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research
Queues with Lévy input and hysteretic control
Authors
A. Chydzinski
A.E. Kyprianou
+31 more
A.E. Kyprianou
E.Y. Lee
F. Avram
H. Takagi
H.C. Tijms
J. Bae
J. Bertoin
J. Bertoin
J.W. Cohen
K. Sigman
L. Kruk
L. Yeh
M. Roughan
M. Rubinovitch
M.J. Faddy
M.R. Pistorius
N.H. Bingham
N.U. Prabhu
O. Kella
O. Kella
O. Kella
O. Kella
P.J. Brockwell
R. Bekker
R. Bekker
R. Bekker
R. Bekker
S. Asmussen
S. Asmussen
S. Asmussen
V.M. Zolotarev
Publication date
1 January 2009
Publisher
Doi
Cite
Abstract
We consider a (doubly) reflected Lévy process where the Lévy exponent is controlled by a hysteretic policy consisting of two stages. In each stage there is typically a different service speed, drift parameter, or arrival rate. We determine the steady-state performance, both for systems with finite and infinite capacity. Thereby, we unify and extend many existing results in the literature, focusing on the special cases of M/G/1 queues and Brownian motion. © The Author(s) 2009
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