ABSTRACT
This chapter is devoted to a very powerful and efficient Monte Carlo algorithm for network reliability estimation which we call “Lomonosov’s turnip”.
The idea of this algorithm was first suggested by M.V. Lomonosov in [36] and developed later in a series of works [11,12,37,38]. The “turnip”, called in [36] evolution process with closure, was primarily designed for estimating network terminal reliability for the case of arbitrary (and nonequal) network edge failure probabilities, in the static setting. Lomonosov’s algorithm introduces closure operation on network edges which eliminates so-called non relevant edges. This allows to accelerate considerably the Monte Carlo simulation process and makes it possible to handle relatively large networks with hundreds of edges. Lomonosov’s algorithm uses specially designed trajectories leading from the initial “zero” state to network UP state. These trajectories allow to identify the “pre-failure” or “border” states of the network and open a way for simulating dynamic network stationary mean UP and DOWN periods as well as the reliability gradient function.
