發(fā)布時(shí)間：2018-07-24 13:17

【摘要】：現(xiàn)實(shí)生活中的網(wǎng)絡(luò)系統(tǒng)都是在特定的條件下來執(zhí)行既定的任務(wù)。由于受自身或外界不確定性因素的影響,系統(tǒng)及其組成單元在運(yùn)行過程中一般會(huì)表現(xiàn)出多種不同的性能水平,這樣的網(wǎng)絡(luò)系統(tǒng)稱之為多態(tài)網(wǎng)絡(luò)系統(tǒng)。相對(duì)于二態(tài)網(wǎng)絡(luò)系統(tǒng)模型(系統(tǒng)及其組成單元只有兩種不同的性能水平),多態(tài)網(wǎng)絡(luò)系統(tǒng)模型能夠更準(zhǔn)確地描述和刻畫網(wǎng)絡(luò)系統(tǒng)的復(fù)雜行為,在系統(tǒng)性能評(píng)估研究領(lǐng)域得到了越來越多的重視和應(yīng)用�？煽啃允乾F(xiàn)代技術(shù)系統(tǒng)安全運(yùn)行的基本屬性。在隨機(jī)性因素相互交織的環(huán)境中,人們?cè)絹碓街匾曄到y(tǒng)提供服務(wù)的可靠性,因此,可靠性已經(jīng)成為系統(tǒng)規(guī)劃、設(shè)計(jì)、運(yùn)行與管理的主要考量指標(biāo)。作為評(píng)估復(fù)雜系統(tǒng)性能的基本工具,可靠性分析的主要目的之一在于對(duì)系統(tǒng)失效的可能性進(jìn)行量化,它為人們提供了一種更有效的方式來理解系統(tǒng)在失效狀態(tài)下的相關(guān)特性。本文根據(jù)可靠性理論及網(wǎng)絡(luò)流理論,重點(diǎn)研究了多態(tài)網(wǎng)絡(luò)系統(tǒng)可靠性評(píng)估的多態(tài)極小路方法/多態(tài)極小割方法,費(fèi)用約束下的多態(tài)網(wǎng)絡(luò)系統(tǒng)可靠性評(píng)估方法,以及可修復(fù)多態(tài)網(wǎng)絡(luò)系統(tǒng)可靠性評(píng)估方法。更具體地講,本論文的研究工作主要有以下幾個(gè)方面:(1)多態(tài)極小路方法是多態(tài)網(wǎng)絡(luò)系統(tǒng)可靠性評(píng)估的一種重要方法,該方法的核心是求解多態(tài)極小路問題。針對(duì)現(xiàn)有多態(tài)極小路數(shù)學(xué)模型的不足,根據(jù)多態(tài)極小路的特性定義了容量下界的概念,并利用容量下界構(gòu)建了多態(tài)極小路的改進(jìn)數(shù)學(xué)模型。在此基礎(chǔ)上,提出了一種求解多態(tài)極小路的高效算法,并把該算法推廣到求解無向網(wǎng)絡(luò)的多態(tài)極小路。理論分析與數(shù)值試驗(yàn)都表明,提出的算法在求解多態(tài)極小路方面具有明顯的效率優(yōu)勢(shì)。(2)多態(tài)極小割方法也是多態(tài)網(wǎng)絡(luò)系統(tǒng)可靠性評(píng)估的一種重要方法,而求解多態(tài)極小路問題是該方法的核心。鑒于最小容量界在多態(tài)極小割問題中的重要作用,提出一種新的方法來尋找邊的最小容量界;根據(jù)最小容量界,構(gòu)建了多態(tài)極小割的改進(jìn)數(shù)學(xué)模型。在多態(tài)極小割問題中,重復(fù)多態(tài)極小割的判定與識(shí)別是最艱巨也是最富有具挑戰(zhàn)性的難題。從多態(tài)極小割的基本模型出發(fā),深入研究了不同極小割產(chǎn)生重復(fù)多態(tài)極小割的深層次原因,并提出兩個(gè)重要的判定準(zhǔn)則來識(shí)別重復(fù)多態(tài)極小割。根據(jù)得到的理論結(jié)果,提出了一種新的、更高效的多態(tài)極小割求解算法,該算法的時(shí)間復(fù)雜度小于等于現(xiàn)有算法的時(shí)間復(fù)雜度,而數(shù)值試驗(yàn)的結(jié)果也表明,提出的算法在求解多態(tài)極小割方面具有顯著的效率優(yōu)勢(shì)。(3)在實(shí)際應(yīng)用中,除了可靠性指標(biāo)之外,系統(tǒng)的運(yùn)行費(fèi)用也是衡量網(wǎng)絡(luò)系統(tǒng)性能的重要指標(biāo)之一。在資源約束條件下,費(fèi)用問題關(guān)系網(wǎng)絡(luò)系統(tǒng)運(yùn)行的成本效率,是管理者在決策過程中必須要考慮的一個(gè)重要因素。把可靠性指標(biāo)和費(fèi)用指標(biāo)結(jié)合起來考慮多態(tài)網(wǎng)絡(luò)系統(tǒng)的綜合性能指標(biāo)—費(fèi)用約束下的可靠性,該性能指標(biāo)可以利用費(fèi)用約束下的多態(tài)極小路來計(jì)算。為了提高費(fèi)用約束下的多態(tài)極小路的搜索效率,提出兩種有效的策略來縮減整個(gè)搜索空間。首先,利用容量下界的概念建立了費(fèi)用約束下的多態(tài)極小路改進(jìn)數(shù)學(xué)模型;其次,采用一種狀態(tài)向量集分解方法把整個(gè)搜索空間分解成多個(gè)互不相交的子空間,丟棄那些不合格的子空間,而僅在剩下的子空間中尋找費(fèi)用約束下的多態(tài)極小路。理論分析與數(shù)值試驗(yàn)都表明,提出的算法在求解費(fèi)用約束下的多態(tài)極小路時(shí)更加實(shí)用、高效。(4)多態(tài)網(wǎng)絡(luò)系統(tǒng)本質(zhì)上是一個(gè)退化系統(tǒng),當(dāng)系統(tǒng)的性能發(fā)生退化而導(dǎo)致其服務(wù)水平不能夠滿足要求時(shí),有必要對(duì)系統(tǒng)開展修復(fù)工作。針對(duì)可修復(fù)多態(tài)網(wǎng)絡(luò)系統(tǒng),提出了一個(gè)新的可靠性指標(biāo)來衡量系統(tǒng)的性能。該可靠性指標(biāo)不僅考慮網(wǎng)絡(luò)系統(tǒng)應(yīng)提供的可接受服務(wù)水平(即容量水平),而且考慮把網(wǎng)絡(luò)系統(tǒng)從退化狀態(tài)恢復(fù)到初始狀態(tài)(最大狀態(tài))時(shí)的修復(fù)費(fèi)用約束問題。提出了一種高效分解算法來計(jì)算該可靠性指標(biāo)。該分解算法首先把滿足容量水平的狀態(tài)向量從整個(gè)狀態(tài)向量空間中分離出來,然后再驗(yàn)證它們是否滿足修復(fù)費(fèi)用約束。由于只需對(duì)部分狀態(tài)向量而不是全部狀態(tài)向量進(jìn)行枚舉驗(yàn)證,該算法的計(jì)算效率明顯勝過傳統(tǒng)方法的計(jì)算效率。
