R., van Zanten, L., & Koole, G. M. (2010). Dimensioning hospital wards using the Erlang loss model. Annals of Operations Research, 178(1), 23–43. doi: 10.1007/s10479-009-0647-8
  • Economou, A., & Fakinos, D. (1999). The infinite server queue with arrivals generated by a non-homogeneous compound Poisson process and heterogeneous customers. Stochastic Models, 15(5), 993–1002.
  • Eick, S. G., Massey, W. A., & Whitt, W. (1993). The physics of the Mt/G/∞ queue. Operations Research, 41(4), 731–742. doi: 10.1287/opre.41.4.731
  • Fakinos, D. (1984). The infinite server queue with arrivals generated by a non-homogeneous compound Poisson process. Journal of the Operational Research Society, 35(5), 439–445. doi: 10.1057/jors.1984.85
  • Fu, M. C. (2014). Handbook of simulation optimization. M. C. Fu (Ed.), New York: Springer.
  • Gallivan, S. (2005). Mathematical methods to assist with hospital operation and planning. Clinical and Investigative Medicine, 28(6), 326–330.
  • Gallivan, S., & Utley, M. (2005). Modelling admissions booking of elective inpatients into a treatment centre. IMA Journal of Management Mathematics, 16(3), 305–315. doi: 10.1093/imaman/dpi024
  • Gallivan, S., Utley, M., Treasure, T., & Valencia, O. (2002). Booked inpatient admissions and hospital capacity: Mathematical modelling study. BMJ, 324(7332), 280–282. doi: 10.1136/bmj.324.7332.280
  • Gross, D., & Harris, C. M. (1985). Fundamentals of queueing theory (2nd ed.), Hoboken, NJ: Wiley.
  • Helm, J. E., & Van Oyen, M. P. (2014). Design and optimization methods for elective hospital admissions. Operations Research, 62(6), 1265–1282. doi: 10.1287/opre.2014.1317
  • Isken, M. W., Ward, T. J., & Littig, S. J. (2011). An open source software project for obstetrical procedure scheduling and occupancy analysis. Health Care Management Science, 14(1), 56–73. doi: 10.1007/s10729-010-9141-8
  • Izady, N., & Worthington, D. (2011). Approximate analysis of non-stationary loss queues and networks of loss queues with general service time distributions. European Journal of Operational Research, 213(3), 498–508. doi: 10.1016/j.ejor.2011.03.029
  • Izady, N., & Worthington, D. (2012). Setting staffing requirements for time dependent queueing networks: The case of accident and emergency departments. European Journal of Operational Research, 219(3), 531–540. doi: 10.1016/j.ejor.2011.10.040
  • Jennings, O. B., Mandelbaum, A., Massey, W. A., & Whitt, W. (1996). Server staffing to meet time-varying demand. Management Science, 42(10), 1383–1394. doi: 10.1287/mnsc.42.10.1383
  • Massey, W. A., & Whitt, W. (1993). Networks of infinite-server queues with nonstationary Poisson input. Queueing Systems, 13(1–3), 183–250. doi: 10.1007/BF01158933
  • Massey, W. A., & Whitt, W. (1994). An analysis of the modified offered load approximation for the Erlang loss model. The Annals of Applied Probability, 4(4), 1145–1160. doi: 10.1214/aoap/1177004908
  • Mitrani, I. (1998). Probabilistic modelling. Cambridge: Cambridge University Press.
  • Monks, T., Worthington, D., Allen, M., Pitt, M., Stein, K., & James, M. (2016). A modelling tool for capacity planning in acute and community stroke services. BMC Health Services Research, 16(1), 530 doi: 10.1186/s12913-016-1789-4
  • Newell, G. (1966). The M/G/∞ queue. SIAM Journal on Applied Mathematics, 14(1), 86–88. doi: 10.1137/0114007
  • Pagel, C., Banks, V., Pope, C., Whitmore, P., Brown, K., Goldman, A., & Utley, M. (2017). Development, implementation and evaluation of a tool for forecasting short term demand for beds in an intensive care unit. Operations Research for Health Care, 15, 19–31. http://dx.doi.org/10.1016/j.orhc.2017.08.003
  • Palm, C. (1943). Intensity variations in telephone traffic. Ericsson Technics, 44, 1–189 (in German), (English translation by North Holland, Amsterdam, 1988).
  • Suen, D. (2015). The development and application of an analytical healthcare model for understanding and improving hospital performance (Doctoral dissertation). Lancaster University, Lancaster.
  • Tan, K. W., Tan, W. H., & Lau, H. C. (2013). Improving patient length-of-stay in emergency department through dynamic resource allocation policies, IEEE International Conference on Automation Science and Engineering (CASE), 984–989.
  • Utley, M., Gallivan, S., Pagel, C., & Richards, D. (2009). Analytical methods for calculating the distribution of the occupancy of each state within a multi-state flow system. IMA Journal of Management Mathematics, 20(4), 345–355. doi: 10.1093/imaman/dpn031
  • Utley, M., Gallivan, S., Treasure, T., & Valencia, O. (2003). Analytical methods for calculating the capacity required to operate an elective booked admissions policy for elective inpatient services. Health Care Management Science, 6(2), 97–104.
  • Utley, M., Jit, M., & Gallivan, S. (2008). Restructuring routine elective services to reduce overall capacity requirements within a local health economy. Health Care Management Science, 11(3), 240–247.
  • Weiss, N. A., Holmes, P. T., & Hardy, M. (2006). A course in probability. Boston, MA: Pearson Addison Wesley.
  • Whitt, W. (2016). Queues with time-varying arrival rates: A bibliography. Working paper. New York: Columbia University.
  • Worthington, D. (2009). Reflections on queue modelling from the last 50 years. Journal of the Operational Research Society, 60(suppl. 1), S83–S92. doi: 10.1057/jors.2008.178
  • Xu, J., Lee, L. H., & Celik, N. (2014). Efficient multi-fidelity simulation optimization. Proceedings of the 2014 Winter Simulation Conference, 3941–3951.