A fluid model with upward jumps at the boundary |
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Authors: | Vidyadhar Kulkarni Keqi Yan |
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Institution: | (1) Department of Statistics and Operations Research, University of North Carolina, Chapel Hill, NC 27599, USA;(2) SAS Institute Inc., 500 SAS Campus Dr. R5435, Cary, NC 27513, USA |
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Abstract: | We consider a single buffer fluid system in which the instantaneous rate of change of the fluid is determined by the current
state of a background stochastic process called “environment”. When the fluid level hits zero, it instantaneously jumps to
a predetermined positive level q. At the jump epoch the environment state can undergo an instantaneous transition. Between two consecutive jumps of the fluid
level the environment process behaves like a continuous time Markov chain (CTMC) with finite state space. We develop methods
to compute the limiting distribution of the bivariate process (buffer level, environment state). We also study a special case
where the environment state does not change when the fluid level jumps. In this case we present a stochastic decomposition
property which says that in steady state the buffer content is the sum of two independent random variables: one is uniform
over 0,q], and the other is the steady-state buffer content in a standard fluid model without jumps.
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Keywords: | Markov process Stochastic fluid-flow system Limiting distribution Stochastic decomposition property Uniform distribution |
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