Summary
There exist a large number of Queueing Systems having a non-stationary behavior. We call non-stationarity, random time-variations of some parameters of the system (i.e. the input or service rates). A typical example is a reliability system which corresponds to the unpredictable breakdown or failure of the server. Random intensity models are natural for describing such phenomena.
We introduce a model with randomly changing service rate. It does not obey a certain independence assumption often made in Queueing Theory. A complete analysis of the model is carried out, explicit results and performance curves are given. Jury's criteria are used to find Necessary and Sufficient Conditions for Stability. These criteria are easy to use and allow us to find the conditions of stability which were not obtained in many previous studies.
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Rosenberg, C. Files d'attente exponentielles ayant des parametres non-stationnaires dans le temps. Acta Informatica 23, 177–192 (1986). https://doi.org/10.1007/BF00289497
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DOI: https://doi.org/10.1007/BF00289497