Parameter Mixing in Infinite-server Queues

Lucas van Kreveld, Onno Boxma

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review


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 languageEnglish
Title of host publicationQueueing Theory 1
Subtitle of host publicationAdvanced Trends
PublisherWiley-Liss Inc.
Number of pages38
ISBN (Electronic)9781119755432
ISBN (Print)9781789450019
Publication statusPublished - 1 Jan 2021

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