2. Review

3. 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

4. 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

5. M outin event t x1x1 y1y1 x2x2 t S s0s0 s1s1 s2s2 s 2 =  ext ((s 0,e),x 1 ) s 1 =  int (x 2 ) t e ta(s 0 )ta(s 1 ) ta(s 2 ) Dynamic behavior of DEVS models

6. Atomic model example: Processing Server

7. Coupled models Structural models (multicomponent)

8. –Petri Net : incremental –DEVS : hierarchical GENBUFPROC out in out done GEN-BUF-PROC BUF-PROC G+B+P B+PG PB ABC Incremental : A and  B: connect ABC Hierarchical : A and BC: connect BC ABC Hierarchical vs. Incremental modelling

9. CM = n X is the set of input events; n Y is the set of output events; n D is an index for the components of the coupled model, and  i  D, M i is a basic DEVS model (that is, an atomic or coupled model), defined by M i = n IC is the set of Input Couplings; n EIC is the set of External Input Couplings; n EOC is the set of External Output Couplings; n Finally, select is the tie-breaking selector. Coupled models formal specification

10. –GEN-BUF-PROC = X =  ; Y = { out } I(GEN) = BUF; I(BUF) = PROC; I(PROC)= {BUF, self} Z(GEN)=BUF; Z(BUF)=PROC; Z(PROC) = BUF; Z(PROC)=self. SELECT : ({GEN, BUF, PROC}) = GEN ({BUF, PROC}) = BUF GENBUFPROC out in out done Coupled DEVS example

11. DN  X, Y, D, {M i }, {I i }, {Z i,j }  DEVS  X, S, Y,  int,  ext,  con, ta,  DEVS  X, S, Y,  int,  ext,  con, ta,  Every DEVS coupled model has a DEVS Basic equivalent Closure Under Coupling

12. n Components (D) n couplings –Internal Couplings (IC) –External Input Couplings (EIC) –External Output Couplings (EOC) repair shop out sent finished repaired faulty generator (genr) transducer (transd) out report stop start Input/output ports concepts

13. –GEN-BUF-PROC = X =  Y = { out } EIC =  EOC = { (PROC.out, GEN_BUF_PROC.out) } IC = { (GEN.out, BUF.in), (BUF.out, PROC.in), (PROC.out, BUF.done)} SELECT : ({GEN, BUF, PROC}) = GEN ({BUF, PROC}) = BUF  : GENBUFPROC out in out done Coupled DEVS example

14. –Internal transition Model knows its schedule time (by time advance) –External transition Model doesn’t know its schedule time  influencer’s schedule –Conflict case Internal and external events External events M1M1 M2M2 M 2 : M 1 ’s influencee M 1 : M 2 ’s influencer Concept of Scheduling and Tie-break

15. GEN BUFFER PROC out in done * GEN =  X =   Y = {out}  S = {G}   int :  int (G) = G   ext :unavailable  (G) = out  ta(G) = GEN_TIME G (out, ta(G)) * PROC =  X =  {in}  Y = {out}  S = { B, F }   int :  int (B) = F   ext :  ext (F, in) = B  (B) = out  ta(B) = PROCESS_TIME BF (in,e) (out, ta(B)) BUF (coupled model) Tie-Breaking example BUFFER: Exercise

16. –conflict schedule is resolved by assigning priority between models that cause schedules. Internal and external events External events –Sel : 2 {Mi}  {M i } n,F out(BUF)in(GEN) Priority(BUF,GEN) = GEN n,B done(PROC)In(GEN) Priority(PROC,GEN) = GEN Tie-breaking