Interactive Markov Chains in Practice

In this chapter we use Interactive Markov Chains to investigate some illustrative examples and case studies. We first study the effect of symmetric composition by means of a simple producer—consumer example. In particular, we compare the growth of the state space to other methods to generate an aggregated state space. In a second case study, we use IMC to model a real world application, namely an ordinary telephony system. The constraint oriented specification of time dependencies will be a central issue. In order to circumvent state space sizes of more than 10 millions of states we make excessive use of the theoretical properties and concepts achieved so far, and obtain a Markov chain of manageable size. These two case studies show how performance estimation can be based on a Markov chain obtained from a highly modular and hierarchical IMC specification. A third example will then be used to highlight some implicit limitations to this approach. In particular, the issue of nondeterminism will discussed.