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Published byDerick Pitts Modified over 9 years ago
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Review
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A_DA_A Ball_A Ball_B player_A B_DB_A Ball_B Ball_A player_B Ball_A Ball_B A_A, B_DA_D, B_A Ball_A Ball_B CFSM Player_A : X S S X A = {Ball_A} { } : internal event A_AA_D /Ball_A A_AA_D Ball_A feedback CFMS for the ping-pong example A_AA_D Ball_B Ball_A Ball_B
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n Ex) ping-pong game –(i) what if “attack” takes 2 steps: one state generating output, other state with no output. State independent of any inputs. –(ii) what if we want to specify time to be spent for state A or D –A takes 0.1sec.(A’s control : output) –D takes ? sec(B’s control : output) input event -> state transition time modeling Infinity No semantics for such sojourn time specification: logical time models. A_AA_D Ball_B Ball_A Ball_B A_A R_B A_A Receiving state A_A A_D Ball_B Ball_A Ball_B R_B Ball_A ? replace Limitation of expressive power in FSM
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n internal transition & time advance function(defined) introducing internal transition function int : S S introducing time advance function ta : S R + 0, Solution : DEVS (Discrete Event System Specification) Formalism
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What is DEVS?
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DEVS = Discrete Event System Specification Provides sound formal M&S framework Supports full range of dynamic system representation capability Supports hierarchical, modular model development (Zeigler, 1976/84/90/00) DEVS Modeling & Simulation Framework
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n Separates Modeling from Simulation n Derived from Generic Dynamic Systems Formalism –Includes Continuous and Discrete Time Systems n Provides Well Defined Coupling of Components n Supports –Hierarchical Construction –Stand Alone Testing –Repository Reuse n Enables Provably Correct, Efficient, Event-Based, Distributed Simulation The DEVS Framework for M&S
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Formalism transformation
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DEVS Formalism Discrete-Event formalism: time advances using a continuous time base. Basic models that can be coupled to build complex simulations. Abstract simulation mechanism
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Atomic model definition Behavioral models
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DEVS Atomic models n Atomic DEVS = X : external input event set Y : external output event set S : sequential state set int : internal transition function ext :external transition function : output function ta : time advance function
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ta : S R + 0, Q = {(s,e) | s S, 0 e ta(s)} : total state set, e: elapsed time int : S S ext : X * Q S : S Y S int ext R X Y DEVS Atomic models (cont.)
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External Event Transition Function ( ext ): transforms state and an input event into another state (e.g., receiving a faulty device, put it into a queue to await its turn for repair.) Output Function ( ): maps a state into an output (e.g., number of parts available falls below a minimum number, issue an order to restock.) Internal Event Transition Function ( int ): transforms state into another state after time has elapsed (e.g., there are 10 parts available and broken part requires 7 of them, after fixing broken part, 3 parts will remain.) Time Advance Function (ta): maps a state into a duration (e.g., how long to fix a device once processing has started.) Atomic model Discrete Event Dynamics
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ta(s) (1) s DEVS = < X, S, Y, int, ext, ta, s y (3) s ’ = int s x (5) s ’ = ext ( s,e,x) (6) (6) DEVS atomic models semantics
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ta(s) (1) s DEVS = < X, S, Y, int, ext, ta, s y (3) s ’ = int s x (5) s ’ = ext ( s,e,x) (6) (6) DEVS atomic models semantics
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–AMplayer_A = X = {Ball_B} Y = {Ball_A} S = {A, D} int (A) = D ext (Ball_B, D) = A ta(A) = thinking_time ta(D) = INFINITY (A) = Ball_A AD Ball_B Ball_A Ball_B Atomic model example: ping-pong
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Dynamic behavior of DEVS models
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M outin event t x1x1 y1y1 x2x2 t S s0s0 s1s1 s2s2 s 2 = ext ((s 0,e),x 1 ) s 1 = int (s 2 ) t e ta(s 0 )ta(s 2 ) ta(s 1 ) Dynamic behavior of DEVS models
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