State-dependent transitions in discrete stochastic models: Deterministic simulation approach

It is more than obvious that once something has been broken and fixed (or even glued back together in some cases), the chance that it will break again is higher than before the breaking. This implies that the probability distribution function that describes the event (e.g. breaking) changes each time the object breaks. This is a situation that is possible to simulate using discrete-event simulation (DES). Deterministic simulation of such a scenario is however almost impossible or at least horribly complicated even for the most simple cases. This class of transitions (events) in theory is known as state-dependent. In our paper we show how discrete stochastic models that involve state-dependent events can be modeled and simulated in a deterministic manner. For this purpose we use the proxel-based simulation method (PBM). In addition, we also redefine state-dependent transitions, such as to reflect non-Markovian behavior in context of the proxel-based method. The benefits of our approach as opposed to DES are again the well known properties of the proxel-based method, i.e. controllability of the accuracy, its flexibility and the smooth transient solution that it produces.