Queueing approximation of suprema of spectrally positive Lévy process

Authors:
M. Czystołowski;W. Szczotka
Affiliations:
Institute of Mathematics, Wrocław University, Wrocław, Poland 50-384;Institute of Mathematics, Wrocław University, Wrocław, Poland 50-384
Venue:
Queueing Systems: Theory and Applications
Year:
2010

Citing 3
Cited 1

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Abstract

Let W=sup驴0驴t(X(t)驴β t), where X is a spectrally positive Lévy process with expectation zero and 0βX, there exists a sequence of M/GI/1 queues for which stationary waiting times converge in distribution to W. The second result shows that condition (III) of Proposition 2 in the paper is not implied by all other conditions.