AbstractIt has been reported in several studies that the probability distribution functions for interarrival times of tasks in multimedia systems cannot be represented by traditional probability distribution functions, such as exponential ones.In this paper we propose an approximation method, based on the Coxian distribution function, to calculate the probability distribution functions used in analyzing multimedia systems. Although the Coxian function can represent arbitrary distribution functions, it is difficult to determine their parameters directly from a given distribution function. In this work, this drawback is remedied by first approximating the given distribution function with a linear combination of Erlang function, and then converting it to a Coxian function. We also present examples of the approximation and evaluate its accuracy. © 2004 Wiley Periodicals, Inc. Syst Comp Jpn, 35(2): 16–24, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.10446