Modelling the transplant waiting list: A queueing model with reneging

Motivated by the problem of organ allocation, we develop a queueing model with reneging that provides a stylistic representation of the transplant waiting list. The model assumes that there are several classes of patients, several classes of organs, and patient reneging due to death. We focus on randomised organ allocation policies and develop closed-form asymptotic expressions for the stationary waiting time, stationary waiting time until transplantation, and fraction of patients who receive transplantation for each patient class. Analysis of these expressions identifies the main factors that underlie the performance of the transplant waiting list and demonstrates that queueing models can prove useful when evaluating the organ allocation system.