Deriving the distributions for the numbers of short message arrivals

In the broadband era, narrowband short message service (SMS) is still the most popular wireless data service. Many studies have been conducted to investigate the performance of SMS based on the arrival rates of short messages. From Chunghwa Telecom's commercial SMS call data records, we observed that even if the SMS arrival rates are the same, the distributions for the number of SMS arrivals per half hour are quite different for various observed days. We further identify that for the SMS traffic in a specific day, there are non-burst and burst periods. This paper investigates the SMS behaviors on weekdays, weekends, and holidays (specifically, new years' days and eves). With the assistance of kernel-based fitting method, we derive the SMS arrival number distributions of various traffic types and observed days. Our approach fits each SMS arrival number distribution by three cubic polynomial functions that can accurately capture the SMS behaviors. On the basis of the SMS arrival number distributions derived from our model, the mobile operators have better understanding about the volumes of short messages in different times and days, which can be used to design more flexible short message charging rates.