Different models are available when scheduling tasks on real-time systems depending on the need for expressiveness and the properties of the system. The Digraph Real-Time (DRT) Task Model is one of the most expressive models, where the feasibility for hard real-time scheduling is computable in pseudo-polynomial time. We expand the DRT task model to the Stochastic Digraph Real-Time (SDRT) Task Model, which contains the stochastic behavior and not just worst-case values or minimum separations. We present the operational semantics of DRT task systems and expand those to fit SDRT task systems with soft deadlines. We implement these semantics using Uppaal  SMC, which we use to simulate a set of SDRT tasks. The simulations are used in performance analysis to obtain metrics such as utilization and the ratio between missed deadlines and the number of released jobs. We show how the increase in size of the task set affects these different metrics of a scheduling system.