The impact of a network split on cascading failure processes

Cascading failure models are typically used to capture the phenomenon where failures possibly trigger further failures in succession, causing knock-on effects. In many networks this ultimately leads to a disintegrated network where the failure propagation continues independently across the various components. In order to gain insight in the impact of network splitting on cascading failure processes, we extend a well-established cascading failure model for which the number of failures obeys a power-law distribution. We assume that a single line failure immediately splits the network in two components, and examine its effect on the power-law exponent. The results provide valuable qualitative insights that are crucial first steps towards understanding more complex network splitting scenarios

Scale-free cascading failures:Generalized approach for all simple, connected graphs

Cascading failures, wherein the failure of one component triggers subsequent failures in complex interconnected systems, pose a significant risk of disruptions and emerge across various domains. Understanding and mitigating the risk of such failures is crucial to minimize their impact and ensure the resilience of these systems. In multiple applications, the failure processes exhibit scale-free behavior in terms of their total failure sizes. Various models have been developed to explain the origin of this scale-free behavior. A recent study proposed a novel hypothesis, suggesting that scale-free failure sizes might be inherited from scale-free input characteristics in power networks. However, the scope of this study excluded certain network topologies. Here, motivated by power networks, we strengthen this hypothesis by generalizing to a broader range of graph topologies where this behavior is manifested. Our approach yields a universal theorem applicable to all simple, connected graphs, revealing that when a cascade leads to network disconnections, the total failure size exhibits a scale-free tail inherited from the input characteristics. We do so by characterizing cascade sequences of failures in the asymptotic regime

Emergence of scale-free blackout sizes in power grids

We model power grids as graphs with heavy-tailed sinks, which represent demand from cities, and study cascading failures on such graphs. Our analysis links the scale-free nature of blackout sizes to the scale-free nature of city sizes, contrasting previous studies suggesting that this nature is governed by self-organized criticality. Our results are based on a new mathematical framework combining the physics of power flow with rare event analysis for heavy-tailed distributions, and are validated using various synthetic networks and the German transmission grid.Comment: 27 pages (6 pages + 21 pages with supplemental material). Accepted for publication in Physical Review Letter

First-passage time asymptotics over moving boundaries for random walk bridges

We study the asymptotic tail behavior of the first-passage time over a moving boundary for a random walk conditioned to return to zero, where the increments of the random walk have finite variance. Typically, the asymptotic tail behavior may be described through a regularly varying function with exponent-1/2, where the impact of the boundary is captured by the slowly varying function. Yet, the moving boundary may have a stronger effect when the tail is considered at a time close to the return point of the random walk bridge, leading to a possible phase transition depending on the order of the distance between zero and the moving boundary

Impact of network splitting on cascading failure blackouts

\u3cp\u3eAs electric transmission networks continue to increase in complexity and volatility, there is a growing potential for cascading failure effects to cause major blackouts. Understanding these effects and assessing the risks involved is of critical importance in operating the electric grid and maintaining high reliability. Analysis of empirical data suggests that blackout sizes obey a power-law with exponents that vary across data sets. For a particular macroscopic cascading failure model, such power-law behavior was also observed with one specific exponent. Motivated by the variation in the exponents revealed by empirical blackout data, we extend this cascading failure model with a network splitting mechanism. We demonstrate the impact of the latter feature on the power-law exponent of the blackout size. Moreover, we identify the most likely scenario for a severe blackout to occur. These insights provide crucial steps towards a deeper understanding of more complex network splitting scenarios.\u3c/p\u3

Delayed Workload Shifting in Many-server Systems

Motivated by the desire to shift workload during periods of overload, we extend established square-root capacity sizing rules for many-server systems in the Quality-and-Efficiency Driven (QED) regime. We propose Delayed Workload Shifting (DWS) which has two defining features: when there are n users in the system, newly arriving users are no longer admitted directly. Instead, these users will reattempt getting access after a stochastic delay until they are successful. The goal of DWS is to release pressure from the system during overloaded periods, and indeed we show that the performance gain can be substantial. We derive nontrivial corrections to classical QED approximations to account for DWS, and leverage these to control stationary and time-varying system behavior

Robustness of power-law behavior in cascading line failure models

Inspired by reliability issues in electric transmission networks, we use a probabilistic approach to study the occurrence of large failures in a stylized cascading line failure model. Such models capture the phenomenon where an initial line failure potentially triggers massive knock-on effects. Under certain critical conditions, the probability that the number of line failures exceeds a large threshold obeys a power-law distribution, a distinctive property observed in empiric blackout data. In this paper, we examine the robustness of the power-law behavior by exploring under which conditions this behavior prevails

The impact of a network split on cascading failure processes

Cascading failure models are typically used to capture the phenomenon where failures possibly trigger further failures in succession, causing knock-on effects. In many networks, this ultimately leads to a disintegrated network where the failure propagation continues independently across the various components. In order to gain insight into the impact of network splitting on cascading failure processes, we extend a well-established cascading failure model for which the number of failures obeys a power-law distribution. We assume that a single line failure immediately splits the network in two components and examine its effect on the power-law exponent. The results provide valuable qualitative insights that are crucial first steps toward understanding more complex network splitting scenarios. Cascading failure models are typically used to capture the phenomenon where failures possibly trigger further failures in succession, causing knock-on effects. In many networks, this ultimately leads to a disintegrated network where the failure propagation continues independently across the various components. In order to gain insight into the impact of network splitting on cascading failure processes, we extend a well-established cascading failure model for which the number of failures obeys a power-law distribution. We assume that a single line failure immediately splits the network in two components and examine its effect on the power-law exponent. The results provide valuable qualitative insights that are crucial first steps toward understanding more complex network splitting scenarios

Complete resource pooling of a load-balancing policy for a network of battery swapping stations

To reduce carbon emission in the transportation sector, there is currently a steady move taking place to an electrified transportation system. This brings about various issues for which a promising solution involves the construction and operation of a battery swapping infrastructure rather than in-vehicle charging of batteries. In this paper, we study a closed Markovian queueing network that allows for spare batteries under a dynamic arrival policy. We propose a provisioning rule for the capacity levels and show that these lead to near-optimal resource utilization, while guaranteeing good quality-of-service levels for electric vehicle users. Key in the derivations is to prove a state-space collapse result, which in turn implies that performance levels are as good as if there would have been a single station with an aggregated number of resources, thus achieving complete resource pooling