The G/G/1 (LCFS/P) queue with service depending on queue size

This paper studies a general single server queue, assuming that customers have service times depending on the queue size and also that they are served in accordance with a last-come-first-served queue discipline with preemption and arbitrary restarting policy. Expressions are given for the queue size limiting distribution when the system is considered at arrival (or departure) epochs and in continuous time, by using very simple arguments.