A cascading failure is a process in a system of interconnected parts in which the failure of one or few parts can trigger the failure of other parts and so on. Such a failure may happen in many types of systems, including power transmission, computer networking, finance, transportation systems, organisms, the human body, and ecosystems.

An animation demonstrating how a single failure may result in other failures throughout a network.

Cascading failures may occur when one part of the system fails. When this happens, other parts must then compensate for the failed component. This in turn overloads these nodes, causing them to fail as well, prompting additional nodes to fail one after another.

## In power transmission

Cascading failure is common in power grids when one of the elements fails (completely or partially) and shifts its load to nearby elements in the system. Those nearby elements are then pushed beyond their capacity so they become overloaded and shift their load onto other elements. Cascading failure is a common effect seen in high voltage systems, where a single point of failure (SPF) on a fully loaded or slightly overloaded system results in a sudden spike across all nodes of the system. This surge current can induce the already overloaded nodes into failure, setting off more overloads and thereby taking down the entire system in a very short time.

This failure process cascades through the elements of the system like a ripple on a pond and continues until substantially all of the elements in the system are compromised and/or the system becomes functionally disconnected from the source of its load. For example, under certain conditions a large power grid can collapse after the failure of a single transformer.

Monitoring the operation of a system, in real-time, and judicious disconnection of parts can help stop a cascade. Another common technique is to calculate a safety margin for the system by computer simulation of possible failures, to establish safe operating levels below which none of the calculated scenarios is predicted to cause cascading failure, and to identify the parts of the network which are most likely to cause cascading failures.[1]

One of the primary problems with preventing electrical grid failures is that the speed of the control signal is no faster than the speed of the propagating power overload, i.e. since both the control signal and the electrical power are moving at the same speed, it is not possible to isolate the outage by sending a warning ahead to isolate the element.

The question if power grid failures are correlated have been studied in Daqing Li et al.[2] as well as by Paul DH Hines et al.[3]

### Examples

Cascading failure caused the following power outages:

## In computer networks

Cascading failures can also occur in computer networks (such as the Internet) in which network traffic is severely impaired or halted to or between larger sections of the network, caused by failing or disconnected hardware or software. In this context, the cascading failure is known by the term cascade failure. A cascade failure can affect large groups of people and systems.

The cause of a cascade failure is usually the overloading of a single, crucial router or node, which causes the node to go down, even briefly. It can also be caused by taking a node down for maintenance or upgrades. In either case, traffic is routed to or through another (alternative) path. This alternative path, as a result, becomes overloaded, causing it to go down, and so on. It will also affect systems which depend on the node for regular operation.

### Symptoms

The symptoms of a cascade failure include: packet loss and high network latency, not just to single systems, but to whole sections of a network or the internet. The high latency and packet loss is caused by the nodes that fail to operate due to congestion collapse, which causes them to still be present in the network but without much or any useful communication going through them. As a result, routes can still be considered valid, without them actually providing communication.

If enough routes go down because of a cascade failure, a complete section of the network or internet can become unreachable. Although undesired, this can help speed up the recovery from this failure as connections will time out, and other nodes will give up trying to establish connections to the section(s) that have become cut off, decreasing load on the involved nodes.

A common occurrence during a cascade failure is a walking failure, where sections go down, causing the next section to fail, after which the first section comes back up. This ripple can make several passes through the same sections or connecting nodes before stability is restored.

### History

Cascade failures are a relatively recent development, with the massive increase in traffic and the high interconnectivity between systems and networks. The term was first applied in this context in the late 1990s by a Dutch IT professional and has slowly become a relatively common term for this kind of large-scale failure.[citation needed]

### Example

Network failures typically start when a single network node fails. Initially, the traffic that would normally go through the node is stopped. Systems and users get errors about not being able to reach hosts. Usually, the redundant systems of an ISP respond very quickly, choosing another path through a different backbone. The routing path through this alternative route is longer, with more hops and subsequently going through more systems that normally do not process the amount of traffic suddenly offered.

This can cause one or more systems along the alternative route to go down, creating similar problems of their own.