[Abstract]:Network systems in real life perform the established tasks under specific conditions. Due to their own or external uncertainties, the system and its components generally show a variety of different performance levels during the process of operation. This network system is called a polymorphic network system. Relative to the two state network system. The model (system and its component units have only two different performance levels). The model of the polymorphic network system can describe and depict the complex behavior of the network system more accurately. It has gained more and more attention and application in the research field of system performance evaluation. Reliability is the basic attribute of the security operation of modern technical system. In the interwoven environment, people pay more and more attention to the reliability of the system providing services. Therefore, reliability has become the main index of system planning, design, operation and management. As a basic tool for evaluating the performance of complex systems, one of the main purposes of reliability analysis is to quantify the possibility of system failure. People provide a more effective way to understand the related characteristics of the system in the state of failure. Based on the reliability theory and the network flow theory, this paper focuses on the study of polymorphic polar approach / polymorphic minima method for the reliability evaluation of polymorphic network systems, the reliability evaluation method of multistate network system under cost constraints, and the repairable method. In particular, the research work of this paper mainly includes the following aspects: (1) the polymorphic path method is an important method for the reliability evaluation of the polymorphic network system. The core of this method is to solve the problem of polymorphic path. The characteristics of the polymorphic polar path define the concept of the lower bound and build the improved mathematical model of the polymorphic path by using the lower bound of capacity. On this basis, an efficient algorithm for solving polymorphic paths is proposed, and the algorithm is extended to the polymorphic minima for solving the undirected network. Both theoretical analysis and numerical experiments show that the proposed algorithm is proposed. The algorithm has obvious efficiency advantage in solving polymorphic path. (2) the method of polymorphic minimum cutting is also an important method for the reliability evaluation of polymorphic network system, and solving the problem of polymorphic path is the core of this method. In view of the important role of the minimum capacity boundary in the polymorphic minimum cut problem, a new method is proposed to find out. According to the minimum capacity bounds, an improved mathematical model for polymorphic minima is constructed according to the minimum capacity boundary. In the problem of polymorphic minimum cut, the determination and recognition of repeated polymorphic minima is the most difficult and the most challenging problem. From the basic model of the polymorphic minimum cut, the repeated polymorphic poles produced by