### Abstract

To study the effect of burstiness in arrival streams on the congestion in queueing systems this paper presents a one-server queueing model in a random environment in discrete time. The environment can be in two states. The number of time slots between two consecutive transitions of the environment follows a geometric distribution with a transition-dependent parameter. In every slot customers arrive in batches, and the batch-size distribution depends on the environment. Each customer requires a generally distributed service time. Arriving customers are put in a queue which is served in FIFO order. Arrivals have precedence over departures and departures have precedence over a change of the environment. The generating functions of the number of customers in the queue and the individual waiting time will be derived. Numerical results will show the effect of the burstiness in the arrival stream on the waiting-time and the queue-size distribution by calculating in parallel the corresponding results for the standard discrete-time model with a mixed batch-size distribution, ceteris paribus.

Original language | English |
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Title of host publication | Queueing Theory and Network Applications |

Subtitle of host publication | 14th International Conference, QTNA 2019, Ghent, Belgium, August 27–29, 2019, Proceedings |

Editors | Tuan Phung-Duc, Shoji Kasahara, Sabine Wittevrongel |

Publisher | Springer |

Pages | 330-348 |

Number of pages | 19 |

ISBN (Electronic) | 9783030271817 |

ISBN (Print) | 9783030271800 |

DOIs | |

Publication status | Published - 2019 |

Event | 14th International Conference on Queueing Theory and Network Applications, QTNA 2019 - Ghent, Belgium Duration: 27 Aug 2019 → 29 Aug 2019 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 11688 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 14th International Conference on Queueing Theory and Network Applications, QTNA 2019 |
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Country | Belgium |

City | Ghent |

Period | 27/08/19 → 29/08/19 |

### Keywords

- Discrete-time queue
- Generating functions
- Random environment

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## Cite this

*Queueing Theory and Network Applications: 14th International Conference, QTNA 2019, Ghent, Belgium, August 27–29, 2019, Proceedings*(pp. 330-348). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11688 LNCS). Springer. https://doi.org/10.1007/978-3-030-27181-7_20