We report in this paper on the potential interest of real-time queueing models to optimize organ allocation policies. We especially focus on building organ shortage resilient policies in terms of equity, as we experienced differential impact of the COVID epidemic organ shortage on transplant access, according to the cause of liver failure. Patient's death on the waiting list or dropout for being too sick, resulting from the absence of a timely available organ, is chosen as the main equity metric. Results obtained with the composite allocation score used in France is challenged against the so-called Early Simulated Deadline First (ESDF) real-time queueing discipline, under increasing levels of organ shortage, by extensive simulations. The ESDF policy is a variant of the well-know Earliest Deadline First (EDF) policy, which was shown as optimal in various contexts in the queueing literature. In the present case, the time to the deadline represents the remaining life duration of patients - which is of course unknown. So we propose to simulate a fictional life-duration, and give priority to the earliest simulated deadline. This leads to a simple and comprehensive representation of the system at hand by a Markov process. Our simulation results clearly show that the ESDF policy allows to maintain equity between indications, conversely to the scoring policy, which was not resilient to increasing levels of organ shortage.