Related systems are also affected in this case. As an example, DNS resolution might fail and what would normally cause systems to be interconnected, might break connections that are not even directly involved in the actual systems that went down. This, in turn, may cause seemingly unrelated nodes to develop problems, that can cause another cascade failure all on its own.

In December 2012, a partial loss (40%) of Gmail service occurred globally, for 18 minutes. This loss of service was caused by a routine update of load balancing software which contained faulty logic—in this case, the error was caused by logic using an inappropriate 'all' instead of the more appropriate 'some'.[4] The cascading error was fixed by fully updating a single node in the network instead of partially updating all nodes at one time.

Certain load-bearing structures with discrete structural components can be subject to the "zipper effect", where the failure of a single structural member increases the load on adjacent members. In the case of the Hyatt Regency walkway collapse, a suspended walkway (which was already overstressed due to an error in construction) failed when a single vertical suspension rod failed, overloading the neighboring rods which failed sequentially (i.e. like a zipper). A bridge that can have such a failure is called fracture critical, and numerous bridge collapses have been caused by the failure of a single part. Properly designed structures use an adequate factor of safety and/or alternate load paths to prevent this type of mechanical cascade failure.[5]

## Other examples

### Biology

Biochemical cascades exist in biology, where a small reaction can have system-wide implications. One negative example is ischemic cascade, in which a small ischemic attack releases toxins which kill off far more cells than the initial damage, resulting in more toxins being released. Current research is to find a way to block this cascade in stroke patients to minimize the damage.

In the study of extinction, sometimes the extinction of one species will cause many other extinctions to happen. Such a species is known as a keystone species.

### Electronics

Another example is the Cockcroft–Walton generator, which can also experience cascade failures wherein one failed diode can result in all the diodes failing in a fraction of a second.

Yet another example of this effect in a scientific experiment was the implosion in 2001 of several thousand fragile glass photomultiplier tubes used in the Super-Kamiokande experiment, where the shock wave caused by the failure of a single detector appears to have triggered the implosion of the other detectors in a chain reaction.

### Finance

In finance, the risk of cascading failures of financial institutions is referred to as systemic risk: the failure of one financial institution may cause other financial institutions (its counterparties) to fail, cascading throughout the system.[6] Institutions that are believed to pose systemic risk are deemed either "too big to fail" (TBTF) or "too interconnected to fail" (TICTF), depending on why they appear to pose a threat.

Note however that systemic risk is not due to individual institutions per se, but due to the interconnections. Frameworks to study and predict the effects of cascading failures have been developed in the research literature.[7][8][9][10][6] A framework based on network theory and cascading failures that provides useful tools for policy makers and for testing macroprudential dynamical stress has been developed.[11]

A related (though distinct) type of cascading failure in finance occurs in the stock market, exemplified by the 2010 Flash Crash.[9]

Fig. 1: Illustration of the interdependent relationship among different infrastructures

Fig. 2. Schematic demonstration of first- and second-order percolation transitions. In the second-order case, the giant component is continuously approaching zero at the percolation threshold p = ${\displaystyle p_{c}}$ . In the first-order case, the giant component approaches zero discontinuously

Furthermore, it was shown that such interdependent systems when embedded in space are extremely vulnerable to localized attacks or failures. Above a critical radius of damage, the failure may spread to the entire system.[19]

Cascading failures spreading of localized attacks on spatial multiplex networks with a community structure has been studied by Vaknin et al.[20] Universal features of cascading failures in interdependent networks have been reported Duan et al.[21] A method for mitigating cascading failures in networks using localized information has been developed by Smolyak et al.[22]

For a comprehensive review on cascading failures in complex networks see Valdez et al.[23]

A model for cascading failures due to overload propagation is the Motter–Lai model.[24] The tempo-spatial propagation of such failures have been studied by Jichang Zhao et al.[25]

