I haven't kept close track over the years, but simulation software for Petri nets has many roots in reliability analysis and that's where I think you may find usable tools. The first hit I find on Google Scholar for "stochastic petri net" is for a tool called SPNP, which I remember was one of the first packages available in the early 1990's. The one that has been around for probably as long is called [GreatSPN](https://books.google.com/books?id=us3tCwAAQBAJ&pg=PA250&lpg=PA250&dq=SPNP+GreatSPN&source=bl&ots=ZoRrY4UkKo&sig=ACfU3U2IMD8BbH3xJW2BzcNTjaNYeaV-4A&hl=en&sa=X&ved=2ahUKEwjc4rrXvb3pAhWRLs0KHdBlAbQQ6AEwAHoECAkQAQ#v=onepage&q=SPNP%20GreatSPN&f=false) and this one still is being maintained and they have a github account with recent commits, so this is far from dead -- https://github.com/greatspn/SOURCES

My own interest in stochastic Petri nets peaked back then as well, and a report I wrote for a NASA fault-tolerance analysis project is on ResearchGate, which has links to a long final report w/ lots of citations + source code snippets and also a link to a short conference paper: