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An M/M/1 Driven Fluid Queue – Continued Fraction Approach

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Abstract

This paper presents complete solutions of the stationary distributions of buffer occupancy and buffer content of a fluid queue driven by an M/M/1 queue. We assume a general boundary condition when compared to the model discussed in Virtamo and Norros [Queueing Systems 16 (1994) 373–386] and Adan and Resing [Queueing Systems 22 (1996) 171–174]. We achieve the required solutions by transforming the underlying system of differential equations using Laplace transforms to a system of difference equations leading to a continued fraction. This continued fraction helps us to find complete solutions. We also obtain the buffer content distribution for this fluid model using the method of Sericola and Tuffin [Queueing Systems 31 (1999) 253–264].

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology, Madras, Chennai, 600 036, India

    P.R. Parthasarathy & K.V. Vijayashree

  2. Department of Mathematics and Computer Science, University of Antwerp, Universiteitsplein 1, B-2610, Wilrijk, Belgium

    R.B. Lenin

Authors
  1. P.R. Parthasarathy
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  2. K.V. Vijayashree
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  3. R.B. Lenin
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Parthasarathy, P., Vijayashree, K. & Lenin, R. An M/M/1 Driven Fluid Queue – Continued Fraction Approach. Queueing Systems 42, 189–199 (2002). https://doi.org/10.1023/A:1020157021703

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