## References

1. ^ Zhai, Chao (2017). "Modeling and Identification of Worst-Case Cascading Failures in Power Systems". arXiv:1703.05232 [cs.SY].
2. ^ Daqing, Li; Yinan, Jiang; Rui, Kang; Havlin, Shlomo (2014-06-20). "Spatial correlation analysis of cascading failures: Congestions and Blackouts". Scientific Reports. 4 (1): 5381. Bibcode:2014NatSR...4E5381D. doi:10.1038/srep05381. ISSN 2045-2322. PMC 4064325. PMID 24946927.
3. ^ Hines, Paul D. H.; Dobson, Ian; Rezaei, Pooya (2016). "Cascading Power Outages Propagate Locally in an Influence Graph that is not the Actual Grid Topology". IEEE Transactions on Power Systems: 1. arXiv:1508.01775. doi:10.1109/TPWRS.2016.2578259. ISSN 0885-8950. S2CID 2097502.
4. ^ "Why Gmail went down: Google misconfigured load balancing servers (Updated)". 11 December 2012.
5. ^ Petroski, Henry (1992). To Engineer Is Human: The Role of Failure in Structural Design. Vintage. ISBN 978-0-679-73416-1.
6. ^ a b Huang, Xuqing; Vodenska, Irena; Havlin, Shlomo; Stanley, H. Eugene (2013). "Cascading Failures in Bi-partite Graphs: Model for Systemic Risk Propagation". Scientific Reports. 3: 1219. arXiv:1210.4973. Bibcode:2013NatSR...3E1219H. doi:10.1038/srep01219. ISSN 2045-2322. PMC 3564037. PMID 23386974.
7. ^ Acemoglu, Daron; Ozdaglar, Asuman; Tahbaz-Salehi, Alireza (2015). "Systemic Risk and Stability in Financial Networks". American Economic Review. American Economic Association. 105 (2): 564–608. doi:10.1257/aer.20130456. hdl:1721.1/100979. ISSN 0002-8282. S2CID 7447939.
8. ^ Gai, Prasanna; Kapadia, Sujit (2010-08-08). "Contagion in financial networks". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 466 (2120): 2401–2423. Bibcode:2010RSPSA.466.2401G. doi:10.1098/rspa.2009.0410. ISSN 1364-5021. S2CID 9945658.
9. ^ a b Elliott, Matthew; Golub, Benjamin; Jackson, Matthew O. (2014-10-01). "Financial Networks and Contagion". American Economic Review. 104 (10): 3115–3153. doi:10.1257/aer.104.10.3115. ISSN 0002-8282.
10. ^ Li, W; Kenett, DY; Yamasaki, K; Stanley, HE; Havlin, S (2017). "Ranking the economic importance of countries and industries". Journal of Network Theory in Finance. 3: 1–17. arXiv:1408.0443. doi:10.21314/JNTF.2017.031. ISSN 2055-7795. S2CID 6729106.
11. ^ Levy-Carciente, Sary; Kenett, Dror Y.; Avakian, Adam; Stanley, H. Eugene; Havlin, Shlomo (2015). "Dynamical macroprudential stress testing using network theory". Journal of Banking & Finance. 59: 164–181. doi:10.1016/j.jbankfin.2015.05.008.
12. ^
13. ^ Rinaldi, S.M.; Peerenboom, J.P.; Kelly, T.K. (2001). "Identifying, understanding, and analyzing critical infrastructure interdependencies". IEEE Control Systems Magazine. 21 (6): 11–25. doi:10.1109/37.969131.
14. ^ V. Rosato, Issacharoff, L., Tiriticco, F., Meloni, S., Porcellinis, S.D., & Setola, R. (2008). "Modelling interdependent infrastructures using interacting dynamical models". International Journal of Critical Infrastructures. 4: 63–79. doi:10.1504/IJCIS.2008.016092.
15. ^ S. V. Buldyrev, R. Parshani, G. Paul, H. E. Stanley, S. Havlin (2010). "Catastrophic cascade of failures in interdependent networks". Nature. 464 (7291): 1025–8. arXiv:1012.0206. Bibcode:2010Natur.464.1025B. doi:10.1038/nature08932. PMID 20393559. S2CID 1836955.
