On the Split Reliability of Graphs

A common model of robustness of a graph against random failures has all vertices operational, but the edges independently operational with probability $p$. One can ask for the probability that all vertices can communicate ({\em all-terminal reliability}) or that two specific vertices (or {\em terminals}) can communicate with each other ({\em two-terminal reliability}). A relatively new measure is {\em split reliability}, where for two fixed vertices $s$ and $t$, we consider the probability that every vertex communicates with one of $s$ or $t$, but not both. In this paper, we explore the existence for fixed numbers $n \geq 2$ and $m \geq n-1$ of an {\em optimal} connected $(n,m)$-graph $G_{n,m}$ for split reliability, that is, a connected graph with $n$ vertices and $m$ edges for which for any other such graph $H$, the split reliability of $G_{n,m}$ is at least as large as that of $H$, for {\em all} values of $p \in [0,1]$. Unlike the similar problems for all-terminal and two-terminal reliability, where only partial results are known, we completely solve the issue for split reliability, where we show that there is an optimal $(n,m)$-graph for split reliability if and only if $n\leq 3$, $m=n-1$, or $n=m=4$.Comment: 12 pages, 9 figure

The Gross-Saccoman Conjecture is True

Consider a graph with perfect nodes but independent edge failures with identical probability ρ. The reliability is the connectedness probability of the random graph. A graph with n nodes and e edges is uniformly optimally reliable (UOR) if it has the greatest reliability among all graphs with the same number of nodes and edges, for all values of ρ. In 1997, Gross and Saccoman proved that the simple UOR graphs for e = n, e = n + 1 and e = n + 2 are also optimal when the classes are extended to include multigraphs [6]. The authors conjectured that the UOR simple graphs for e = n + 3 are optimal in multigraphs as well. A proof of the Gross-Saccoman conjecture is introduced.Agencia Nacional de Investigación e Innovació

Reliability of Partial k-tree Networks

133 pagesRecent developments in graph theory have shown the importance of the class of partial k- trees. This large class of graphs admits several algorithm design methodologies that render efficient solutions for a large number of problems inherently difficult for general graphs. In this thesis we develop such algorithms to solve a variety of reliability problems on partial k-tree networks with node and edge failures. We also investigate the problem of designing uniformly optimal 2-trees with respect to the 2-terminal reliability measure. We model a. communication network as a graph in which nodes represent communication sites and edges represent bidirectional communication lines. Each component (node or edge) has an associated probability of operation. Components of the network are in either operational or failed state and their failures are statistically independent. Under this model, the reliability of a network G is defined as the probability that a given connectivity condition holds. The l-terminal reliability of G, Rel1 ( G), is the probability that any two of a given set of I nodes of G can communicate. Robustness of a network to withstand failures can be expressed through network resilience, Res( G), which is the expected number of distinct pairs of nodes that can communicate. Computing these and other similarly defined measures is #P-hard for general networks. We use a dynamic programming paradigm to design linear time algorithms that compute Rel1( G), Res( G), and some other reliability and resilience measures of a partial k-tree network given with an embedding in a k-tree (for a fixed k). Reliability problems on directed networks are also inherently difficult. We present efficient algorithms for directed versions of typical reliability and resilience problems restricted to partial k-tree networks without node failures. Then we reduce to those reliability problems allowing both node and edge failures. Finally, we study 2-terminal reliability aspects of 2-trees. We characterize uniformly optimal 2-trees, 2-paths, and 2-caterpillars with respect to Rel2 and identify local graph operations that improve the 2-terminal reliability of 2-tree networks

Aerospace medicine and biology: A continuing bibliography with indexes, supplement 190, February 1979

This bibliography lists 235 reports, articles, and other documents introduced into the NASA scientific and technical information system in January 1979

Solving the multistage PMU placement problem by integer programming and equivalent network design model

Recently, phasor measurement units (PMUs) are becoming widely used to measure the electrical waves on a power grid to determine the health of the system. Because of high expense for PMUs, it is important to place minimized number of PMUs on power grids without losing the function of maintaining system observability. In practice, with a budget limitation at each time point, the PMUs are placed in a multistage framework spanning in a long-term period, and the proposed multistage PMU placement problem is to find the placement strategies. Within each stage for some time point, the PMUs should be placed to maximize the observability and the complete observability should be ensured in the planned last stage. In this paper, the multistage PMU placement problem is formulated by a mixed integer program (MIP) with consideration of the zero-injection bus property in power systems. To improve the computational efficiency, another MIP, based on the equivalent network flow model for the PMU placement problem, is proposed. Numerical experiments on several test cases are performed to compare the two MIPs.12 month embargo; published online: 13 June 2018This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

High-reliability architectures for networks under stress

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2003.Includes bibliographical references (p. 157-165).This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.In this thesis, we develop a methodology for architecting high-reliability communication networks. Previous results in the network reliability field are mostly theoretical in nature with little immediate applicability to the design of real networks. We bring together these contributions and develop new results and insights which are of value in designing networks that meet prescribed levels of reliability. Furthermore, most existing results assume that component failures are statistically independent in nature. We take initial steps in developing a methodology for the design of networks with statistically dependent link failures. We also study the architectures of networks under extreme stress.by Guy E. Weichenberg.S.M

