Appointments in care pathways: the Geox/D/1 queue with slot reservations

Maartje E. Zonderland*, Richard J. Boucherie, Ahmad Al Hanbali

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Motivated by the increasing popularity of care pathways in outpatient clinics, where some patients complete a significant part of the path in one day, hospitals aim to optimize the flow of these patients by prioritizing them in the appointment planning process. This paper considers the Geox/D/1 queue with slot reservations that serves regular patients and priority patients. Priority patients reserve a time slot in a reservation window and are blocked when all slots in the reservation window are occupied by other priority patients. The reservation window models the advance reservation of service slots by patients on a care pathway. We model the Geox/D/1 queue as a M/G/1-type queue and apply a matrix-analytic approach, which simplifies to a matrix-geometric solution. We use the vector generating functions to derive the patients’ waiting times. Numerical experiments illustrate the influence of the reservation window on the number of regular and priority patients present and the blocking probabilities for priority patients.

Original languageEnglish
Pages (from-to)37-51
Number of pages15
JournalQueueing Systems
Issue number1
StatePublished - Jan 2014
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2014, Springer Science+Business Media New York.


  • Appointment planning
  • Care pathways
  • Healthcare
  • Matrix-geometric analysis
  • Probability generating functions

ASJC Scopus subject areas

  • Statistics and Probability
  • Computer Science Applications
  • Management Science and Operations Research
  • Computational Theory and Mathematics


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