1. Review

2. 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 

3. 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

4. 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

5. What is DEVS?

6. 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

7. 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

8. Formalism transformation

9. 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

10. Atomic model definition Behavioral models

11. 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

12. 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.)

13. 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

14. 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

15. 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

16. –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

17. Dynamic behavior of DEVS models

18. 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