Robust Multiclass Queuing Theory for Wait Time Estimation in Resource Allocation Systems

Chaithanya Bandi (), Nikolaos Trichakis () and Phebe Vayanos ()
Additional contact information
Chaithanya Bandi: Kellogg School of Management, Northwestern University, Evanston, Illinois 60208
Nikolaos Trichakis: MIT Sloan School of Management and Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Phebe Vayanos: Departments of Industrial and Systems Engineering and Computer Science and Center for Artificial Intelligence in Society, Viterbi School of Engineering, University of Southern California, Los Angeles, California 90089

Management Science, 2019, vol. 65, issue 1, 152-187

Abstract: In this paper, we study systems that allocate different types of scarce resources to heterogeneous allocatees based on predetermined priority rules—the U.S. deceased-donor kidney allocation system or the public housing program. We tackle the problem of estimating the wait time of an allocatee who possesses incomplete system information with regard, for example, to his relative priority, other allocatees’ preferences, and resource availability. We model such systems as multiclass, multiserver queuing systems that are potentially unstable or in transient regime. We propose a novel robust optimization solution methodology that builds on the assignment problem. For first-come, first-served systems, our approach yields a mixed-integer programming formulation. For the important case where there is a hierarchy in the resource types, we strengthen our formulation through a drastic variable reduction and also propose a highly scalable heuristic, involving only the solution of a convex optimization problem (usually a second-order cone problem). We back the heuristic with an approximation guarantee that becomes tighter for larger problem sizes. We illustrate the generalizability of our approach by studying systems that operate under different priority rules, such as class priority. Numerical studies demonstrate that our approach outperforms simulation. We showcase how our methodology can be applied to assist patients in the U.S. deceased-donor kidney waitlist. We calibrate our model using historical data to estimate patients’ wait times based on their kidney quality preferences, blood type, location, and rank in the waitlist.

Keywords: queuing theory; robust optimization; resource allocation; healthcare (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://doi.org/10.1287/mnsc.2017.2948 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:65:y:2019:i:1:p:152-187

Access Statistics for this article

More articles in Management Science from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().