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.
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.
All delays in a CTMC need to be modelled as exponential distributions. This is what makes them efficient to analyse. If you included a transition whose delay was deterministic, i.e. which always occurred after exactly the same delay, the model would no longer be a CTMC.
One solution to this, if your model require such a delay, is to approximate a deterministic delay with an Erlang distribution (a special case of a phase-type distribution). See for example this PRISM model:
In the model, the occurrence of the the go-labelled action occurs with an Erlang distribution with mean
mean and shape
k. The special case of
k=1 is just an exponential distribution. The graph below shows the probability distribution of the delay, i.e. of
P=? [ F<=T x=1 ] for different values of
There is an obvious trade-off here between the accuracy (how close it is to modelling a deterministic time delay) and the resulting blow-up in the size of the model that you add this to. For
k=1000, you can see that the shape is quite "deterministic" but this would increase your model size by a factor of ~1000.