Abstract
Piecewise homogeneous Markov fluid models are composed by homogeneous intervals where the model is governed by an interval dependent pair of generators and the model behaviour changes at the boundaries. The main difficulty of the transient analysis of piecewise homogeneous Markov fluid models is the appropriate description of the various boundary cases. The paper proposes an analytical approach to handle the wide variety of the possible boundary cases in a relatively simple to describe and implement manner.
Highlights
Markov fluid models (MFMs) gained significant popularity in modeling telecommunication systems in the 1980’s (Anick et al 1982)
Both methods provide numerically stable analysis, e.g., for the stationary distribution of the fluid level, but the approach based on matrix analytic methods gained more popularity due to the fact that it provides a stochastic interpretation of the considered performance measures
The analysis approaches available for homogeneous (with infinite (Ahn and Ramaswami 2005) and finite (Ahn et al 2005) buffer) MFMs describe the transient behaviour on the level of matrix blocks in Laplace transform domain using explicit expressions
Summary
Markov fluid models (MFMs) gained significant popularity in modeling telecommunication systems in the 1980’s (Anick et al 1982). The analysis approaches available for homogeneous (with infinite (Ahn and Ramaswami 2005) and finite (Ahn et al 2005) buffer) MFMs describe the transient behaviour on the level of matrix blocks in Laplace transform domain using explicit expressions. The extension of this approach for PHMFMs gets prohibitively cumbersome because the proper description of the boundary behaviour at internal boundaries requires the consideration of all possible cases of sign changes separately.
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