### Abstract

The authors consider the queue arising in a
multiservice network using ATM (asynchronous transfer mode) when a
superposition of periodic streams of constant-length cells is
multiplexed on a high-speed link. An exact closed formula is derived for
the queue length distribution in the case where all streams have the
same period, and tight upper and lower bounds are obtained on this
distribution when the periods are different. Numerical results confirm
that the use of a Poisson approximation (i.e. the M/D/1 queue) can lead
to a significant overestimation of buffer requirements, particularly in
the case of heavy loads. Buffer requirements for a mixture of different
period streams can be accurately estimated from the upper bound on the
queue length distribution. For given load, requirements increase with
the number of long-period (i.e. low-bit rate) sources. The results are
deduced from a novel characterization of the single-server constant
service time queue, which should be useful in other
applications.

Original language | English |
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Pages (from-to) | 298 - 303 |

Number of pages | 6 |

Journal | IEEE Transactions on Communications |

Volume | 39 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1991 |

MoE publication type | A1 Journal article-refereed |

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## Cite this

Roberts, J., & Virtamo, J. (1991). The superposition of periodic cell arrival streams in an ATM multiplexer.

*IEEE Transactions on Communications*,*39*(2), 298 - 303. https://doi.org/10.1109/26.76467