[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82698-en":3,"doc-seo-82698-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},82698,4810365810221,"Aurora","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",8,"Research & Report","Overload-Based Cascades in Multiplex Flow Networks with Partial Functionality","Overload-driven cascading failures are common in networks such as power grids, supply chains, and cloud systems, yet most flow-network models assume joint functionality where a node either works or fails as a whole. This work studies multiplex flow networks with partial functionality, where a node supports multiple layer-specific flows sharing limited resources. Cross-layer influence factors quantify how heavy load in one functionality reduces capacity in others. Mean-field analysis yields recursive equations for final surviving fractions after cascades stop, validated by simulations, and robustness features and allocation strategies are characterized.","arXiv :2607 .02844v1 [ ee ss . SY] 3 Jul 2026  \nOverload-Based Cascades in Multiplex Flow Networks with Partial Functionality  \nOrkun ˙Irsoy 1, ∗ and Osman Ya˘gan 1,†  \n1 Department of Electrical and Computer Engineering,  \nCarnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA  \n(Dated: July 7, 2026)  \nCascading failures driven by load/flow redistribution are widespread in networked systems such as power grids, supply chains, and cloud computing centers. Most existing flow-network models assume that a node either functions or fails as a whole (which we refer to as joint functionality), but in many real systems a node supports several distinct flows/functionalities that share node-level resources, and failure in one of them does not necessarily imply failure in the others. We study this setting through multiplex flow networks with partial functionality, in which nodes’ functionalities share limited resources, but a node can remain operational in some functionalities while having failed in others. Due to shared resources, a heavy load on one functionality reduces the capacity available to the others, which is quantified by cross-layer influence factors. When a node fails in one layer, its load is redistributed among the surviving nodes in that layer, while the node may continue to operate in the others. Using mean-field analysis, we derive recursive equations for the final system sizes, i.e. the fraction of surviving nodes in each layer after the cascade stops, as a function of the initial fraction of failed nodes and the joint distribution of initial loads and capacities. We validate our analysis across several initial load–capacity distributions through simulations, and then analyze several characteristics of the cascade dynamics, such as non-monotone robustness curves, different cascade-outcome regimes, and their relation with increased cross-layer influence. We map the cascade outcomes to distinct steady-state regimes, including single-layer survival phases that are absent in joint-functionality models, and we show that partial functionality can increase robustness relative to the joint-functionality case. Finally, we study robustness maximization under a fixed total capacity budget by comparing several capacity allocation strategies. We propose a strategy that combines the cross-layer influence with local neighborhood information on load and degree, and show that it achieves the strongest robustness performance across the configurations considered.  \nI. INTRODUCTION  \nIn October 2025, a major outage in Amazon Web Services (AWS) disrupted internet platforms worldwide after a routing fault caused congestion and traffic redistribution, overloading multiple servers and triggering cascading service disruptions [1] . Earlier that year, in April 2025, an overload in the Iberian power grid initiated a cascade of generation losses and load shedding, resulting in a large-scale blackout across Spain and Portugal [2] . In both events, the failure of one component transferred excess load to dependent components, propagating through the network and leading to a system-wide collapse: the Iberian blackout alone affected tens of millions of people and severely interrupted transportation, telecommunications, and industrial activities across the region [2] . Such cascading failures [3] are a recurring hazard in a diverse range of networked systems such as supply chains [4, 5] and cloud data centers [6], and understanding how they propagate is essential for designing more robust infrastructure.  \nExisting studies on cascading failures consider various mechanisms of failure propagation. The percolation-based models [3, 7–11] focus on structural connectedness and apply to networks where system functionality depends  \n∗  \n†  \n[oirsoy@andrew.cmu.edu](oirsoy@andrew.cmu.edu)[oyagan@andrew.cmu.edu](oyagan@andrew.cmu.edu)  \non mutual reachability. These models are particularly suitable for communication and cyber-physical systems, where the ","cbCaihoHCrelSo3q","https://ap.wps.com/l/cbCaihoHCrelSo3q","pdf",4938396,1,18,"English","en",105,"# Introduction\n## Cascading failures and flow-redistribution background\n## Limits of joint-functionality and single-layer models\n## Motivation for multiplex flow networks with shared resources\n## Prior work and coupling approaches","[{\"question\":\"What is meant by “partial functionality” in multiplex flow networks?\",\"answer\":\"A node can remain operational in some layer-specific functionalities while failing in others. The different functionalities share limited node-level resources, so failure or heavy load in one layer affects the capacity available to the others.\"},{\"question\":\"How does overload in one functionality influence other functionalities?\",\"answer\":\"A heavy load in one layer reduces the capacity available to the other layer functionalities through cross-layer influence factors. This coupling determines how cascades propagate when load is redistributed among surviving nodes in a layer.\"},{\"question\":\"What does the mean-field analysis compute in this study?\",\"answer\":\"It derives recursive equations for the final system sizes, i.e., the fraction of surviving nodes in each layer after the cascade stops. These outcomes depend on the initial failed-node fraction and the joint distribution of initial loads and capacities.\"}]",1784182360,45,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"overload-based-cascades-in-multiplex-flow-networks-with-partial-functionality","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/overload-based-cascades-in-multiplex-flow-networks-with-partial-functionality/82698/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What is meant by “partial functionality” in multiplex flow networks?","Question",{"text":75,"@type":76},"A node can remain operational in some layer-specific functionalities while failing in others. The different functionalities share limited node-level resources, so failure or heavy load in one layer affects the capacity available to the others.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does overload in one functionality influence other functionalities?",{"text":80,"@type":76},"A heavy load in one layer reduces the capacity available to the other layer functionalities through cross-layer influence factors. This coupling determines how cascades propagate when load is redistributed among surviving nodes in a layer.",{"name":82,"@type":73,"acceptedAnswer":83},"What does the mean-field analysis compute in this study?",{"text":84,"@type":76},"It derives recursive equations for the final system sizes, i.e., the fraction of surviving nodes in each layer after the cascade stops. These outcomes depend on the initial failed-node fraction and the joint distribution of initial loads and capacities.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":45,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":45,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":45,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":45,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":45,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":45,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":45,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]