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IMA Journal of Management Mathematics Advance Access published online on January 25, 2006
IMA Journal of Management Mathematics, doi:10.1093/imaman/dpi042
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© The authors 2006. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
Received December 13, 2004
Accepted September 22, 2005

Article

A queueing model of activities in an intensive care unit

J. D. Griffiths 1 *, N. Price-Lloyd 1, M. Smithies 2, and J. Williams 1

1 School of Mathematics, Cardiff University, UK
2 Critical Care Unit, University of Wales Hospital, Cardiff, UK

* To whom correspondence should be addressed.
J. D. Griffiths, E-mail: griffiths{at}cardiff.ac.uk


  Abstract

Activities in an intensive care unit (ICU) at a major teaching hospital are modelled by means of a queue-theoretic approach. Using data supplied by the ICU relating to the admissions process, the bed availability and the length of stay of patients, it was possible to fit theoretical distributions to the observed ‘arrival’ and ‘service’ distributions. Queueing equations relevant to a multi-channel system having random arrivals and hyper-exponential service times for each channel are set up, and solved iteratively. Results obtained match well with observations, and the model is then utilised to investigate several ‘what if?’ scenarios. Reference is made to a simulation model developed in conjunction with the queueing model.

Keywords: queues; intensive care unit; bed-management.
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