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On the GI/M/∞ queue with batch arrivals of constant size

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Abstract

In this note, the GI/M/∞ queue with batch arrivals of constant sizek is investigated. It is shown that the stationary probabilities that an arriving batch findsi customers in the system can be computed in terms of the corresponding binomial moments (Jordan's formula), which are determined by a recursive relation. This generalizes well-known results by Takács [12] for GI/M/∞. Furthermore, relations between batch arrival- and time-stationary probabilities are given.

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Authors and Affiliations

  1. Sektion Mathematik, Humboldt Universität zu Berlin, PSF, 1297, 1086, Berlin, German Democratic Republic

    A. Brandt & H. Sulanke

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  1. A. Brandt
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  2. H. Sulanke
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Brandt, A., Sulanke, H. On the GI/M/∞ queue with batch arrivals of constant size. Queueing Syst 2, 187–200 (1987). https://doi.org/10.1007/BF01158399

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  • DOI: https://doi.org/10.1007/BF01158399

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