CS626 Data Analysis and Simulation Instructor: Peter Kemper R 104A, phone 221-3462, email:kemper@cs.wm.edu Office hours: Tuesday,Thursday 3-5 pm Today: Modeling Discrete Event Dynamic Systems with Möbius™ Reference: Möbius™ 2.3 Presentation at DSN 2009 https://www.mobius.illinois.edu/ see https://www.mobius.illinois.edu/papers.html for Manual & research papers 1
Cookbook recipe for conducting a simulation study Statement of the decision problem and objectives Verification Output Analysis Data System Analysis Validation Collection Input Modeling Removal of initial- Experimental Design Development condition bias Design and coding of Determination of the Simulation runs Model Building the simulation replication number program for error control Statistical analysis of Comparison Rough-cut Static Dynamic results and system via Simulation Model (Spreadsheet) System design comparison Simulation Simulation Development Simulation Recommendation for Optimization decisions and Static Dynamic implementation of Models Models the model Final documentation from WSC 2010 Tutorial by Biller and Gunes, CMU, slides used with permission 2
Modeling Discrete Event Dynamic Systems with Möbius™ Discrete Event Dynamic System System Model: State: Finite set of variables with values Discrete Events: individual events change value setting of variables Dynamic: events happen over time at certain points in time Issues What drives the dynamics? time, state What aspects are subject to random variables? time between events, selection of event, state change What state descriptions are possible? fixed set of variables vs dynamic set of variables What measures are of interest the time a system is in a particular state? # of particular events? Scalability Largeness of models, potential behavior, design/configuration spaces Application areas Dependability and other -abilities, Security, Performance 3
DEDS: Some examples ATM at a bank and customers using it System Model: State: What variables describe the state? Discrete Events: Which events need to be defined? Issues What drives the dynamics? time, state What aspects are subject to random variables? time between events, selection of event, state change What state descriptions are possible? fixed set of variables vs dynamic set of variables What measures are of interest? the time a system is in a particular state? # of particular events? Scalability Largeness of models, potential behavior, design/configuration spaces Application areas Dependability and other -abilities, Security, Performance 4
DEDS: Some examples ATM at a bank and customers using it System Model: State: What variables describe the state? Discrete Events: Which events need to be defined? Issues What drives the dynamics? time, state What aspects are subject to random variables? time between events, selection of event, state change What state descriptions are possible? fixed set of variables vs dynamic set of variables What measures are of interest? the time a system is in a particular state? # of particular events? Scalability Largeness of models, potential behavior, design/configuration spaces Type of model Queueing system, queuing network 5
DEDS: Some examples R3 R4 Reliability block diagram R1 R2 R3 R5 R4 System Model: R3 What variables describe the state? Which events need to be defined? Issues What drives the dynamics? time, state What aspects are subject to random variables? time between events, selection of event, state change What state descriptions are possible? fixed set of variables vs dynamic set of variables What measures are of interest? the time a system is in a particular state? # of particular events? Scalability Largeness of models, potential behavior, design/configuration spaces Type of model State-transition system, stochastic automaton 6
DEDS: Some examples Evacuation of an area System Model: What variables describe the state? Which events need to be defined? Issues Photo: thepipe26, flickr, creative commons What drives the dynamics? time, state, What aspects are subject to random variables? time between events, selection of event, state change What state descriptions are possible? fixed set of variables vs dynamic set of variables What measures are of interest? the time a system is in a particular state? # of particular events? Scalability Largeness of models, potential behavior, design/configuration spaces Type of model Agent-based model 7
Addressing Challenges in Modeling Complex Dynamic Systems • Dealing with many levels of abstraction in models • Modeling many different types of system components • Solving many types of models, with differing assumptions and characteristics • Challenging to support solution of extremely large and stiff models in both simulation and analytic/numerical solution • Challenging to explore large design spaces to find optimal system designs/configurations Courtney, Gaonkar, Keefe, Rozier, Sanders, UIUC, Mobius presentation, DSN 2009, slides used with permission
Model Specification in the Möbius Framework Submodel Interaction Framework Component Implemented Formalisms PEPA Process Algebra, Atomic Model Stochastic Activity Networks, Buckets and Balls, Fault/Attack Trees, External Atomic Composed Model Graph interconnection Replicate/Join Action Synchronization Reward Model Rate/Impulse reward variables Path-based reward variables Domain-specific formalisms Range and Set Variation Study Methods Design of Experiments Solution Methods Simulation Methods: Terminating and Steady State Simultaneous Simulation Numerical Methods: Transient, Iterative Steady State, Direct Steady State, Accumulated Reward, Adaptive Transient, Model Specification Deterministic Iterative Steady State Courtney, Gaonkar, Keefe, Rozier, Sanders, UIUC, Mobius presentation, DSN 2009, slides used with permission
Mobius Workflow • Define DES Model – Atomic Models • select suitable formalism, express aspects, details in individual submodels, encodes an automaton (initial state, state transition rules), can carry parameters – Composed Model • combine atomic models into an overall model, composition by sharing/merging variables or by synchronizing/merging transition rules • Define Measurement – Reward Model • define how DES behavior should impact a measure of interest • rate reward for being in a state, impulse reward for performing an event • Decide on Design Space – Study Editor • assign values/value ranges to parameters • Evaluate dynamic behavior – Solution method: Simulation, numerical analysis
Model Representation • Multiple modeling formalisms available: –Stochastic Activity Networks (‘SANs’, advanced stochastic Petri nets), PEPA (textual-based process algebra), Fault/Attack trees, Buckets and Balls (inc. Markov chains), –Parameters of the model can be specified variables and set at analysis time. Courtney, Gaonkar, Keefe, Rozier, Sanders, UIUC, Mobius presentation, DSN 2009, slides used with permission
SAN Formalism • Places: – are variables with a value in {0,1,2,...,n} and n limited by #bits, e.g. 256 • Extended Places: – are variables of other types, e.g. real values, arrays of primitive types • Timed Activity: – describes a rule with a precondition and state change as its effect – timed activity happens after a delay, possibly random • Instantaneous Activity: –describes a rule with a precondition and state change as its effect – activity happens with no delay and as soon as precondition holds • Input Gate: –specifies complex precondition • Output Gate: –specifies complex state change
Model Support of the Abstract Functional Interface: State Variables, Actions, and Properties • Formally, a model in the M ö bius framework is a set of “state variables,” a set of “actions,” and set of “properties” • State variables “contain” information about the state of the system being modeled –They have a type, which defines their “structure” –They have a value, which defines the “state” of the variable • Actions prescribe how the value of state variables may change as a function of time • Properties specify characteristics that may effect the solution of a model Courtney, Gaonkar, Keefe, Rozier, Sanders, UIUC, Mobius presentation, DSN 2009, slides used with permission
Model Composition • Hierarchical model construction –System model constructed from multiple component models. –Can combine models built with different formalisms • Rapid model development • Multiple composition techniques provide flexibility in model construction –Replicate/Join, Graph, Action Synchronization Courtney, Gaonkar, Keefe, Rozier, Sanders, UIUC, Mobius presentation, DSN 2009, slides used with permission
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