  For a large Markovian model, a "product form" is an explicit description of
the steady-state behaviour which is otherwise generally untractable. Being
first introduced in queueing networks, it has been adapted to Markovian Petri
nets. Here we address three relevant issues for product-form Petri nets which
were left fully or partially open: (1) we provide a sound and complete set of
rules for the synthesis; (2) we characterise the exact complexity of classical
problems like reachability; (3) we introduce a new subclass for which the
normalising constant (a crucial value for product-form expression) can be
efficiently computed.
