  Consider a Markovian Petri net with race policy. The marking process has a
"product form" stationary distribution if the probability of viewing a given
marking can be decomposed as the product over places of terms depending only on
the local marking. First we observe that the Deficiency Zero Theorem of
Feinberg, developped for chemical reaction networks, provides a structural and
simple sufficient condition for the existence of a product form. In view of
this, we study the classical subclass of free-choice nets. Roughly, we show
that the only such Petri nets having a product form are the state machines
which can alternatively be viewed as Jackson networks.
