An explicit, analytical model is presented of finite‐amplitude waves in shallow water. The waves in question have two independent spatial periods, in two independent horizontal directions. Both short‐crested and long‐crested waves are available from the model. Every wave pattern is an exact solution of the Kadomtsev‐Petviashvili equation, and is based on a Riemann theta function of genus 2. These biperiodic waves are direct generalizations of the well‐known (simply periodic) cnoidal waves. Just as cnoidal waves are often used as one‐dimensional models of “typical” nonlinear, periodic waves in shallow water, these biperiodic waves may be considered to represent “typical” nonlinear, periodic waves in shallow water without the assumption of one‐dimensionality.
A single fault in a telecommunication network frequently results in a number of alarms being reported to the network operator. This multitude of alarms can easily obscure the real cause of the fault. In addition, when multiple faults occur at approximately the same time, it can be difficult to determine how many faults have occurred, thus creating the possibility that some may be missed. A variety of solution approaches have been proposed in the literature, however, practically deployable, commercial solutions remain elusive. The experiences of the Network Fault and Alarm Correlator and Tester (NetFACT) project, carried out at IBM Research and described in this paper, provide some insight as to why this is the case, and what must be done to overcome the barriers encountered. Our observations are based on experimental use of the NetFACT system to process a live, continuous alarm stream from a portion of the Advantis physical backbone network, one of the largest private telecommunications networks in the world.The NetFACT software processes the incoming alarm stream and determines the faults from the alarms. It attempts to narrow down the likely root causes of each fault, to the greatest extent possible, given the available information. To accomplish this, NetFACT employs a novel combination of diagnostic techniques supported by an object-oriented model of the network being managed. This model provides an abstract view of the underlying network of heterogeneous devices. A number of issues were explored in the project including the extensibility of the design to other types of networks, and impact of the practical realities that must be addressed if prototype systems such as NetF ACT are to lead to commercial products.
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