延遲與可靠度於多使用者系統之靜態與動態傳輸策略分析

Abstract

可靠度，延遲與大量的使用者形成物聯網之中的黃金三角。在這篇論文，我們探討了它們在多使用者系統慢衰減多輸入多輸出通道下，彼此的關係。在跨階層系統模型下，整體的延遲包括物理層的傳輸時間以及網路層的佇列延遲需要被考慮，我們探討這個問題的兩種情境，首先我們聚焦在靜態的傳輸策略及延遲界線的指標上，我們的目標是在給定系統錯誤率低於預設門檻下，找出可以最小化延遲界線之最佳策略，藉由高訊雜比的分析方法，原本的問題可以公式化成一個非凸函數的最佳化問題，進而使用KKT條件找出最佳解。結果顯示到達分佈的參數、錯誤率的預設門檻、使用者的數量決定了最佳策略的選擇，此外整體延遲的成長與使用者數量的之間的關係超越線性。接著，我們考慮動態的策略以及平均延遲的指標，並透過馬可夫決定程序解出此問題，藉由值函數的非凸和對稱特性，我們找出了最佳策略，此外我們也提出了兩種找出最佳策略的演算法。

Reliability, latency, and the number of connected users form the golden triangle of Internet of Things. In this thesis, the fundamental trade-off among them are investigated in the multi-user system with quasi-static MIMO channel. By a cross-layer system model, the overall latency including transmission time at the physical layer as well as queuing delay at the network layer is considered. We study two different scenarios of this problem. First, we focus on the static transmission policy and delay-bound metric. Our goal is to find the optimal policy that can minimize the delay-bound, given that the system error probability is below a prescribed threshold. By taking the problem to the high SNR asymptotic regime, it can be formulated into a convex optimization problem. Hence Karush-Kuhn-Tucker (KKT) conditions can be used to find the optimal solution. The result shows that the parameters of arrival distribution, the prescribed threshold of the error probability, and the number of users determine the choice of the optimal policy. In addition, the overall latency grows super-linearly with the number of users. Then we turn to the dynamic policy and average delay metric. We solve this problem based on Markov decision process. By convexity and symmetry of the value function, we can find the optimal policy. In addition, two algorithms for finding the optimal policy are proposed.