Analysis of the GI/GI/1 Queue and its Variations via the LCFS Preemptive Resume Discipline and Its Random Walk Interpretation

Abstract

The unfinished work at arrival instants (FCFS waiting time) can be computed via the LCFS preemptive resume discipline. Analyzing the GI/GI/1 queue in this way gives full interpretation in queuing theoretic language to Feller's analysis of the fluctuations of the random walk. Also, this approach leads naturally to stochastic decompositions for the queue with set-up times, and for other variations of the standard queue. For the M/G/1 queue, the derivations are qualitative, and there are additional connections to branching processes.