Skip Navigation



IMA Journal of Management Mathematics Advance Access published online on December 3, 2008
IMA Journal of Management Mathematics, doi:10.1093/imaman/dpn031
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
20/4/345    most recent
dpn031v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Utley, M.
Right arrow Articles by Richards, D.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The authors 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Analytical methods for calculating the distribution of the occupancy of each state within a multi-state flow system

Martin Utley{dagger}, Steve Gallivan{ddagger} and Christina Pagel§

Clinical Operational Research Unit, University College London,Gower Street, London WC1E 6BT, UK

David Richards

Department of Health Sciences, University of York, Heslington, York YO10 5DD, UK

{dagger} Corresponding author. Email: m.utley{at}ucl.ac.uk

{ddagger} Email: s.gallivan{at}ucl.ac.uk

§ Email: c.pagel{at}ucl.ac.uk

Email: dr17{at}york.ac.uk

Received on 1 May 2007. Accepted on 1 January 2008.

We present analytical techniques for estimating the time-varying occupancy of each state within any multi-state flow system that can be represented as a particular type of directed graph called a rooted directed tree. Such systems have a single point of entry from which each other state within the system can be reached by exactly one directed path. The discrete-time model presented incorporates the use of time-varying and general distributions for the number of individuals entering the system and of general sojourn time distributions for each state. We illustrate the use of such analysis in the context of the delivery of mental health services in the community for people with common mental health problems and then discuss the possibility of adapting these methods with relation to systems that have a structure more complex than that of a rooted directed tree.

Keywords: stochastic analysis; capacity planning; patient flow; rooted directed trees; compartmental models


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.