Markov-modulated feedforward fluid networks

With the aim of studying a multi-station feedforward fluid network with Markov-modulated input and output rates we first study a two-dimensional parallel network having the property that the second station cannot be empty unless the first 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 fluid 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 and it turns out that in order to compute conditional means and the covariance 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.