Dependence structure of sojourn times via partition separated ordering

We investigate the joint distribution of successive sojourn times of a customer traversing a path in a Jackson network. It is shown in a general setting that sojourn times for a broad class of such paths exhibit positive dependence. This applies to paths which admit overtaking due to the network topology as well as due to the internal node structure. Our proofs utilize the concept of partition separated orders on multidimensional ordered spaces.