A preemptive resume queue with an expiry time for retained service

This paper introduces a new variant of the classical preemptive resume priority queue, in which the partially rendered service of an interrupted task is retained only if the time spent serving the higher priority work falls below a specified threshold. Both preemptive repeat-different (RD) and preemptive repeat-identical (RI) strategies are considered in the event that service is to start over. The Laplace–Stieltjes transforms (LSTs) of the waiting time and flow time distributions are derived for each class. Using a recursive procedure to derive the moments of interruption times, the first two moments of the waiting time and flow time are also obtained. The results are then applied to two numerical examples.