TY - JOUR

T1 - A double-ended queueing model for dynamic allocation of live organs based on a best-fit criterion

AU - Elalouf, Amir

AU - Perlman, Yael

AU - Yechiali, Uri

N1 - Publisher Copyright:
© 2018 Elsevier Inc.

PY - 2018/8

Y1 - 2018/8

N2 - We propose a novel approach, based on a Human Leukocyte Antigen (HLA) best-fit criterion, to dynamically allocate live organs (specifically, kidneys) to candidates needing transplantation. A ‘reward’ is assigned to each level of HLA fit, such that higher rewards are attributed to transplants between better-matched candidates and kidneys. We also envision future technologies by which it will be possible to store organs so that two queues may form: waiting candidates or stored kidneys. Consequently, a double-ended queue of candidates and kidneys is constructed, where the lifetime of a stored kidney is random, and candidates queueing for transplantation may die (‘renege’) while waiting. We derive expressions for the probability that a candidate gets a kidney before reneging; for the mean numbers of waiting candidates and of stored kidneys; and for a candidate's or kidney's mean sojourn time. Assuming a best-HLA-fit matching policy, we study three measures of effectiveness: (i) Rate of Reward from Transplantation (RRT); (ii) Expected Reward per Transplantation (ERT), calculated as RRT divided by the rate of performed transplantations, and (iii) Gained rate of reward per one dollar of expenditure. The optimal fraction of kidneys that should be stored so as to maximize the rate of reward per one dollar of expenditure is numerically determined.

AB - We propose a novel approach, based on a Human Leukocyte Antigen (HLA) best-fit criterion, to dynamically allocate live organs (specifically, kidneys) to candidates needing transplantation. A ‘reward’ is assigned to each level of HLA fit, such that higher rewards are attributed to transplants between better-matched candidates and kidneys. We also envision future technologies by which it will be possible to store organs so that two queues may form: waiting candidates or stored kidneys. Consequently, a double-ended queue of candidates and kidneys is constructed, where the lifetime of a stored kidney is random, and candidates queueing for transplantation may die (‘renege’) while waiting. We derive expressions for the probability that a candidate gets a kidney before reneging; for the mean numbers of waiting candidates and of stored kidneys; and for a candidate's or kidney's mean sojourn time. Assuming a best-HLA-fit matching policy, we study three measures of effectiveness: (i) Rate of Reward from Transplantation (RRT); (ii) Expected Reward per Transplantation (ERT), calculated as RRT divided by the rate of performed transplantations, and (iii) Gained rate of reward per one dollar of expenditure. The optimal fraction of kidneys that should be stored so as to maximize the rate of reward per one dollar of expenditure is numerically determined.

KW - Double-ended queue

KW - Dynamic organ allocation

KW - HLA best-fit

KW - Organ preservation

KW - Reneging

UR - http://www.scopus.com/inward/record.url?scp=85044750792&partnerID=8YFLogxK

U2 - 10.1016/j.apm.2018.03.022

DO - 10.1016/j.apm.2018.03.022

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SN - 0307-904X

VL - 60

SP - 179

EP - 191

JO - Applied Mathematical Modelling

JF - Applied Mathematical Modelling

ER -