在這篇碩士論文中,我們提出了一個有效率無死結(deadlock-free)的繞徑(routing)演算法━ DOWN/UP routing. 此繞徑演算法的理論基礎為轉動模組(turn model)適用於任何蟲洞(wormhole)交換技術相連接的網路. 在一個使用延伸樹(spanning tree)為基礎所建立的繞徑演算法,在延伸樹根節點周圍的熱點(hot spots)和不平均的流量分布是繞徑演算法效能降低的兩個主要原因.為了解決在延伸樹根節點周圍的熱點和不平均的流量分布這兩個問題,我們在DOWN/UP routing 設法將流量往延伸樹的葉子部分推進,並對每一個點消除具有完全相反方向的轉動組(turn pairs)來分別解決這兩個問題. 當我們有一個網路拓樸(topology), DOWN/UP routing 包含以下三個階段. 第一個階段中,使用這個拓樸建立一個基於座標樹(coordinated tree)的溝通圖(communication graph). 在溝通圖中,屬於延伸樹的邊和其它的邊將被視做不同的邊. 我們這樣做是為了使選擇禁止的轉動更為精確. 同時,我們也提出一個較佳的方法來建立座標樹,繞徑演算法可以達到較佳的產量(throughput)基於這較佳方式所建造出的延伸樹. 在第二階段中, 基於最大方向圖（maximal direction graph）和轉動模組,我們建立一個最大無圈方向相依圖(maximal acyclic direction dependency graph)來得到一個禁止轉動的集合. 在此階段,我們小心的選擇一個禁止轉動的集合使得流量可以盡量被推向延伸樹的樹葉結點並且達成平均分布流量的目的. 在第三階段,我們將此找到的禁止轉動集合實施在溝通圖的每一個結點中,並且釋放掉不需要禁止的轉動. 可以針對每一個溝通圖結點的禁止轉動推導出適用於任意連接(irregular)的拓樸的DOWN/UP routing 演算法. 為了得到DOWN/UP routing的效能,我們使用了模擬的方式. 我們將DOWN/UP routing 和L-turn routing 實作在IRFlexSim0.5 模擬器上, 並模擬了含有4阜或8阜128交換器(switch)任意連接的網路. 由模擬的結果得知我們提出的繞徑演算法不論在熱點的程度上,流量的分布上,產量上都勝過L-turn routing對於所有測試的個案.

In this thesis, we proposed an efficient deadlock-free tree-based routing algorithm, the DOWN/UP routing, for irregular wormhole-routed networks based on the turn model. In a tree-based routing algorithm, hot spots around the root of a spanning tree and the uneven traffic distribution are the two main facts degrade the performance of the routing algorithm. To solve the hot spot and the uneven traffic distribution problems, in the DOWN/UP routing, it tries to push the traffic downward to the leaves of a spanning tree as much as possible and remove prohibited turn pairs with opposite directions in each node, respectively. Given an irregular network topology, the construction of the DOWN/UP routing consists of three phases. In the first phase, a communication graph based on the coordinated tree of the given topology is constructed. In a communication graph, tree links and cross links are considered as different links. This will make the prohibited turn selection more precisely. In this phase, we also proposed a better way to construct the coordinated tree such that a better throughput can be obtained when a routing algorithm is performed. In the second phase, based on the maximal direction graph and the turn model, we construct a maximal acyclic direction dependency graph to obtain the set of prohibited turns. In this phase, we careful select the set of prohibited turns such that the traffic can be pushed downward to leaves of a spanning tree as much as possible and a more even distribution of traffic load can be achieved. In the third phase, we apply the set of prohibited turns to each node in the communication graph and release unnecessary prohibited turns for each node. Then the DOWN/UP routing algorithm for the give irregular network can be derived based on the prohibited turns of each node. To evaluate the performance of DOWN/UP routing, the simulation is conducted. We have implemented the DOWN/UP routing along with the L-turn routing on the IRFlexSim0.5 simulator. Irregular networks that contain 128 switches with 4-port and 8-port configurations are simulated. The simulation results show that the proposed routing algorithm outperforms the L-turn routing for all test samples in terms of the degree of hot spots, the traffic load distribution, and throughput.

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