A MAP-modulated fluid flow model with multiple vacations
Baek, Jung Woo
Lee, Ho Woo
Lee, Se Won
Date of Issue2012
School of Mechanical and Aerospace Engineering
We consider a MAP-modulated fluid flow queueing model with multiple vacations. As soon as the fluid level reaches zero, the server leaves for repeated vacations of random length V until the server finds any fluid in the system. During the vacation period, fluid arrives from outside according to the MAP (Markovian Arrival Process) and the fluid level increases vertically at the arrival instance. We first derive the vector Laplace–Stieltjes transform (LST) of the fluid level at an arbitrary point of time in steady-state and show that the vector LST is decomposed into two parts, one of which the vector LST of the fluid level at an arbitrary point of time during the idle period. Then we present a recursive moments formula and numerical examples.
Annals of operations research
© 2012 Springer Science+Business Media, LLC. This is the author created version of a work that has been peer reviewed and accepted for publication by Annals of Operations Research, Springer. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at DOI: [http://dx.doi.org/10.1007/s10479-012-1100-y].