A statistic approach for deriving the short message transmission delay distributions

Short Message Service (SMS) is one of the most popular mobile data services. This paper develops a Web-based short message system and analyzes the short message transmission delays based on 40 000 measured data collected from commercial operation. We investigate the distributions of SMS round-trip transmission delays. These distributions are roughly approximated by truncated normal, gamma, log-normal, and Weibull distributions with various parameters, which can be utilized in theoretical analysis. Furthermore, with the nonparametric fitting approach, we use the rejection method to develop random number generators for these delays, which can be used in any simulation models that employ SMS transmission delays.