Calculation of the Laplace Transform of the Length of the Busy Period for the M|G|1 Queue Via Martingales

Walter A. Rosenkrantz

25 citations0/0 files storedThe Annals of Probability

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Advanced Queuing Theory Analysis Probability and Statistical Research Probability and Risk Models

Abstract

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.

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1999Distributions of stopping times for compound poisson processes with positive jumps and linear boundaries 1989Dynamic, Transient and Stationary Behavior of the $M/GI/1$ Queue Via Martingales 2005Some Time-Dependent Properties of Symmetric M/G/1 Queues 2001Busy Periods of Poisson Arrival Queues with Loss 2000A new approach to the busy period of the M/M/1 queue

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