[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-126603-en":3,"doc-seo-126603-105":30,"detail-sidebar-cat-0-en-105":92},{"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":27,"seo_description":14,"update_tm":28,"read_time":29},126603,687207020761,"Patrick","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",8,"Research & Report","Optimal Control of Multiclass Fluid Queueing Networks - A Machine Learning Approach","We propose a machine learning approach to the optimal control of multiclass fluid queueing networks (MFQNETs) that yields explicit and interpretable control policies. The study proves that a threshold-type optimal policy exists, with threshold curves given by hyperplanes through the origin. Optimal Classification Trees with hyperplane splits (OCT-H) learn policies using numerical MFQNET solutions as training data, achieving 100% test accuracy. Offline training may take days for large systems, while online execution takes milliseconds.","arXiv :2307 . 12405v 1 [ cs .LG] 23 Jul 2023  \nOptimal Control of Multiclass Fluid Queueing Networks: A Machine Learning  \nApproach  \nDimitris Bertsimasa,􀀃, Cheol Woo Kimb  \naSloan School of Management, Massachusetts Institute of Technology, 100 Main Street, Cambridge, 02142, United  \nStates  \nb Operations Research Center, Massachusetts Institute of Technology, 1 Amherst Street, Cambridge, 02142, United  \nStates  \nAbstract  \nWe propose a machine learning approach to the optimal control of multiclass fluid queueing networks (MFQNETs) that provides explicit and insightful control policies. We prove that a threshold type optimal policy exists for MFQNET control problems, where the threshold curves are hyperplanes passing through the origin. We use Optimal Classification Trees with hyperplane splits (OCT-H) to learn an optimal control policy for MFQNETs. We use numerical solutions of MFQNET control problems as a training set and apply OCT-H to learn explicit control policies. We report experimental results with up to 33 servers and 99 classes that demonstrate that the learned policies achieve 100% accuracy on the test set. While the offline training of OCT-H can take days in large networks, the online application takes milliseconds.  \nKeywords: Queueing Network Control, Optimal Decision Trees, Machine Learning, Fluid Approximation, Optimal Control  \n1. Introduction  \nMulticlass queueing networks (MQNETs) are complex systems that model the behavior of multiple classes of jobs, each with their own arrival and service rates, routing paths and holding costs. These networks find numerous applications in diverse fields, including manufacturing (Kumar, 1993), healthcare (Cochran & Roche, 2009) and communication networks (Srikant & Ying, 2014) among many. The control of MQNETs is of great importance in improving system efficiency, optimizing resource allocation, and reducing operational costs. However, the inherent complexity of these systems makes their analysis and control a challenging task.  \nMulticlass fluid queueing networks (MFQNETs) have been developed as a deterministic, continuous approximation of MQNETs, primarily to provide a tractable method for analyzing the stability of the underlying MQNETs. (Dai, 1995; Stolyar, 1995) demonstrate that the stability of MFQNETs implies the stability of underlying MQNETs. Several related studies including (Meyn, 1995; Dumas, 1999; Gamarnik & Hasenbein, 2005) have also explored the topic. See (Bertsimas & Gamarnik, 2022) for a comprehensive review.  \n􀀃 Corresponding author  \nEmail addresses: [dbertsim@mit.edu](dbertsim@mit.edu) (Dimitris Bertsimas), [acwkim@mit.edu](acwkim@mit.edu) (Cheol Woo Kim)  \nPreprint submitted to Operations Research July 25, 2023  \nMFQNETs also provide a useful way to construct control policies for MQNETs as the optimal control of MFQNETs is often much more tractable than the optimal control of underlying MQNETs. To this end, several approaches have been proposed in the literature. (Maglaras, 1999, 2000) propose discrete review policies and show that they achieve asymptotic optimality and stability under fluidscailing. (Bertsimas et al., 2015) provide a robust formulation of MFQNET control problem and translate the resulting policy to the underlying MQNET. (Bertsimas & Sethuraman, 2002; Dai & Weiss, 2002) propose methods to approximately minimize make-span based on the associated fluid models. For a comprehensive review of the topic, see (Meyn, 2007) and (Bertsimas & Gamarnik, 2022) .  \nMathematically, optimal control of MFQNETs falls into a subclass of infinite dimensional linear optimization models known as separated continuous linear programs (SCLPs) . Several researchers have investigated the theoretical properties of SCLPs, such as (Anderson et al. , 1983; Pullan, 1995, 1996, 1997) . (Avram et al., 1995) find closed-form optimal policies for specific MFQNETs using optimality conditions from optimal control theory. Other works have proposed numerical algorithms for solving SCLPs","cbCaioAZZTmv0ZQQ","https://ap.wps.com/l/cbCaioAZZTmv0ZQQ","pdf",826251,1,21,"English","en",105,"# Introduction\n## Multiclass and fluid queueing networks\n## Separated continuous linear programs\n## Motivation and related machine learning work\n## Paper contribution and approach","[{\"question\":\"What problem does the paper address?\",\"answer\":\"The paper addresses optimal control of multiclass fluid queueing networks (MFQNETs), aiming to obtain efficient and explicit control policies rather than only numerical solutions.\"},{\"question\":\"What type of optimal policy is shown to exist?\",\"answer\":\"It proves that a threshold-type optimal policy exists, where threshold curves are hyperplanes passing through the origin.\"},{\"question\":\"How does the proposed method learn the control policy and what are its performance results?\",\"answer\":\"The method uses Optimal Classification Trees with hyperplane splits (OCT-H) trained on numerical MFQNET solutions, and experiments (up to 33 servers and 99 classes) show 100% accuracy on the test set, with milliseconds for online application.\"}]","Optimal Control of Multiclass Fluid Queueing Networks - A Machine Learning Approach | PDF",1785933666,53,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":87,"head_meta":89,"extra_data":91,"updated_unix":28},"optimal-control-of-multiclass-fluid-queueing-networks-a-machine-learning-approach","",{"@graph":36,"@context":86},[37,54,69],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/optimal-control-of-multiclass-fluid-queueing-networks-a-machine-learning-approach/126603/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-22","2026-08-05",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"What problem does the paper address?","Question",{"text":76,"@type":77},"The paper addresses optimal control of multiclass fluid queueing networks (MFQNETs), aiming to obtain efficient and explicit control policies rather than only numerical solutions.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"What type of optimal policy is shown to exist?",{"text":81,"@type":77},"It proves that a threshold-type optimal policy exists, where threshold curves are hyperplanes passing through the origin.",{"name":83,"@type":74,"acceptedAnswer":84},"How does the proposed method learn the control policy and what are its performance results?",{"text":85,"@type":77},"The method uses Optimal Classification Trees with hyperplane splits (OCT-H) trained on numerical MFQNET solutions, and experiments (up to 33 servers and 99 classes) show 100% accuracy on the test set, with milliseconds for online application.","https://schema.org",{"og:url":52,"og:type":88,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":90,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":93},[94,98,102,106,111,116,121,124,129,132,136],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":95,"show_sort_weight":96,"slug":97},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":103,"show_sort_weight":104,"slug":105},"Exam",70,"exam",{"id":107,"doc_module":4,"doc_module_name":46,"category_name":108,"show_sort_weight":109,"slug":110},5,"Comic",60,"comic",{"id":112,"doc_module":4,"doc_module_name":46,"category_name":113,"show_sort_weight":114,"slug":115},6,"Technology",50,"technology",{"id":117,"doc_module":4,"doc_module_name":46,"category_name":118,"show_sort_weight":119,"slug":120},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":122,"slug":123},30,"research-report",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":126,"show_sort_weight":127,"slug":128},9,"Religion & Spirituality",20,"religion-spirituality",{"id":127,"doc_module":4,"doc_module_name":46,"category_name":130,"show_sort_weight":127,"slug":131},"World Cup","world-cup",{"id":133,"doc_module":4,"doc_module_name":46,"category_name":134,"show_sort_weight":133,"slug":135},10,"Lifestyle","lifestyle",{"id":137,"doc_module":4,"doc_module_name":46,"category_name":138,"show_sort_weight":107,"slug":139},19,"General","general"]