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We are concerned with the computation of the mean-time-to-absorption (MTTA)for a large system of loosely interconnected components, modeled as continuoustime Markov chains. In particular, we show that splitting the local andsynchronization transitions of the smaller subsystems allows to formulate analgorithm for the computation of the MTTA which is proven to be linearlyconvergent. Then, we show how to modify the method to make it quadraticallyconvergent, thus overcoming the difficulties for problems with convergent rateclose to $1$.  In addition, it is shown that this decoupling of local and synchronizationtransitions allows to easily represent all the matrices and vectors involved inthe method in the tensor-train (TT) format - and we provide numerical evidenceshowing that this allows to treat large problems with up to billions of states- which would otherwise be unfeasible.

Tensor methods for the computation of MTTA in large systems of loosely interconnected components