Ensuring the existence of home states is a more difficult task. In [7] this problem is tackled for ordinary GSPNs, if inhibitor arcs and different priority levels for immediate transitions are absent. Note that such kind of GSPNs are a subset of QPNs. It is shown that GSPNs with an EFC-net structure satisfying condition EQUAL-Conflict do have home states, provided the underlying P/T-net is live and bounded, which implies the existence of home states in the EFC case.
In [5] the same problem is discussed for an older version
of QPNs comprising immediate transitions and timed queueing places only.
[6] proves the existence of home states if
and the preconditions of Theorem 5 are satisfied.