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Queueing Systems of INAR(1) Processes with Compound Poisson Arrivals

Integer valued autoregressive processes of order 1 (or INAR(1) processes) that may be interpreted as discrete timeG/Geom/∞ queue length processes are considered. The arrivals are assumed to be compound Poisson distributed. It is shown that then the stationary distribution of the queue length process...

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Hauptverfasser: Schweer, Sebastian (VerfasserIn) , Wichelhaus, Cornelia (VerfasserIn)
Dokumenttyp: Article (Journal)
Sprache:Englisch
Veröffentlicht: 30 Jul 2015
In: Stochastic models
Year: 2015, Jahrgang: 31, Heft: 4, Pages: 618-635
ISSN:1532-4214
DOI:10.1080/15326349.2015.1060862
Online-Zugang:Verlag, Volltext: http://dx.doi.org/10.1080/15326349.2015.1060862
Volltext
Verfasserangaben:Sebastian Schweer and Cornelia Wichelhaus

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520 |a Integer valued autoregressive processes of order 1 (or INAR(1) processes) that may be interpreted as discrete timeG/Geom/∞ queue length processes are considered. The arrivals are assumed to be compound Poisson distributed. It is shown that then the stationary distribution of the queue length process as well as the distribution of the departures from the system are again members of the class of compound Poisson distributions. This reveals remarkable invariance properties of the model. The derived explicit expressions allow for the calculation of important performance measures. It is further shown that time-reversibility of the queue length process as well as an analogue of Burke’s theorem hold only if the arrival process is Poisson. 
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