### Abstract

We consider a discrete-time single server queue which models the input buffer of an IP switch/router. The packets arrive according to a batch Bernoulli process and the packet lengths (service times) are independent and identically distributed with a general distribution. We assume that the system has a finite buffer of size K. In contrast to ordinary queues where one packet occupies one place in the buffer, we assume that one packet occupies as many places as its length. We study an asymptotic behavior of the loss probability for this queueing system as the buffer size K tends to infinity, and then use this result to approximate the exact loss probability. Numerical examples show that the approximation is very accurate.

Original language | English |
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Pages (from-to) | 209-223 |

Number of pages | 15 |

Journal | Performance Evaluation |

Volume | 54 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2003 Nov 1 |

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### Keywords

- Asymptotic analysis
- Discrete-time queue
- IP packet
- IP switch/router
- Loss probability
- Packets of variable length

### ASJC Scopus subject areas

- Computer Networks and Communications
- Software
- Modelling and Simulation
- Statistics and Probability

### Cite this

*Performance Evaluation*,

*54*(3), 209-223. https://doi.org/10.1016/S0166-5316(03)00045-2