In this paper, we consider the different performance parameters that influence the scheduling of soft real time tasks on uni-processor systems. This environment is rich of parameters that affect the rejection ratio of the system. This work models such stochastic environment and proposes a baseline model that estimates the rejection ratio of the system before applying any special scheduling algorithm. The model presents many cases where the system produces a small rejection ratio without the need for any special scheduling algorithm. We validate our analytical model with simulations that represent the real computing environment. The results of our simulations show that our mathematical model can predict the expected percentage of tasks that miss their deadline accurately.