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

Chaithanya Bandi (c-bandi***at***kellogg.northwestern.edu)
Nikolaos Trichakis (ntrichakis***at***mit.edu)
Phebe Vayanos (phebe.vayanos***at***usc.edu)

Abstract: In this paper we study systems that allocate different types of scarce resources to heterogeneous allocatees based on predetermined priority rules, e.g., 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:

Category 1: Robust Optimization

Category 2: Applications -- OR and Management Sciences

Citation: In this paper we study systems that allocate different types of scarce resources to hetero- geneous allocatees based on predetermined priority rules, e.g., 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 as- signment 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.

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Entry Submitted: 04/07/2016
Entry Accepted: 04/07/2016
Entry Last Modified: 10/29/2017

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