簡訊傳輸延遲時間之分佈

Abstract

簡訊服務是最受歡迎的行動通訊服務之一。例如在中國大陸每年有超過八百億的的簡訊使用量。在遠傳電信公司及國立交通大學的合作案中，我們發展了一個網頁式的簡訊系統（NCTU-SMS），而此系統目前正由宜蘭縣政府使用中。本論文利用在商業運作中獲得的四萬多筆簡訊發送資料來分析 NCTU-SMS 系統的傳輸延遲時間。我們研究簡訊服務來回傳輸延遲時間的分佈。我們使用不同的截略常態（truncated normal）、截略伽馬（truncated gamma）、截略對數常態（truncated log-normal）以及截略 Weibull 分佈來粗估簡訊傳輸延遲時間的分佈。此粗估的結果可用於數學模型的分析。我們更進一步的使用無母數配適法 （non-parametric fitting） 及棄卻抽樣法 （rejection method） 兩種方法來發展這些延遲時間的亂數產生器。此亂數產生器可以用於任何有使用到簡訊傳輸延遲時間的電腦模擬研究。

Short Message Service (SMS) is one of the most popular mobile data services. In China, more than 80 billion short messages are delivered annually. In a joint project between FarEasTone Telecom. Corp. and National Chiao Tung University (NCTU), we developed a web-based short message system called NCTU-SMS, which is now operated by Taiwan Government (i.e., E-Land County). In this thesis, we analyze the NCTU-SMS 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 analytic analysis. Furthermore, with the non-parametric 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.