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We study the relation of Markov fluid queues and QBD processes in this paper. Ahn and Ramaswami presented results about this relation and provided a stochastic interpretation based reasoning in [1]. In the current work, first we provide an algebraic proof for that relation. After that, we present a negative result about the potential extension of the QBD based analysis Markov fluid queues to Markov fluid queues with two buffers. We present a 2-dimensional QBD process, which could be a candidate for describing the stationary behaviour of the related Markov fluid queue, but it turns out that the QBD based behaviour is different from the one of the Markov fluid queue.

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An Algebraic Proof of the Relation of Markov Fluid Queues and QBD Processes

  • 会议论文

  • 发表日期：

    2025年

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  • Peter Buchholz,
  • Andras Meszaros,
  • Miklos Telek

摘要

We study the relation of Markov fluid queues and QBD processes in this paper. Ahn and Ramaswami presented results about this relation and provided a stochastic interpretation based reasoning in [1]. In the current work, first we provide an algebraic proof for that relation. After that, we present a negative result about the potential extension of the QBD based analysis Markov fluid queues to Markov fluid queues with two buffers. We present a 2-dimensional QBD process, which could be a candidate for describing the stationary behaviour of the related Markov fluid queue, but it turns out that the QBD based behaviour is different from the one of the Markov fluid queue.