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Queues with service speed adaptations
Author(s) -
Bekker R.,
Boxma O.J.,
Resing J.A.C.
Publication year - 2008
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.2008.00389.x
Subject(s) - poisson distribution , workload , queue , computer science , queueing theory , probabilistic logic , service (business) , fork–join queue , observer (physics) , mathematical optimization , real time computing , distributed computing , computer network , mathematics , queue management system , statistics , artificial intelligence , physics , economy , quantum mechanics , economics , operating system
In this paper, we consider various queueing models in which the server can work at two different service speeds. The speed of the server depends on either the number of customers or the workload. Our main interest is in the model in which service speed adaptations can take place only at the arrival instants of an external Poisson observer. Using insightful probabilistic arguments, we give the structure of the steady‐state queue length and workload distributions in the various models. In addition, in case the service speed can only be adapted right after departure instants based on the number of customers, we provide explicit and intuitively appealing expressions for the steady‐state distribution of the number of customers present.