Note on the GI/GI/1 queue with LCFS-PR observed at arbitrary times (Q2731304)

The present paper deals with the steady-state distribution of queue length and residual service times at arbitrary times in the \(GI/GI/1\) queue with Last-Come-First-Served Preemptive-Resume (LCFS-PR) discipline. In the standard treatment in queueing literature, these distributions have been given either via the stationary distributions at arrival and departure epochs or by the help of balance equations. The author's arguments apply directly to the system in continuous time, thus explaining the geometric nature of the queue length distribution as well as the fact that the remaining service times are indpendent and all but one are identically distributed. The proposed analysis can be extended to the case where the requests arrive in geometrically distributed batch sizes. Another possible extension is to the batch service with generally distributed batch sizes.