## Abstract

In this chapter, the authors consider two infinite-server queueing models with a so-called mixed arrival process. First, they study the case of Coxian service times. Second, the authors consider a Markov-modulated infinite-server queue with general service times. In queueing theory, it is often assumed that the arrival process is a Poisson process with a constant rate. The authors consider an infinite-server queue where the arrival parameter repeatedly resamples after i.i.d. (independent, identically distributed) exponential amounts of time. They analyze the behavior of this queue and make comparisons to “standard” infinite-server queues with a fixed deterministic arrival parameter. The authors indicate how the differential equation can be used to obtain queue length moments.

Original language | English |
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Title of host publication | Queueing Theory 1 |

Subtitle of host publication | Advanced Trends |

Publisher | Wiley-Liss Inc. |

Pages | 107-144 |

Number of pages | 38 |

ISBN (Electronic) | 9781119755432 |

ISBN (Print) | 9781789450019 |

DOIs | |

Publication status | Published - 1 Jan 2021 |

### Bibliographical note

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