Joost-Pieter Katoen On The Need for Probabilistic and Stochastic Modelling
I'd like to answer to the question on the need for stochastic and probabilistic modeling (and analysis). Some concrete examples of case studies provided by industry for which probabilistic aspects are very important are listed below. The importance of explicitly modeling random effects explicitly stands or falls with the kind of property to be established, of course, so I am definitely not claiming that these examples cannot (and should not) be modeled by techniques that do not support random phenomena.
1. Leader election in IEEE 1394: in case of a conflict (two nodes
pretend to be a leader), the contending nodes send a message (be
my parent) and randomly wait either short or long. What is the
optimal policy to resolve the contention the fastest? (This turns
out to be a slightly unbiased coin).
2. In the Ametist EU-project, the German industrial partner Axxom
generated schedules for a lacquer production plant. While doing
so, they abstracted from many details that the lacquer producer
supplies such as: the average fraction of time a resource is not
operational, the fraction of (operational) time the resource can
be used because necessary human support is present, and so
forth. In their abstraction they scheduled tasks conservatively
and they were interested in whether they could improve their
schedules while reducing the probability to miss the deadline.
Clearly, a stochastic modeling is needed, and indeed has been
carried out using a stochastic process algebra.
3. Hubert and Holger should be able to say much more about
a recent project they are pursuing with a French company on
the validation of multiprocessor multi-threaded architectures.
I do not know exactly what they are investigating, but they use
stochastic process algebras to model!
Finally, let me say that (as Moshe is also indicating) that the
interest in probabilistic modeling is growing steadily. To give
an example, the European Space Agency (ESA) is currently
considering to use probabilistic modeling and analysis in the
context of AADL, an architecture specification language where
an important ingredient ais the failure rates of components.
All in all, it is fair to say that there is a quest for probabilistic