Transition splitting for estimation of rare events with applications to high speed data networks

We develop here an approach for rare event estimation in Markov systems via simulations. In the case of discrete time Markov chain we split the matrix of transition probabilities into linear combination of two matrices one of which “drives” the system to the rare states. Then we consider the simulation process as the sequence of transitions governed by one of the matrices. The actual simulation is performed only for some selected sets of sequences which contain “rare” matrix more often. We consider unbiasedness and variance properties of resulting estimates and provide results of numerical experiments. Application to high speed data networks is considered.