In this paper, we study the basic properties of last-in first-out (LIFO) preemptive repeat single-server queues in which the server needs to start service from scratch whenever a preempted customer reaches the server. In particular, we study the question of when such queues are stable (in the sense that the equilibrium time-in-system is finite-valued with probability one), and show how moments of the equilibrium customer sojourn time can be computed when the system is stable. A complete analysis of stability is provided in the setting of Poisson arrivals and in that of the Markovian arrival process. The stability region depends upon the detailed structure of the interarrival- and service time distributions, and can not be expressed purely in terms of expected values. This is connected to the fact that such preemptive repeat queues are not work-conserving.

Keywords: Branching process, Iterative scheme, Markovian arrival process, Random walk, Sojourn time, Stability, Stochastic fixpoint equation