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

Consider the GI0GI01 queue with the Last-Come First-Served Preemptive-Resume service discipline+We give intuitive explanations for ~1! the geometric nature of the stationary queue length distribution and ~2! the mutual independence of the residual service requirements of the customers in the queue, both considered at arbitrary time points+ These distributions have previously been established in the literature by either first considering the system at arrival instants or using balance equations+ Our direct arguments provide further understanding of properties 1 and 2.