在最近這幾年，網路編碼已被廣泛應用在改善無線網路的效能，其中不僅資料成功送達率而且能源效率、複雜度、拓展性、封包傳輸延遲和封包損失機率都可獲得改善。另一方面，不同的服務可能會有不同的服務品質需求。舉例來說，即時性服務在延遲方面是敏感的而在損失方面是可承受的，而非即時性服務在損失方面是敏感的而在延遲方面是可承受的。因此如何結合網路編碼和服務差異化變成無線網路設計的另一個關鍵議題。在這篇論文中，我們研究可應用在無線網路中繼節點之三種優先權化機會式網路編碼方法。在方法1中，封包的平均服務時間只受到優先權影響。在方法2與3中，封包的平均服務時間同時受到優先權和緩衝器占有度的影響。我們假設無線網路鏈結可能發生錯誤，也就是說封包傳輸時間是不固定的。我們也假設系統有兩種類別的封包，其中類別一的封包的優先權高於類別二。除此之外，不像大多數的研究假設緩衝器大小是無限的，我們考慮有限緩衝器情境，而且修改原始網路編碼以解決鎖死情況。在每一個優先權化機會式網路編碼方法中，我們考慮了三種情境：原始網路編碼，無優先權之非原始網路編碼和有優先權之非原始網路編碼。根據離散時間馬可夫鏈，我們推導我們考慮的系統的解析模型。我們也開發一個疊代演算法去求得穩態機率分布和感興趣的效能指標。我們感興趣的效能指標為封包傳輸延遲、編碼機率、來源端損失機率、中繼端損失機率、整體封包延遲、整體封包損失機率和成功送達率。我們研究不同系統參數，例如封包到達速率、封包服務速率和網路編碼服務速率，對於系統效能指標的影響。透過廣泛的數值實驗，我們發現方法1可達成最好的服務差異化而方法2可達成最好的整體效能。最後但不是最不重要的，我們使用電腦模擬去驗證我們的解析結果。在大多數的情況下我們的解析結果很接近我們的模擬結果。

In recent years, network coding has demonstrated a wide range of applications for improving the performance of wireless networks not only in term of throughput, but also in terms of energy efficiency, complexity, scalability, packet delivery delay, and packet loss probability. On the other hand, different services may have different QoS requirements. As an example, the real-time service is delay-sensitive but loss-insensitive, whereas the non-real-time service is delay-insensitive but loss-sensitive. Therefore, how to combine network coding and service differentiation becomes another critical issue for the design of wireless networks. In this work, we study a wireless butterfly network where three prioritized opportunistic network coding (ONC) schemes are applied at the relay. The mean packet service time of scheme 1 depends only the priority, and those of schemes 2 and 3 depends on both the priority and buffer occupancy. We assume there may be errors in the wireless link, i.e., the packet transmission time is not fixed. It is assumed that there are two classes of packets. Class-1 packets have priority over class-2 packets. Furthermore, unlike the most studies assuming buffer space is infinite, we consider the finite buffer scenarios and propose a modification to solve the deadlock situation in the pure network coding (PNC). For each scheme, we consider three scenarios: PNC, non-PNC without priority, and non-PNC with priority. We derive an analytical model of the considered systems based on the discrete-time Markov chain. We develop an iterative algorithm to find the steady state probability distribution and the performance measures of interest. The performance measures of interest are the packet delivery delay, the coding probability, the source loss probability, the relay loss probability, the aggregate packet delivery delay, the aggregate loss probability, and the throughput. We study the effect of different system parameters, i.e., the packet arrival rate, the packet service rate, and the coding rate, on different performance measures. After extensive numerical experiments, it is found that scheme 1 achieves the best service differentiation, whereas scheme 2 achieves the best overall performance. Last but not least, we use computer simulation to verify our analytical results. In most cases our analytical results are very close to simulation results.

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