摘要
網路通訊系統中的封包延遲的統計特性對許多網路管理與網路同步都是很重要的資訊。我們須控制節點之間的封包延遲變(packet delay variation)來保證服務品質；另一方面，封包延遲之變異通常是利用交換帶有時間資訊的封包之網路同步方式最主要的估計誤差來源。亦即，沿著主從路徑(master-to-slave route)，在交換式集線器的佇列緩衝區之封包轉接延遲變異乃是網路(時鐘)同步系統最主要的不確定性來源。而這些封包延遲的統計資訊除了可被應用在時間同步之外，對於網路的資源分配也十分重要。 我們考慮一個混合式的Weibull封包延遲分佈，其混和係數與個別的Weibull參數讓我們可以描述許多不同型態的網路延遲。我們則使用動差匹配(moment matching)的概念先去估計混合係數與時鐘偏差與模型參數間的關係，接著利用三階動差的最小平方誤差找出時鐘偏差的解並同時估計封包延遲機率分佈。我們修改了交叉熵(cross entropy)方法去解決其中的多參數最佳化問題。當部分混和係數變得非常小時，這個方法可能無法得到可靠的估計值。為了解決這個缺點，我們增加了一個模型選擇步驟，將混和係數組合劃分成了七種模型。模型選擇標準是基於採樣的延遲分佈與量化模型分佈之間的KL散度(Kullback-Leibler divergence)。 我們另外探討了同時找低階動差與高階動差的最小平方誤差合的估計法，這方法牽涉到一個多目標最佳化問題。我們因此利用多目標基因演算法( NSGA-II )同時找到二階動差與三階動差的最小平方誤差合。每一個方法我們都利用電腦模擬來檢驗其效能，我們同時也分析的動差匹配所造成的均方誤差與理論的CR下限。
並列摘要
Node-to-node delay variation (DV) needs to be controlled for latency-sensitive network communications, the packet delay variation (PDV) is also a major error source in a packet-based synchronization system. The PDV at the queue buffer in each switching hub along the master-to-slave route presents a considerable uncertainty in the clock recovery system. The network delay statistics are needed not only for timing synchronization application but for network resource allocation in a software defined network. In this thesis, we consider a general parametric network delay model, which enables us to deal with a general class of network traffics. We assume that the packet delay follows a mixed-Weibull distribution. The mixing coefficients along with component Weibull parameters allow the model to describe a very wide range of statistical delay behaviors. For this model-based method, we invoke the concept of moment matching to perform joint mixing coefficients, unknown parameters and clock offset estimation. We apply the cross entropy (CE) method for the associated multi-variable optimization problem. The CE method is modified to deal with larger uncertainty dimension cases. Still it may fail when the model degenerates (i.e., a subset of the mixing coefficients becomes very small). To overcome this shortcoming, we add a Kullback-Leibler (KL) divergence based model identification step by dividing the mixing combinations into seven models. The KL divergence is used to measure the similarity between the sampled delay distribution and the quantized model distribution. By using moment-matching and forcing the lower-order sample moments to be equal to the ensemble moments, we seek the optimal model parameters that give the least higher-order moment mismatches. An alternative approach is to minimize both lower-order and higher-order moment mismatches which can be formulated as a multi-object optimization problem. Based on this idea, we employ the NSGA-II algorithm to minimize the mismatches of the second-order and third-order moments simultaneously. Note that our methods can be used to estimate either or both node clock offset and routing delays.