Beschreibung:
We consider stochastic Markovian processes, which describe e.g. queueing network processes, in a random environment. The environment in uences the network by determining random breakdown of nodes, and the necessity of repair thereafter. Starting from an explicit steady state distribution of product form available in the literature, we notice that this steady state distribution does not provide information about the correlation structure in time and space (over nodes). We study this correlation structure via one step correlations for the queueing-environment process. Although formulas for absolute values of these correlations are rather complicated, it turns out that differences of correlations of related networks are surprisingly simple and have a nice structure. We therefore compare two networks in a random environment having the same invariant distribution, and focus on questions such as: What happens to the time behaviour of the processes when in such a network the environment changes or the rules for travelling are perturbed? We show that evaluating these comparison formulas we can compare spectral gaps and asymptotic variances of related processes.