A note on Jackson networks with state-dependent rejection probabilities

In general capacity constraints prohibit a product form limiting distribution for a queueing network. An exception to this rule is the case when jobs jump over a saturated node as if they were served at an infinite speed. This note generalizes the principle of ‘jumping-over’ in that a job arriving at a node is rejected with a state dependent probability. It is shown that also in this more general situation the steady state distribution exhibits a product form. This generalization requires a proof from a different point of view, which is of interest in itself.