Markov-modulated Feedforward Fluid Networks

With the aim of studying a multi-station feedforward uid network with Markov modulated input and output rates we rst study a two dimensional parallel network having the property that the second station cannot be empty unless the rst station is. A method for computing the steady state characteristics of such a process is given and it is shown that this can be used to determine the steady state characteristics of two dimensional tandem uid networks and more general networks. Finally a multi-station feedforward network is considered. Under appropriate conditions, it is explained how to determine the joint steady state Laplace-Stieltjes transform (LST) and it turns out that in order to compute conditional means and the co-variance structure (given the state of the underlying Markov chain) all that is needed is the methods developed for the two dimensional parallel model together with some trivial linear algebra.