[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-657259-105":59,"doc-detail-657259-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","lecture-8-stock-and-flows-2","Lecture 8 - Stock and Flows 2","","Lecture covers the fundamentals of system dynamics using stock-and-flow models. It defines stocks (levels, state variables, compartments) as accumulations that capture the system state and change only through inflows and outflows, creating delay and inertia. The lecture then introduces flows (fluxes, rates, derivatives) and explains how rates are expressed per unit time and over measurement periods. Multiple examples and diagram-based interpretations illustrate net flow impact on stocks and show how altering a flow rate changes system behavior over time.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/lecture-8-stock-and-flows-2/657259/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/lecture-8-stock-and-flows-2/657259.png","ImageObject",300,407,{"name":92,"@type":93},"AfterMidnight","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","2026-10-26",true,{"@type":102,"interactionType":103,"userInteractionCount":8},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What are stocks in a stock-and-flow system dynamics model?","Question",{"text":112,"@type":113},"Stocks represent accumulations that capture the system’s state. They can be measured at a single instant, and they only change through flows into and out of them.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How are flows (rates) defined and expressed in the lecture?",{"text":117,"@type":113},"Flows are the mechanisms that cause changes to stocks. They are always expressed per some unit time, such as people/year, $/month, or litres/minute.",{"name":119,"@type":110,"acceptedAnswer":120},"Why do stocks create delay and inertia in system behavior?",{"text":121,"@type":113},"Because stocks change only via flows, any change in system state depends on the flow rates over time. This makes stocks the source of delay and supports inertia in the system.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},657259,1792976457,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":8,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":129,"read_time":144},962090896061,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","Introduction to Stocks & Flows  \nNathaniel Osgood  \n( [osgood@cs.usask.ca](osgood@cs.usask.ca) )  \nCMPT 858  \nState of the System: Stocks (“Levels”,“State Variables”,“Compartments”)  \n• Stocks (Levels) represent accumulations  \n– These capture the “state of the system”  \n– Mathematically, we will call these “state variables”  \n• These can be measured at one instant in time  \n• Stocks start with some initial value & are thereafter changed only by flows into & out of them  \n– There are no inputs that immediately change stocks  \n• Stocks are the source of delay in a system  \n• In a stock & flow diagram, shown as rectangles  \nExamples of Stocks  \n• Water in a tub or reservoir  \n• People of different types  \n– {Susceptible, infective, immune} people  \n– Pregnant women  \n– Women between the age of x and y  \n– High-risk individuals  \n• Healthcare workers  \n• Medicine in stocks  \n• Money in bank account  \n• CO 2 in atmosphere  \n• Blood sugar  \n• Stored Energy  \n• Degree of belief in X  \n• Stockpiled vaccines  \n• Goods in a warehouse  \n• Beds in an emergency room  \n• Owned vehicles  \nExample Model: Stocks  \nThe Critical Role of Stocks in Dynamics  \n• Stocks determine current state of system  \n– Stocks often provide the basis for making choices  \n• Stocks central to most disequilibria phenomena (buildup, decay)  \n• Lead to inertia  \n• Give rise to delays  \nState Changes: Flows (“Fluxes”,“Rates”,“Derivatives”)  \n• All changes to stocks occur via flows  \n• Always expressed per some unit time: If these flow into/out of a stock that keeps track of things of type X (e.g. persons), the rates are measured in X/(Time Unit) (e.g. persons/year, $/month, gallons/second)  \n• Typically measure over certain period of time (by considering accumulated quantity over a period of time)  \n– e.g. Incidence Rates is calculated by accumulating people over a year, revenue is $/Time, water flow is litres/minute  \n– Can be estimated for any point in time  \nExamples of Flows  \n• Inflow or outflow of a bathtub (litres/minute)  \n• Rate of incident cases (e.g. people/month)  \n• Rate of recovery  \n• Rate of mortality (e.g. people/year)  \n• Rate of births (e.g. babies/year)  \n• Rate of treatment (people/day)  \n• Rate of caloric consumption (kcal/day)  \n• Rate of pregnancies (pregnancies/month)  \n• Reactivation Rate (\\# of TB cases reactivating per unit time)  \n• Revenue ($/month)  \n• Spending rate ($/month)  \n• Power (Watts)  \n• Rate of energy expenditure  \n• Vehicle sales  \n• Vaccine sales  \n• Shipping rate of goods  \nExample Model: Flows  \nKey Component: Stock & Flow  \nFlow Stock  \n+  \nFlow  \nStock  \nNet Flow Impact on Stock  \nFlow  \n10  \n9.5  \n9  \n8.5  \n8  \n\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n\n0 10 20 30 40 50 60 70 80 90 100  \nTime (Month)  \nFlow : Current ~~ ~~  \nStock  \n2,000  \n1,500  \n1,000  \n500  \n0  \n0 10 20 30 40 50 60 70 80 90 100  \nTime (Month)  \nStock : Current ~~ ~~  \nImpact of Lowering Flow (Rate) to 5/Month?  \nFlow  \n10  \n8.5  \n7  \n5.5  \n4  \n0 10 20 30 40 50 60 70 80 90 100  \nTime (Month)  \nFlow : Stock and Flow Alternative ~~  ~~Flow : Current ~~ ~~  \nStock  \n2,000  \n1,500  \n1,000  \n500  \n0  \n0 10 20 30 40 50 60 70 80 90 100  \nTime (Month)  \nStock : Stock and Flow Alternative ~~  ~~Stock : Current ~~ ~~","cbCailL3Rsx5R6ZB","https://ap.wps.com/l/cbCailL3Rsx5R6ZB","pdf",634983,48,"English","# State of the System: Stocks (Levels, State Variables, Compartments)\n## Examples of Stocks\n# State Changes: Flows (Fluxes, Rates, Derivatives)\n## Examples of Flows\n# Key Component: Stock & Flow\n## Net Flow Impact on Stock\n## Impact of Lowering Flow (Rate)","[{\"question\":\"What are stocks in a stock-and-flow system dynamics model?\",\"answer\":\"Stocks represent accumulations that capture the system’s state. They can be measured at a single instant, and they only change through flows into and out of them.\"},{\"question\":\"How are flows (rates) defined and expressed in the lecture?\",\"answer\":\"Flows are the mechanisms that cause changes to stocks. They are always expressed per some unit time, such as people/year, $/month, or litres/minute.\"},{\"question\":\"Why do stocks create delay and inertia in system behavior?\",\"answer\":\"Because stocks change only via flows, any change in system state depends on the flow rates over time. This makes stocks the source of delay and supports inertia in the system.\"}]","Lecture 8 - Stock and Flows 2 | PDF",121]