Scale functions of Lévy processes and busy periods of finite-capacity M/GI/1 queues

Parijat Dube · Fabrice M. Guillemin · Ravi R. Mazumdar

16 citations0/0 files storedJournal of Applied Probability

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

Abstract

In this paper we use the exit time theory for Lévy processes to derive new closed-form results for the busy period distribution of finite-capacity fluid M/G/1 queues. Based on this result, we then obtain the busy period distribution for finite-capacity queues with on–off inputs when the off times are exponentially distributed.

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References

2004Exit problems for spectrally negative Lévy processes and applications to (Canadized) Russian options 2004On Exit and Ergodicity of the Spectrally One-Sided Lévy Process Reflected at Its Infimum 2004A Martingale Review of some Fluctuation Theory for Spectrally Negative Lévy Processes 1973Exit problem for a spectrally positive process 1989Dynamic, Transient and Stationary Behavior of the $M/GI/1$ Queue Via Martingales

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