**P. Ballarini and A. Horváth**

The problem we deal with is the analysis of a class of large structured
Markov chains. In particular we assume that the whole state space can be
partitioned into disjoint sets (called macro states) in which the process
corresponds to the parallel execution of independent jobs. Petri nets and
process algebras with phase type (PH) distributed execution times give rise to
this kind of model. These models are subject to the phenomenon of state
space explosion. It is known that the infinitesimal generator of such
models can be handled in a memory efficient way by storing only the
``structure'' of the infinitesimal generator as Kronecker expressions or
decision diagrams. Less is known instead on how to perform the analysis of
the model in a memory efficient manner because in case of most of the
available methods the vector of transient or steady state probabilities are
stored in an explicit manner.

In this paper we consider the calculation of measures connected to the probability that the process passes through a given series of macrostates. We show that such measures can be calculated in a memory efficient manner by Laplace transform techniques. The method is illustrated by numerical examples.