Structured analysis techniques for large Markov chains

Analysis of large and realistic Markov models suffers mainly from the so-called state space explosion. Large systems of equations have to be solved to obtain the result measures. The limiting factors of a solution are space and time. Apart from using more powerful computers for the solution, sophisticated data structures have been used for a compact storage of huge Markov chains and new efficient analysis techniques have been developed recently to exploit structure in the model for a more efficient analysis of the Markov chains. This paper gives an overview of analysis techniques based on model structure, describes the availability of these new techniques and outlines future research directions in the field.