This paper studies heavy traffic behavior of a G/G/1 last-in-first-out (LIFO) preemptive resume queue, by extending the techniques developed in Limic (1999). The queue length process exhibits a perhaps unexpected heavy traffic behavior. The diffusion limit depends on the type of arrivals (and services) in a fairly intricate way, related to the Wiener-Hopf factorization for random walks.
"On the Behavior of LIFO Preemptive Resume Queues in Heavy Traffic." Electron. Commun. Probab. 5 13 - 27, 2000. https://doi.org/10.1214/ECP.v5-1014