There is no definitive answer to this. Because of PRISM's symbolic implementation, using data structures based on binary decision diagrams (BDDs), its performance can be unpredictable in this respect. There are also several factors that affect performance, including the type of model and property being checked and the engine being used (PRISM has several different engines, which have varying performance).
Having said that, using the default engine in PRISM (the “hybrid” engine), you can normally expect to be able to handle models with up to 10^7-10^8 states on a typical PC. Using the MTBDD engine, you may be able to analyse much larger models (on some of the PRISM case studies, for example, PRISM can do numerical analysis of models with as many as 10^10 or 10^11 states). The manual has more information about PRISM's engines.
The size of a probabilistic model (i.e. the number of states/transitions) is critical to the efficiency of performing probabilistic model checking on it, since both the time and memory required to do so are often proportional to the model size. Unfortunately, it is very easy to create models that are extremely large. Below are a few general tips for reducing model size.
Because PRISM is a symbolic model checker, the amount of memory required to store the probabilistic model can vary (sometime unpredictably) according to several factors. One example is the order in which the variables of your model appear in the model file. In general, there is no definitive answer to what the best ordering is but the following heuristics are a good guide.
Variables x
and y
are "related" if, for example, the value of one is has an effect on how the other changes (e.g. (y'=x+1)
) or if both appear together in an expression (e.g. a guard).
These heuristics also apply to the ordering of modules within the model file.
For technical details about variable ordering issues, see e.g. section 8 of [HKN+03] or section 4.1.2 of [Par02].