On the approximation of probability distribution functions by Cox distribution to evaluate multimedia systems

摘要

Several studies have reported that the probability distribution function for inter task arrival time of multimedia systems cannot be represented by traditional probability distribution functions, such as exponential distribution function. This paper proposes an approximation method for the probability distribution functions used for analyzing multimedia systems by using Cox distribution function. Cox distribution function can represent arbitrary distribution functions, however, their parameters are difficult to be determined directly from the given distribution function. In the paper, the approximation is made indirectly, i.e. the given distribution function is approximated by linear combination of the Erlang distribution function, then they are converted to Cox distribution function. The paper also shows examples of approximation and evaluate the accuracy of the approximation.