ON THE WORKLOAD PROCESS IN A FLUID QUEUE WITH A RESPONSIVE
BURSTY INPUT AND SELECTIVE DISCARDING
Parijat Dube a1andEitan Altman a2 a1 IBM T.J. Watson Research Center, Yorktown
Heights, New York 10598, E-mail: pdube@us.ibm.com a2 INRIA, Sophia Antipolis Cedex,
France, E-mail: altman@sophia.inria.fr
Abstract
We analyze a feedback system consisting of a finite buffer
fluid queue and a responsive source. The source alternates between
silence periods and active periods. At random epochs of times,
the source becomes ready to send a burst of fluid. The length
of the bursts (length of the active periods) are independent
and identically distributed with some general distribution.
The queue employs a threshold discarding policy in the sense
that only those bursts at whose commencement epoch (the instant
at which the source is ready to send) the workload (i.e., the
amount of fluid in the buffer) is less than some preset threshold
are accepted. If the burst is rejected then the source backs
off from sending. We work within the framework of Poisson
counter-driven stochastic differential equations and obtain
the moment generating function and hence the probability density
function of the stationary workload process. We then comment
on the stability of this fluid queue. Our explicit
characterizations will further provide useful insights and
“engineering” guidelines for better network designing.
