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Fluid queues driven by an M / M / 1 / N queue

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  • R. B. Lenin
  • P. R. Parthasarathy

Abstract

In this paper, we consider fluid queue models with infinite buffer capacity which receives and releases fluid at variable rates in such a way that the net input rate of fluid into the buffer (which is negative when fluid is flowing out of the buffer) is uniquely determined by the number of customers in an M / M / 1 / N queue model (that is, the fluid queue is driven by this Markovian queue) with constant arrival and service rates. We use some interesting identities of tridiagonal determinants to find analytically the eigenvalues of the underlying tridiagonal matrix and hence the distribution function of the buffer occupancy. For specific cases, we verify the results available in the literature.

Suggested Citation

  • R. B. Lenin & P. R. Parthasarathy, 2000. "Fluid queues driven by an M / M / 1 / N queue," Mathematical Problems in Engineering, Hindawi, vol. 6, pages 1-22, January.
    • Handle: RePEc:hin:jnlmpe:852632
    DOI: 10.1155/S1024123X00001423
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    Cited by:

    1. R. B. Lenin & P. R. Parthasarathy, 2000. "A Computational Approach for Fluid Queues Driven by Truncated Birth–Death Processes," Methodology and Computing in Applied Probability, Springer, vol. 2(4), pages 373-392, December.

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