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Abstractm Despite BGP's critical importance as the de-facto Internet inter-domain routing protocol, there is little understanding of how BGP actually performs under stressful conditions when dependable routing is most needed. In this paper, we examine BGP's behavior during one stressful period, the Code Red/Nimda attack on September 18, 2001. The attack was correlated with a 30-fold increase in the BGP update messages at a monitoring point which peers with a number of Internet service providers. Our examination of BGP's behavior during the event concludes that BGP exhibited no significant abnormality, and that over 40% of the observed updates can be attributed to the monitoring artifact in current BGP measurement settings. Our analysis, however, does reveal several weak points in both the protocol and its implementation, such as BGP's sensitivity to the transport session reliability, its inability to avoid the global propagation of small local changes, and its certain implementation features whose otherwise benign effects only get amplified under stressful conditions. We also identify areas for improvement in the current network measurement and monitoring effort.

Maximum Boolean satisfiability (max-SAT) is the optimization counterpart of Boolean satisfiability (SAT), in which a variable assignment is sought to satisfy the maximum number of clauses in a Boolean formula. A branch and bound algorithm based on the Davis-Putnam-Logemann-Loveland procedure (DPLL) is one of the most competitive exact algorithms for solving max-SAT. In this paper, we propose and investigate a number of strategies for max-SAT. The first strategy is a set of unit propagation or unit resolution rules for max-SAT. We summarize three existing unit propagation rules and propose a new one based on a nonlinear programming formulation of max-SAT. The second strategy is an effective lower bound based on linear programming (LP). We show that the LP lower bound can be made effective as the number of clauses increases. The third strategy consists of a a binary-clause first rule and a dynamicweighting variable ordering rule, which are motivated by a thorough analysis of two existing well-known variable orderings. Based on the analysis of these strategies, we develop an exact solver for both max-SAT and weighted max-SAT. Our experimental results on random problem instances and many instances from the max-SAT libraries show that our new solver outperforms most of the existing exact max-SAT solvers, with orders of magnitude of improvement in many cases.

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Measurements have shown evidences of inter-domain packet forwarding loops in the Internet, but the exact cause of these loops remains unclear. As one of the efforts in identifying the causes, this paper examines how transient loops can be created at the inter-domain level via BGP, and what are the major factors that contribute to duration of the routing loops. As a path-vector routing protocol, BGP messages list the entire AS path to each destination and the path information enables each node to detect, thus break, arbitrarily long routing loops involving itself. However, delays due to physical constrains and protocol mechanisms slow down routing updates propagation and the routing information inconsistencies among the nodes lead to loop formation during convergence. We show that the duration of transient BGP loops match closely to BGP's routing convergence time and the looping duration is linearly proportional to BGP's Minimum Route Advertisement Interval Timer (MRAI) value. We also examine four BGP routing convergence enhancements and show that two enhancements effective in speeding up routing convergence are also effective in reducing routing loops.

Summary In naturally fractured reservoirs, complex fracture systems can easily develop along a horizontal wellbore during hydraulic fracturing. In the fracture systems, multiple, discrete secondary fractures are connected to the multiple-fractured horizontal well (MFHW). Because of the fracture complexity, most studies about performance forecast of such MFHWs highly depend on numerical simulators. In this paper, a new semianalytical approach is proposed to overcome the challenge to analyze the pressure behavior of MFHWs in complex-fracture systems. First, a mathematical model for MFHWs with secondary-fracture networks is established. Then, with Gauss elimination and the Stehfest numerical algorithm (Stehfest 1970), the transient-pressure solution of the mathematical model is solved, and type curves of MFHWs with secondary-fracture networks are obtained. After that, model validation and sensitivity analysis are conducted. It is found that the presented approach can rapidly and accurately generate type curves of MFHWs with secondary-fracture networks. This work provides very meaningful references for reservoir engineers in fracturing evaluations as well as performance estimations of MFHWs in naturally fractured reservoirs.

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