A Storage Model for Data Communication Systems
| Autor: | N. U. Prabhu, António Pacheco |
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| Rok vydání: | 1995 |
| Předmět: |
Statistics and Probability
Mathematical optimization Supply chain management Markov chain Laplace transform Generalization Process (computing) Markov process Management Science and Operations Research Communications system Storage model Infimum and supremum Computer Science Applications symbols.namesake Computational Theory and Mathematics symbols Infinitesimal generator Statistics Probability and Uncertainty Algorithm Mathematics |
| Zdroj: | Theory of Probability & Its Applications. 39:604-627 |
| ISSN: | 1095-7219 0040-585X |
| DOI: | 10.1137/1139046 |
| Popis: | We consider a storage model where the input and demand are modulated by an underlying Markov chain. Such models arise in data communication systems. The input is a Markov-compound Poisson process and the demand is a Markov linear process. The demand is satisfied if physically possible. We study the properties of the demand and its inverse, which may be viewed as transformed time clocks. We show that the unsatisfied demand is related to the infimum of the net input and that, under suitable conditions, it is an additive functional of the input process. The study of the storage level is based on a detailed analysis of the busy period, using techniques based on infinitesimal generators. The Laplace transform of the busy period is the unique solution of a certain matrix-functional equation. Steady state results are also obtained; these are not obvious generalizations of the results for simple storage models. In particular, a generalization of the Pollaczek-Khinchin formula brings new insight. |
| Databáze: | OpenAIRE |
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