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

The un nished work at arrival instants FCFS waiting time can be computed via the LCFS preemptive resume discipline Analyzing the GI GI queue in this way gives full interpretation in queueing theoretic language to Feller s analysis of the uctuations 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 stan dard queue For the M G queue the derivations are qualitative and there are additional connections to branching processes

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