Lecture 11: System Dynamics: Stocks and FlowsSystem DynamicsModel of the World(Simulated) Behavior of the WorldDestabilizing FactorsPositive FeedbackNegative FeedbackPositive or Negative?Model Components (Stella)Stocks and FlowsConverters and ConnectorsSlide 12Causal DiagramsSlide 14Slide 15Feedback LoopsWater Cycle in BiosphereConverting to Stocks and FlowsConverting to EquationsFirst Order Delay: Growth and Decay2nd Order Delay "Pipeline" ModelCausal DiagramIdentify Stocks, Flows, ConvertersConvert to Stock & Flow ModelCOMP155Computer SimulationOctober 6, 2008System Dynamicsfrom “System Dynamics, Systems Thinking and Soft OR” by Jay Forrester, MIT Sloan School of Management, 1992Model of the Worldfrom “Counterintuitive Behavior of Social Systems” by Jay W. Forrester1971(Simulated) Behavior of the Worldfrom “Counterintuitive Behavior of Social Systems” by Jay W. Forrester, 1971Destabilizing FactorsPositive Feedbackbirths increase populationincreased population increases births+Negative Feedbackdeaths decrease populationdecreased population decreases deaths-Positive or Negative?+Model Components (Stella)StockFlowConverterAction ConnectorInformation ConnectorStocks and FlowsStocks are accumulatorsStocks represent quantitiesconcrete stuff: water, dollarsabstract stuff: anger, hungerFlows drain and fill accumulatorsflows are always defined as rates: stuff / timeConverters and Connectors Converters are general input  output blocksconstants, external inputs, functions/relationshipsConverters can affect flows or other convertersConnectors are information pathsallow components to access values in other componentsSystem DynamicsSystem Dynamics is a methodology for engineering simulation modelsstep 1: rough design: causal diagramsstep 2: add detail: positive or negative feedbackstep 3: convert to stock and flow graphstep 4: convert to equationsCausal DiagramsCausal diagrams capture causal relationships between system componentspositive causality, A + B: increasing factor A causes factor B to increasedecreasing factor A causes factor B to decreasenegative causality, A - B:increasing factor A causes factor B to decreasedecreasing factor A causes factor B to increasePositive Feedbackincreasing salary produces increased performanceincreasing performance produces increasing salaryNegative Feedbackincreasing inventory increases customers increasing customer decreases inventoryFeedback Loopseven number of negatives:positive feedbackodd number of negatives:negative feedbackWater Cycle in BiosphereCausality diagrams don’t distinguish between stocks and flows. We’re simply trying to identify relationships.Converting to Stocks and FlowsConverting to EquationsFirst Order Delay: Growth and Decay2nd Order Delay "Pipeline" ModelCausal DiagramCapitalReinvestedProfitsCumulative SalesSales per YearCapitalTurnoverProfit per YearPercentageProfit per YearIdentify Stocks, Flows, Converters CapitalReinvestedProfitsCumulative SalesSales per YearCapitalTurnoverProfit per YearPercentageProfit per YearstockstockconstantconstantflowflowfunctionConvert to Stock & Flow ModelFlows must connect directly to/from stocks.Converters: Connections from stocks or other converters. Connections to flows or other