Performance Bounds and Pathwise Stability for Generalized Vacation and Polling Systems

Performance Bounds and Pathwise Stability for Generalized Vacation and Polling Systems

We consider a generalized vacation or polling system, modeled as an input-output process operating over successive "cycles," in which the service mechanism can be in an "up" mode (processing) or "down" mode (e.g., vacation, walking). Our primary motivation is polling sy...

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Veröffentlicht in:Operations Research. - Institute for Operations Research and the Management Sciences, 1956. - 46(1998), 1, Seite 137-148
1. Verfasser: Altman, Eitan (VerfasserIn)
Weitere Verfasser: Foss, Serguei, Riehl, Eric, Stidham,, Shaler
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 1998
Zugriff auf das übergeordnete Werk:Operations Research
Schlagworte:Queues: polling and vacation systems, pathwise analysis, performance bounds Communications: token-ring local area networks Stochastic Models Biological sciences Business Applied sciences Mathematics Philosophy
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520 |a We consider a generalized vacation or polling system, modeled as an input-output process operating over successive "cycles," in which the service mechanism can be in an "up" mode (processing) or "down" mode (e.g., vacation, walking). Our primary motivation is polling systems, in which there are several queues and the server moves cyclically between them providing some service in each. Our basic assumption is that the amount of work that leaves the system in a "cycle" is no less than the amount present at the beginning of the cycle. This includes the standard gated and exhaustive policies for polling systems in which a cycle begins whenever the server arrives at some prespecified queue. The input and output processes satisfy model-dependent conditions: pathwise bounds on the average rate and the burstiness (Cruz bounds); existence of long-run average rates; a pathwise generalized Law of the Iterated Logarithm; or exponentially or polynomially bounded tail probabilities of burstiness. In each model we show that these properties are inherited by performance measures such as the workload and output processes, and that the system is stable (in a model-dependent sense) if the input rate is smaller than the up-mode processing rate. 
540 |a Copyright 1998 The Institute for Operations Research and the Management Sciences 
650 4 |a Queues: polling and vacation systems, pathwise analysis, performance bounds 
650 4 |a Communications: token-ring local area networks 
650 4 |a Stochastic Models 
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650 4 |a Applied sciences  |x Systems science  |x Systems theory  |x Dynamical systems  |x Ergodic theory 
650 4 |a Mathematics  |x Pure mathematics  |x Probability theory  |x Stochastic models 
650 4 |a Mathematics  |x Pure mathematics  |x Discrete mathematics  |x Number theory  |x Numbers  |x Real numbers  |x Rational numbers  |x Integers 
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655 4 |a research-article 
700 1 |a Foss, Serguei  |e verfasserin  |4 aut 
700 1 |a Riehl, Eric  |e verfasserin  |4 aut 
700 1 |a Stidham,, Shaler  |e verfasserin  |4 aut 
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773 1 8 |g volume:46  |g year:1998  |g number:1  |g pages:137-148 
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