窄頻物聯網是第三代合作夥伴(3GPP)計劃用於支援廣域物聯網的標準，甚至作為第五代行動通訊網路(5G)中大規模機器型通訊(mMTC)項目的基礎。在窄頻物聯網系統中，本篇論文用數學分析去驗證窄頻物聯網系統之時間前置隨機接入程序(timing advance based random access procedure, TARA)的效能並與傳統隨機接入程序的效能做比較，其中在性能指標的部分主要探討隨機接入程序的成功接入機率與平均接入延遲。TARA透過比對基地台端傳送的時間前置值與物聯網裝置的時間前置值來讓一些在傳統型隨機接入程序中碰撞的物聯網裝置有機會能夠完成隨機接入程序，由數學分析式發現用TARA能增加在隨機接入程序中成功接入的物聯網裝置數量並降低隨機存取所花費之傳送次數，並讓部分碰撞裝置中提早離開碰撞之隨機存取程序，以提升裝置成功聯網機率。

Narrowband Internet of Things (NB-IoT) is a new 3GPP standard aiming to support a massive number of device features long range, low complexity, low power, and low data rate. The 5th generation mobile communication (5G) massive machine type communication (mMTC) field will base on NB-IoT system. In this paper, we use mathematical analysis to verify the performance of the timing advance random access procedure (TARA) of the NB-IoT system and compare with the traditional random access (RA) procedure. TARA procedure allows some of collision NB-IoT devices in the traditional RA procedure to have the opportunity to complete the RA procedure by match function between the timing advance value from base station and the timing advance value stored in NB-IoT device. From mathematical analysis, we found that TARA procedure can increase the access success probability and reduce the average access delay.

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