本篇論文中，針對具有隨機交通模型、有限節點與干擾主導的無線存取網路，我們提出了兩種媒體存取控制的演算法，即預測與群播演算法與分裂樹演算法。在干擾主導的無線存取網路中，只要訊號相對於干擾加上背景噪音的比率超過事先定義的門檻值，則每一個接收端可具有同時接收多個從不同傳送端送出的封包之能力。本篇論文中，我們針對每一個在無線網路中的節點具有大小有限且大於一的佇列。我們利用離散時間馬可夫鏈、馬可夫報酬過程與馬可夫重生過程來推導系統效能，包括了封包輸出量、封包阻斷機率、平均封包延遲與平均系統大小。經由數學與模擬數據除了得知預測式群播輪詢演算法藉由一點點額外的佇列大小即可重大改善了系統效能，而且得知分裂樹演算法的精確系統效能是隨著無線網路中的總節點數而改變的。除此之外，經由嚴格的數學證明與電腦模擬來印證論文所提之演算法的數據結果。

In this dissertation, we propose using and analytically evaluate the predictive multicast polling scheme and the tree splitting algorithm for medium access control in interference dominating wireless access networks with random traffic and finite nodes. In an interference dominating wireless network, a receiver could simultaneously receive multiple packets from a variety of transmitters, as long as the signal-to-interference-plus-noise ratio exceeds a predetermined threshold. We concentrate on the case of in which the maximum queue size in a node is finite. We use discrete-time Markov chains, reward processes and regenerative processes to derive the throughput, the packet blocking probability, the average packet delay, and the average system size. We show that the system performance of the predictive multicast polling scheme can be significantly improved with a few additional buffers in the queues. Our study also shows that exact performance of the splitting algorithm depends on the total number of nodes in the networks. We verify our numerical results by rigorous mathematical proof and computer simulations.

Acknowledgements ii
Abstract (in Chinese) iii
Abstract (in English) iv
1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Motivation and Contributions . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Predictive Multicast Polling in Wireless Access Networks with Multipacket
Reception 7
2.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.1 System Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Predictive Multicast Polling . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.1 Polling Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.2 Update of the Estimated System State . . . . . . . . . . . . . . . . 13
2.3 Markov Chain Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.1 Perfect State Information . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.2 Imperfect State Information . . . . . . . . . . . . . . . . . . . . . . 20
2.3.3 Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.4 Numerical and Simulation Results . . . . . . . . . . . . . . . . . . . . . . . 27
2.4.1 Perfect System State . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.4.2 Imperfect System State . . . . . . . . . . . . . . . . . . . . . . . . . 31
3 The Splitting Algorithm in Wireless Access Networks with MultiPacket
Reception 39
3.1 System Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2 Analytical Results for The Case in Which B = 1 . . . . . . . . . . . . . . . 41
3.2.1 Discrete-Time Markov Chain Modeling . . . . . . . . . . . . . . . . 42
3.2.2 The Throughput and The Packet Blocking Probability . . . . . . . 46
3.2.3 The Average System Size and The Average Packet Delay . . . . . . 48
3.2.4 Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.3 Analytical Results for The Case in Which B = 2 . . . . . . . . . . . . . . . 55
3.3.1 Discrete-Time Markov Chain Modeling . . . . . . . . . . . . . . . . 55
3.3.2 The Throughput and The Packet Blocking Probability . . . . . . . 58
3.4 Numerical and Simulation Results . . . . . . . . . . . . . . . . . . . . . . . 59
3.5 On Computational Complexity . . . . . . . . . . . . . . . . . . . . . . . . 62
3.5.1 When B = 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.5.2 When B = 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4 Conclusion 65
References 69

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