The Annals of Probability · 1983 · 28 citations · 0 references
BusinessMathematicsProbability TheoryQueuing TheoryStochastic ProcessesFinite Capacity QueuesMarkov ProcessesMarkovian Queueing ModelsQueueing ProcessesQueueing SystemsQueueing TheoryLaplace TransformLaplace Transform AnalysisM/g/1 QueuesQueue Length Generating FunctionsQueue Length MomentsQueueing ModelsStochastic Arrival Processes
In this paper we derive a new explicit formula for the Laplace transform of the length of the busy period for the $M|G|1$ queue by a direct martingale method of independent interest. The method is probabilistic, of general character and avoids tedious calculations with complex variables.