Queueing Systems

, Volume 79, Issue 1, pp 87–115 | Cite as

A model for deceased-donor transplant queue waiting times

  • Steve Drekic
  • David A. Stanford
  • Douglas G. Woolford
  • Vivian C. McAlister


In many jurisdictions, organ allocation is done on the basis of the health status of the patient, either explicitly or implicitly. This paper presents a self-promoting priority queueing model for patient waiting times which takes into account changes in health status over time. In this model, most patients arrive as “regular” customers to the queue, but as the health of a patient degrades, their status is promoted to “priority” to reflect the increased urgency of the transplant. We model the queueing system as a level-dependent quasi-birth-and-death process, and the steady-state joint queue length distribution as well as the marginal delay distributions for each queue are computed via the use of matrix analytic techniques. The model is calibrated using liver transplantation wait-list data, provided by a regional health centre in Canada, which tracked approximately 1,100 patients over nearly 13 years. Blood-type-specific models are fit and performance measures, such as the mean and distribution of the time until transplant, are obtained and compared to empirical estimates calculated using the raw data.


Abandonments Competing risks Estimation Liver transplantation Phase-type distribution Quasi-birth-and-death process Reneging 

Mathematics Subject Classification

60K25 90B22 



The authors thank the Associate Editor and the referees for their useful comments and valuable suggestions that helped improve this paper. The authors also wish to thank D. Bellhouse who suggested we consider a competing risks framework for calibrating our model. This research was supported by the Natural Sciences and Engineering Research Council of Canada through its Discovery Grants program.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Steve Drekic
    • 1
  • David A. Stanford
    • 2
  • Douglas G. Woolford
    • 3
  • Vivian C. McAlister
    • 4
  1. 1.Department of Statistics and Actuarial ScienceUniversity of WaterlooWaterlooCanada
  2. 2.Department of Statistical & Actuarial SciencesWestern UniversityLondonCanada
  3. 3.Department of MathematicsWilfrid Laurier UniversityWaterlooCanada
  4. 4.Department of SurgeryWestern UniversityLondonCanada

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