16. ^ Bashan, Amir; Berezin, Yehiel; Buldyrev, Sergey V.; Havlin, Shlomo (2013). "The extreme vulnerability of interdependent spatially embedded networks". Nature Physics. 9 (10): 667–672. arXiv:1206.2062. Bibcode:2013NatPh...9..667B. doi:10.1038/nphys2727. ISSN 1745-2473. S2CID 12331944.
17. ^ Zhou, D.; Bashan, A.; Cohen, R.; Berezin, Y.; Shnerb, N.; Havlin, S. (2014). "Simultaneous first- and second-order percolation transitions in interdependent networks". Phys. Rev. E. 90 (1): 012803. arXiv:1211.2330. Bibcode:2014PhRvE..90a2803Z. doi:10.1103/PhysRevE.90.012803. PMID 25122338. S2CID 180058.
18. ^ Di Muro, M. A.; La Rocca, C. E.; Stanley, H. E.; Havlin, S.; Braunstein, L. A. (2016-03-09). "Recovery of Interdependent Networks". Scientific Reports. 6 (1): 22834. arXiv:1512.02555. Bibcode:2016NatSR...622834D. doi:10.1038/srep22834. ISSN 2045-2322. PMC 4783785. PMID 26956773.
19. ^ Berezin, Yehiel; Bashan, Amir; Danziger, Michael M.; Li, Daqing; Havlin, Shlomo (2015-03-11). "Localized attacks on spatially embedded networks with dependencies". Scientific Reports. 5 (1): 8934. Bibcode:2015NatSR...5E8934B. doi:10.1038/srep08934. ISSN 2045-2322. PMC 4355725. PMID 25757572.
20. ^ D Vaknin, B Gross, SV Buldyrev, S Havlin (2020). "Spreading of localized attacks on spatial multiplex networks with a community structure". Physical Review Research. 2 (4): 043005. arXiv:1912.05677. Bibcode:2020PhRvR...2d3005V. doi:10.1103/PhysRevResearch.2.043005. S2CID 209324155.CS1 maint: multiple names: authors list (link)
21. ^ Duan, Dongli; Lv, Changchun; Si, Shubin; Wang, Zhen; Li, Daqing; Gao, Jianxi; Havlin, Shlomo; Stanley, Eugene; Boccaletti, Stefano (2019). "Universal behavior of cascading failures in interdependent networks". Proceedings of the National Academy of Sciences. 116 (45): 22452–22457. Bibcode:2019PNAS..11622452D. doi:10.1073/pnas.1904421116. PMC 6842597. PMID 31624122.
22. ^ A Smolyak, O Levy, I Vodenska, S Buldyrev, S Havlin (2020). "Mitigation of cascading failures in complex networks". Scientific Reports. `0 (1): 16124. Bibcode:2020NatSR..1016124S. doi:10.1038/s41598-020-72771-4. PMC 7528121. PMID 32999338. S2CID 222109558.CS1 maint: multiple names: authors list (link)
23. ^ Lucas D Valdez, Louis Shekhtman, Cristian E La Rocca, Xin Zhang, Sergey V Buldyrev, Paul A Trunfio, Lidia A Braunstein, Shlomo Havlin (2020). "Cascading failures in complex networks". Journal of Complex Networks. 8 (2).CS1 maint: multiple names: authors list (link)
24. ^ Motter, A. E.; Lai, Y. C. (2002). "Cascade-based attacks on complex networks". Phys. Rev. E. 66 (6 Pt 2): 065102. arXiv:cond-mat/0301086. Bibcode:2002PhRvE..66f5102M. doi:10.1103/PhysRevE.66.065102. PMID 12513335. S2CID 17189308.
25. ^ Zhao, J.; Li, D.; Sanhedrai, H.; Cohen, R.; Havlin, S. (2016). "Spatio-temporal propagation of cascading overload failures in spatially embedded networks". Nature Communications. 7: 10094. Bibcode:2016NatCo...710094Z. doi:10.1038/ncomms10094. PMC 4729926. PMID 26754065.