different minimal cuts are deeply studied. Two important criteria are proposed to identify repeated polymorphic minimal cuts. According to the theoretical results obtained, a new and more efficient algorithm for solving polymorphic minimum cut is proposed. The time complexity of the algorithm is less than equal to the time complexity of the existing algorithm, and the results of numerical experiments show that the proposed algorithm is proposed. The method has significant efficiency advantages in solving polymorphic minima. (3) in practical applications, in addition to the reliability index, the operating cost of the system is also one of the most important indicators to measure the performance of the network system. In the resource constraints, the cost efficiency of the network system operation is necessary for the managers in the decision-making process. An important factor to be considered. Combining the reliability index with the cost index, considering the comprehensive performance index of the polymorphic network system, the reliability under the cost constraint, the performance index can be calculated using the polymorphic path under the cost constraint. In order to improve the search efficiency of the polymorphic pole under the cost constraint, two kinds of methods are proposed. The effective strategy to reduce the entire search space. First, the concept of the lower bound of capacity is used to establish the improved mathematical model of polymorphic polar path under the cost constraint. Secondly, a state vector set decomposition method is used to decompose the entire search space into multiple intersected subspaces, discarding those substandard subspaces, but only in the remaining subspaces. The theoretical analysis and numerical experiments show that the proposed algorithm is more practical and efficient in solving the polymorphic path under cost constraints. (4) the polymorphic network system is essentially a degraded system, when the performance of the system is degenerated and the service level can not meet the requirements, It is necessary to repair the system. For the repairable network system, a new reliability index is proposed to measure the performance of the system. The reliability index not only considers the acceptable service level (that is, capacity level) provided by the network system, but also considers the network system from the degenerate state to the initial state (the largest form). A high efficiency decomposition algorithm is proposed to calculate the reliability index. The decomposition algorithm first separates the state vectors that satisfy the capacity level from the whole state vector space, and then verifies that they satisfy the repair cost constraints. It is necessary for only partial state vectors but not all shapes. Enumeration of state vectors verifies that the computational efficiency of the algorithm is much better than that of traditional methods.
【學(xué)位授予單位】：北京交通大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2017
【分類號(hào)】：N945.17

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