Timed-Arc Petri nets (TAPN) are a timed extension of Petri nets where tokens have their age and each arc is associated with a time interval restricting the ages of tokens available for transition firing. Additionally, a TAPN can also contain place invariants constraining the ages of tokens in places, inhibitor arcs preventing a transition from firing and transport arcs that preserve a token’s age upon firing. This set of features, as much as it allows us to model complex systems, also often makes verification problems computationally hard or even undecidable. Moreover, in order to model real-life examples, additional stochastic aspects are often necessary to capture the desired behaviour. We suggest (to the best of our knowledge) the first stochastic semantics for TAPNs and design and implement the Statistical Model Checking (SMC) algorithms in the model checker TAPAAL. We argue for the semantic choices we made in the stochastic semantics and prove that the semantics is well-behaving. On a number of case studies we demonstrate the practical applicability of our modelling formalism and its SMC implementation.