Several probability distribution functions such as exponential distribution function have been used to represent the task arrival process and processing time of task for multimedia systems. These distribution functions are simple, memory less, and easy-to-use, however, they are difficult to represent the task arrival process of multimedia stream data or audio data having real-time properties.

This paper proposes a method for obtaining Approximate probability distribution functions for given task arrival process for multimedia systems by using the Cox distribution function. The Cox distribution function can represent arbitrary distribution functions but their parameters are difficult to be determined for representing given function. In the method, first, an objective probability distribution function is approximated by a linear combination of exponential distribution functions and Erlan distribution functions, then the parameters of the Cox distribution function is determined from the linear combination of the functions obtained above. The examples of the approximations show that the method is effective for approximating given probability distribution functions.