Sample-path analysis of stochastic discrete-event systems
type: Item
instance of: scholarly article
title: Sample-path analysis of stochastic discrete-event systems
zbMATH Open document ID: 0801.93056
DOI: 10.1007/BF01439158
author: Muhammad El-Taha
author: Shaler jun. Stidham
published in: Discrete Event Dynamic Systems
publication date: 1993-01-01T00:00:00Z
review text: The paper presents a unified sample-path approach for deriving distribution-free relations between performance measures for stochastic discrete-event systems. Follow from the sample-path version of the renewal-reward theorem \((Y=\lambda X)\) the authors derive a version of the rate-conservation law under general conditions. The authors investigate the relations between continuous-time state frequencies and frequencies at the point of an imbedded point process, giving necessary and sufficient conditions for the so-called ASTA (arrivals see time averages), conditional ASTA, and reversed ASTA properties. They provide a unified approach for proving various relations involving forward and backward recurrence times. Finally, sufficient conditions for rate stability of an input-output system are given. These results are applied to obtain an elementary proof of the relation between the workload and attained-waiting-time process in a \(G/G/\ell\) queue.
reviewed by: Bernd Mathiszik
Mathematics Subject Classification ID: 93E03
Mathematics Subject Classification ID: 60G55
zbMATH DE Number: 508732
zbMATH Keywords: arrivals see time averages
zbMATH Keywords: sample-path
zbMATH Keywords: rate stability
describes a project that uses: ASTA
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 508732