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On a synchronization queue with two finite buffers

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Abstract

In this paper, we consider a synchronization queue (or synchronization node) consisting of two buffers with finite capacities. One stream of tokens arriving at the system forms a Poisson process and the other forms a PH-renewal process. The tokens are held in the buffers until one is available from each flow, and then a group-token is instantaneously released as a synchronized departure. We show that the output stream of a synchronization queue is a Markov renewal process, and that the time between consecutive departures has a phase type distribution. Thus, we obtain the throughput of this synchronization queue and the loss probabilities of each type of tokens. Moreover, we consider an extended synchronization model with two Poisson streams where a departing group-token consists of several tokens in each buffer.

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Authors and Affiliations

  1. Department of Systems Engineering, The University of Electro-Communications, Tokyo, 182-8585, Japan

    Misa Takahashi & Takehisa Fujisawa

  2. College of Business Administration, Aichi-Gakusen University, Toyota, 471-8532, Japan

    Hideo Ōsawa

Authors
  1. Misa Takahashi
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  2. Hideo Ōsawa
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  3. Takehisa Fujisawa
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Takahashi, M., Ōsawa, H. & Fujisawa, T. On a synchronization queue with two finite buffers. Queueing Systems 36, 107–123 (2000). https://doi.org/10.1023/A:1019127002333

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  • DOI: https://doi.org/10.1023/A:1019127002333

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