A storage model for data communication systems
N. U. Prabhua, A. Pachecob
a School of Operation Research and Industrial Engineering, Cornell University, Ithaca, NY, USA
b Departamento de Matemática, Instituto Superior Téchico, Lisboa, Portugal
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.
additive functional, busy period communication systems, infinitesimal generator, integral equation, anufacturing, Markov-additive processes, Markov-compound Poisson process, Markov modulation, matrix-functional equation, Pollaczek–Khinchin formula, storage models.
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Theory of Probability and its Applications, 1994, 39:4, 604–627
N. U. Prabhu, A. Pacheco, “A storage model for data communication systems”, Teor. Veroyatnost. i Primenen., 39:4 (1994), 766–795; Theory Probab. Appl., 39:4 (1994), 604–627
Citation in format AMSBIB
\by N.~U.~Prabhu, A.~Pacheco
\paper A storage model for data communication systems
\jour Teor. Veroyatnost. i Primenen.
\jour Theory Probab. Appl.
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