Transient analysis of one-sided Lévy-driven queues. Issue 3 (2nd July 2016)

• Record Type: Journal Article
• Authors: Starreveld, N. J.; Bekker, R.; Mandjes, M.
• Is Part Of: Stochastic models. Volume 32:Issue 3(2016)
• Page Start: 481
• Page End: 512
• Publication Date: 2016-07-02
• Subjects: Fluctuation theory -- Lévy processes -- queueing -- spectrally one-sided input -- transient analysis; 60G51 -- 60K05 -- 60K25 -- 60F05; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/15326349.2016.1170615
• Languages: English
• ISSNs: 1532-6349

Abstract

ABSTRACT: In this article, we analyze the transient behavior of the workload process in a Lévy-driven queue. We are interested in the value of the workload process at a random epoch; this epoch is distributed as the sum of independent exponential random variables. We consider both cases of spectrally one-sided Lévy input processes, for which we succeed in deriving explicit results. As an application, we approximate the mean and the Laplace transform of the workload process after a deterministic time.