The behaviors of real time software systems do not depend only on the values of input and output signals, but also on the times of their occurrences. Real time systems (RTS) interact with their environments using time constrained input/output signals. The complexity of Real Time Systems is continually increasing which makes their design very challenging. In RTS, the scheduling of tasks with hard deadlines has been an important area of research. Unified Modeling Language (UML), the standard visual object-oriented modeling language, is suitable to deal with this complexity. The main objective of this paper is to compare two protocols using UML 2.0 models. The shortcomings of the existing Priority Inheritance protocol are represented using one UML model. Further, the Stack Based Priority Ceiling protocol is used to overcome this difficulty using an improved model.