Performability Analysis: A New Algorithm
IEEE Transactions on Computers
Transient analysis of stochastic fluid models
Performance Evaluation
Nonsymmetric Algebraic Riccati Equations and Wiener--Hopf Factorization for M-Matrices
SIAM Journal on Matrix Analysis and Applications
An approximation method for complete solutions of Markov-modulated fluid models
Queueing Systems: Theory and Applications
A fluid queue driven by a Markovian queue
Queueing Systems: Theory and Applications
Transient and Asymptotic Analysis of General Markov Fluid Models
Queueing Systems: Theory and Applications
Asymptotic solution of stochastic fluid models
Performance Evaluation
Steady State Analysis of Finite Fluid Flow Models Using Finite QBDs
Queueing Systems: Theory and Applications
Time to stationarity for general Markov fluid models: Research Articles
International Journal of Communication Systems
Matrix-analytic methods for fluid queues with finite buffers
Performance Evaluation
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We investigate the asymptotic workload distribution of fluid models with input and output rates which are modulated by an irreducible Markov process. An analytical solution is proposed in [H. Nabli, Asymptotic solution of stochastic fluid models, Perform. Eval. 57 (2004) 121-140] for general Markov fluid model. This probability distribution is controlled by a linear differential system with specific boundary conditions. The solution uniqueness is proved under a conjecture in the field of linear algebra. This conjecture is valid for all particular fluid models considered in the literature. In this paper, we will prove this conjecture for general fluid models. The numerical computation of the stationary distribution will be also discussed.