수도권 통합대중교통체계 교통카드 자료 기반 수입금 산정 방안

학위논문(박사) -- 서울대학교대학원 : 공과대학 건설환경공학부, 2022.2. 고승영.The Integrated Fare System for the Seoul Metropolitan Public Transportation Network) is one in which the metropolises of Seoul, Gyeonggi, Incheon, However the Smartcard data indicates the movement of passengers based on subway terminal IDs. Therefore, it is difficult to analyze the exact route of passengers in the presence of transfer stations. This unknown information in turn leads to the problem of fare calculation and revenue allocation by transportation agencies. In the case of the passenger's undetermined route, the fare is calculated by assuming that the fare is based on the minimum travel distance, not based on the actual route of the passenger. As these routes and fare routes appear as different results, the settlement between bus and subway is established on day-to-day settlement between operating agencies of the current metropolitan integrated fare system. However, settlement between subway operating agencies is carried out every to 5 years by establishing a model that estimates the actual travel route of passengers. Currently, the issue of settlement of subway transport agencies has become a very important role in the operation of transport agencies. Also, due to the agreement on transfer loss compensation between local governments, the situation of the dispute is expanding to a problem that is extended at the government level. This problem is expected to be exacerbated by the entry of new private transportation means such as GTX, light rail, and KTX, and regional expansion of the fare system. This study, estimate the fares charged to passengers as settlement fees, additional fees, separate fees, and independent fees by modeling the minimum time route search and minimum distance route search linking the departure and arrival terminal IDs of the Smartcard. In this case, the minimum time route was assumed to represent the actual movement of passengers and applied as a method for distribution of revenues by transport agencies along with separate fares from privately financed agencies. The minimum distance route was applied to simulate the added fare method currently applied in the subway. As a route search technique, the metropolitan subway was recognized as a network composed of terminal IDs, and Big Node was applied as a station name composed of a set of terminal IDs. Also, due to the need to consider transfers and multiple stages in the subway network, we proposed a method to ensure an optimal solution without network expansion by introducing link-label method. Theories and case studies that are used in the allocation of revenues of actual transportation organizations are presented.스마트카드자료는 수도권 지하철의 승객의 이동을 단말기ID로 나타내기 때문에 환승역이 존재하는 상황에서 승객의 이동경로를 분석하기 어렵다. 따라서 지하철 승객의 이동은 요금산정 및 운송기관의 수입금배분과 관련되어 승객이동경로의 미확정문제가 확대되고 있는 실정이다. 본 연구는 스마트카드의 출발-도착 단말기ID를 연결하는 최소시간경로탐색과 최소거리경로타색을 시행하여 승객에게 부과되는 요금을 추가요금, 별도요금으로 추정하는 방안을 마련하였다. 이때 최소시간경로는 승객의 실제이동을 대변하는 것으로 가정하고 민자기관의 별도요금과 함께 운송기관의 수입금배분 방안으로 적용하였다. 최소거리경로는 현재 지하철에서 적용하는 추가요금부과방식을 모사하기 위하여 적용하였다. 경로탐색기법으로 수도권 지하철을 단말기ID로 구성된 네트워크로 인식하고 빅노드를\ 단말기ID 집합으로 구성된 역사명으로 적용하였다. 또한 빅도드로 구축된 지하철 네트워크가 환승과 다수단을 고려할 필요성으로 인하여 링크표지를 도입하여 네트워크확장없이 최적해를 보장하는 방안을 제안하였다. 탐색된 최소거리 및 시간경로를 통하여 요금을 산정하고 누락된 민자기관의 별도요금을 개선하며 무임승차에 대한 운송기관의 수입금 배분기여도를 산정하여 사례연구로서 제시하였다.Chapter 1. Introduction 1 1.1. Study Background 1 1.2. Purpose of Research 4 Chapter 2. Literature Review 6 2.1. Metropolitan Smart Card Data 6 2.2. Integrated Fare System for the Metropolitan Public Transportation Network 9 2.3. Limits of the Smart Card Data 12 2.4. Review of related literature on Fare and Revenue allocation using Smart Card Data 17 2.5. International cases of Transit Fare and Revenue allocation 19 2.6. Smart Card based Subway Route Choice Method 20 2.7. Subway Information Provision Platform 26 2.8. Research Contribution 27 Chapter 3. Methodology 29 3.1. Smart Card Data Trip Chain Subway Mode Route Choice Model 29 3.2. Smart Card Data Trip Chain Fare Calculation Model 34 3.3. Smart Card Data Trip Chain IFS Revenue Calculation Model 35 3.4. Smart Card Data Trip Chain Subway Revenue Allocation Model 36 Chapter 4. Result 37 4.1. Input data 37 4.2. Subway Passenger Route, Fare, and Revenue Allocation 43 4.3. Smart Card Data Trip Chain Fare Analysis 45 4.4. Verification of Optimal Route Search Accuracy 47 4.5. Estimation of omitted extra fare for subway private agencies 48 4.6. Case Stuy 49 Chapter 5. Conclusion 75 5.1. Conclusion 75 5.2. Future Research 76 Bibliography 77 Abstract in Korean 80박