Sample-path analysis of stochastic discrete-event systems
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.
scientific article; zbMATH DE number 508732
scientific article