Invariant measures and error bounds for random walks in the quarter-plane based on sums of geometric terms

Yanting Chen (), Richard J. Boucherie () and Jasper Goseling ()
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Yanting Chen: Hunan University
Richard J. Boucherie: University of Twente
Jasper Goseling: University of Twente

Queueing Systems: Theory and Applications, 2016, vol. 84, issue 1, No 2, 48 pages

Abstract: Abstract We consider homogeneous random walks in the quarter-plane. The necessary conditions which characterize random walks of which the invariant measure is a sum of geometric terms are provided in Chen et al. ( arXiv:1304.3316 , 2013, Probab Eng Informational Sci 29(02):233–251, 2015). Based on these results, we first develop an algorithm to check whether the invariant measure of a given random walk is a sum of geometric terms. We also provide the explicit form of the invariant measure if it is a sum of geometric terms. Second, for random walks of which the invariant measure is not a sum of geometric terms, we provide an approximation scheme to obtain error bounds for the performance measures. Our results can be applied to the analysis of two-node queueing systems. We demonstrate this by applying our results to a tandem queue with server slow-down.

Keywords: Random walk; Quarter-plane; Geometric terms; Error bounds; Performance measure; Tandem queue; 60G50; 60J10 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11134-016-9483-0

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